commit 2149d342956ef4b28cd2cc1b753438ec08786b78 Author: Sven Riwoldt Date: Sat Oct 24 13:47:37 2020 +0200 init diff --git a/06_2.eps b/06_2.eps new file mode 100644 index 0000000..3ac122c --- /dev/null +++ b/06_2.eps @@ -0,0 +1,3273 @@ +%!PS-Adobe-2.0 +%%Creator: dvips(k) 5.94b Copyright 2004 Radical Eye Software +%%Title: 2dgrafiken.dvi +%%CreationDate: Fri Jun 02 13:19:48 2006 +%%Pages: 1 +%%PageOrder: Ascend +%%BoundingBox: 0 0 595 842 +%%DocumentFonts: CMMI5 CMR5 CMSY10 +%%DocumentPaperSizes: a4 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips.exe 2dgrafiken.dvi +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2006.06.02:1319 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +%! +% PostScript prologue for pstricks.tex. +% Version 1.00, 2005/09/18 +% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.01, 2005/09/27 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2005/09/28 : - rename it to pstricks-add.pro +% - agg support for Gouraud shading +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression +% 2004/12/16 : addition of SUM and IFTE +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { InitParser SetExpr LexStr 0 exch AnalyzeListOfE ExpressionVector /ExpressionVector [] def} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/SetExpr { RemoveWS /ExpressionString exch def } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/InitParser { + /ExpressionVector [] def /AddVector [] def + /AddVectorfree [] def /MulVector [] def + /MulVectorfree [] def /PowVector [] def + /PowVectorfree [] def /OpParVector [] def + /ClParVector [] def /ParVectorFree [] def + %%/CompVector [] def /CompVectorFree [] def + /BraVector [] def /SemVector [] def + /ComVector [] def /ExpressionVector [] def + /LoopLevel -1 def /LoopContext [] def %%% NEW for SUM function +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/FLbreak { tst not {/L exch def /F exch def 2 copy L eq exch F eq and /tst exch def} {pop pop} ifelse} def +/Negbreak { tst not { dup 0 lt /tst exch def } if } def +/STOP { tst {TOUF} if} def +/tst false def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List +%% first last +/AnalyzeListOfE { + exch SemVector { + exch 1 index 1 sub AnalyzeExpr 1 add + } forall%%last_char + exch AnalyzeExpr +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expr +%% first last +/AnalyzeExpr { + FindFirstAdd%% first last pos+ + 2 copy abs 1 sub ne + { 3 -1 roll 1 index abs 1 sub AnalyzeExpr dup abs 1 add 3 -1 roll AnalyzeTerm EvalAdd } + { pop AnalyzeTerm } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Term +%% first last +/AnalyzeTerm {%%19 28 FLbreak STOP + FindFirstMul%% first last pos* + 2 copy abs 1 sub ne + { 3 -1 roll 1 index abs 1 sub AnalyzeTerm dup abs 1 add 3 -1 roll AnalyzeSignedFactor EvalMul }%%% NEW 2004/11/14 + { pop AnalyzeSignedFactor } ifelse%%% NEW 2004/11/14 +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NEW 2004/11/14 +%% analyze Signed Factor +%% first last -> +/AnalyzeSignedFactor { + ExpressionString 2 index get + dup 45 eq%% a - sign + { pop exch 1 add exch AnalyzeSignedFactor EvalNeg } + { 43 eq%%a + sign + { exch 1 add exch AnalyzeSignedFactor } + { AnalyzeFactor } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Factor +%% first last -> +/AnalyzeFactor { + FindFirstPow%% first last pos* + 2 copy abs 1 sub ne +% { 3 -1 roll 1 index abs 1 sub AnalyzeFactor dup abs 1 add 3 -1 roll AnalyzePower EvalPow } + { 3 -1 roll 1 index abs 1 sub AnalyzeFactor dup abs 1 add 3 -1 roll AnalyzeSignedFactor EvalPow }% NEW 2004/11/14 + { pop AnalyzePower } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Power +%% first last -> +/compteur 0 def +/AnalyzePower { + ExpressionString 2 index get + dup 40 eq%% an open parenthesis + { pop 1 index UnfreePar 1 sub exch 1 add exch AnalyzeExpr } + { dup 45 eq%% a - sign + { pop exch 1 add exch AnalyzePower EvalNeg } + { dup 43 eq%%a + sign + { pop exch 1 add exch AnalyzePower } + { dup 46 eq 1 index 48 ge 2 index 57 le and or%%a digit or a dot + { pop AnalyzeNumber } + { pop AnalyzeLiteral } ifelse } ifelse } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze parameters list +%% first last +/AnalyzeParam { + { FindFirstCom%% first last pos, + 3 -1 roll 1 index 1 sub AnalyzeExpr + 2 copy 1 sub ne { 1 add exch } { pop pop exit } ifelse + } loop +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual addition at this level +%% first last -> position +/FindFirstAdd { + 2 copy /Last exch def /First exch def false 0 + AddVector { + AddVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos abs First gt pos abs Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeAdd} %% find one mul + { Last 1 add } ifelse +} def +%% { +%% 2 copy /Last exch def /First exch def false 0 +%% AddVector { +%% AddVectorFree 2 index get +%% { /pos exch def +%% true 0 1 ClParVector length 1 sub +%% { ParVectorFree 1 index get +%% { OpParVector 1 index get pos abs le +%% ClParVector 2 index get pos abs ge and +%% pos abs First lt pos abs Last gt or or +%% { pop pop false exit } if +%% } if +%% pop +%% } for +%% { pop pop true dup exit } if +%% } +%% { pop } ifelse +%% 1 add +%% } forall +%% pop +%% { pos UnfreeAdd}%% find one add +%% { Last 1 add } ifelse +%% } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual multiplication at this level +%% first last -> first last position +/FindFirstMul { + 2 copy /Last exch def /First exch def false 0 + MulVector { + MulVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos abs First gt pos abs Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeMul} %% find one mul + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual power at this level +%% first last -> first last position +/FindFirstPow { + 2 copy /Last exch def /First exch def false 0 + PowVector { + PowVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos First gt pos Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreePow} %% find one ^ + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual comma at this level +%% first last -> first last position +/FindFirstCom { + 2 copy /Last exch def /First exch def false 0 + ComVector { + ComVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos First gt pos Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesisSTOP + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeCom} %% find one comma + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the first opened parenthesis (only for func call) +%% first last -> first last position +/FindFirstPar { + 2 copy /Last exch def /First exch def false 0 + OpParVector { + ParVectorFree 2 index get + { /pos exch def + pos First gt pos Last lt and + { exch not exch exit } if + } { pop } ifelse + 1 add + } forall + pop + { pos dup UnfreePar }%% find one par + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the first opening bracket +%% first last -> first last position +/FindFirstBra { + 2 copy /Last exch def /First exch def + BraVector { + /pos exch def + pos First gt pos Last lt and + { exit } if + } forall + pos dup UnfreePar%% finding it is mandatory +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Read the number and push it in the vector +%% first last -> +/AnalyzeNumber { + 1 index sub 1 add ExpressionString 3 1 roll getinterval cvr /n exch def + /ExpressionVector ExpressionVector aload length n exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Read the literal and push it in the vector +%% first last -> +/AnalyzeLiteral { + ExpressionString 1 index get dup 41 eq %%close par at the end => function call + { pop FindFirstPar%%first last parpos + ExpressionString 3 index dup 3 index exch sub getinterval + dup (SUM) eq { sumation } + { dup (IFTE) eq { condition } + { 1 index 1 add 3 index 1 sub AnalyzeParam + dup cvn /n exch def TrigoFunc + /ExpressionVector ExpressionVector aload length + /tx@addDict cvx /begin cvx n cvx /end cvx 5 -1 roll 4 add array astore def + %%n cvx exch 1 add array astore def + pop pop pop } ifelse } ifelse } + { 93 eq%%close bracket => vector element + { FindFirstBra%%first last brapos + ExpressionString 3 index dup 3 index exch sub getinterval cvn /n exch def + /ExpressionVector ExpressionVector aload length n cvx exch 1 add array astore def + 2 copy 1 add exch 1 sub AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def + pop pop pop + } + { 1 index sub 1 add ExpressionString 3 1 roll getinterval cvn /n exch def + /ExpressionVector ExpressionVector aload length n cvx exch 1 add array astore def } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push add in the vector +%% kind -> +%% if kind>0 then add else sub +/EvalAdd { + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll + 0 gt { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push mul in the vector +%% -> +/EvalMul { + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll + 0 gt { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push exp in the vector +%% -> +/EvalPow { + pop /ExpressionVector ExpressionVector aload length + /tx@addDict cvx exch /begin cvx exch /EXP cvx exch /end cvx exch 4 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push neg in the vector +%% -> +/EvalNeg { + /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Lexical Analyzis of the string +%% -> +/LexStr { + /freepar 0 def /lastpar 0 def /lastchar 0 def + 0 ExpressionString + { dup 40 eq 1 index 91 eq or %% open parenthesis + { /OpParVector OpParVector aload length dup 3 add index exch 1 add array astore def + /ClParVector ClParVector aload length -1 exch 1 add array astore def + /lastpar freepar def /freepar freepar 1 add def /NoPar false def} if + dup 41 eq 1 index 93 eq or %% close parenthesis + { ClParVector lastpar 3 index put lastpar + dup 0 eq + { pop } + { { 1 sub dup ClParVector exch get -1 eq { /lastpar exch def exit } { dup 0 eq { pop exit} if } ifelse } loop } + ifelse } if + dup 42 eq %% * operator + %%{ /MulVector MulVector aload length dup 3 add index exch 1 add array astore def } if + { /MulVector 2 index MulVector aload length 1 add array astore def } if + dup 43 eq %% + operator + { %%test if it is a real operator and not the unary operator + lastchar dup 40 ne %% open parenthesis + 1 index 59 ne and %% ; + 1 index 42 ne and %% * + 1 index 43 ne and %% + + 1 index 44 ne and %% , + 1 index 45 ne and %% - + 1 index 47 ne and %% / + 1 index 0 ne and %% first char + 1 index 94 ne and %% ^%%2004/11/14 + exch 124 ne and %% | + %%{/AddVector AddVector aload length dup 3 add index exch 1 add array astore def } if} + {/AddVector 2 index AddVector aload length 1 add array astore def } if} + if + dup 44 eq %% , separator + { /ComVector ComVector aload length dup 3 add index exch 1 add array astore def } + if + dup 45 eq %% - operator + { %%test if it is a real operator and not the unary operator + lastchar dup 40 ne %% open parenthesis + 1 index 59 ne and %% ; + 1 index 42 ne and %% * + 1 index 43 ne and %% + + 1 index 44 ne and %% , + 1 index 45 ne and %% - + 1 index 47 ne and %% / + 1 index 0 ne and %% first char + 1 index 94 ne and %% ^%%2004/11/14 + exch 124 ne and %% | + %%{/AddVector AddVector aload length dup 3 add index neg exch 1 add array astore def } if} + {/AddVector 2 index neg AddVector aload length 1 add array astore def } if} + if + dup 47 eq %% / operator + %%{ /MulVector MulVector aload length dup 3 add index neg exch 1 add array astore def } + { /MulVector 2 index neg MulVector aload length 1 add array astore def } + if + dup 59 eq 1 index 124 eq or%% ; separator | + { /SemVector SemVector aload length dup 3 add index exch 1 add array astore def } + if + dup 91 eq %% open bracket + { /BraVector BraVector aload length dup 3 add index exch 1 add array astore def } + if + dup 94 eq %% ^ operator + %%{ /PowVector PowVector aload length dup 3 add index exch 1 add array astore def } + { /PowVector 2 index PowVector aload length 1 add array astore def }%%2004/11/14 + if + /lastchar exch def 1 add + } forall + /AddVectorFree AddVector CreateFree def + /MulVectorFree MulVector CreateFree def + /ParVectorFree OpParVector CreateFree def + /PowVectorFree PowVector CreateFree def + /ComVectorFree ComVector CreateFree def + 1 sub +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Create Free vector +%% -> +/CreateFree { + dup length array exch + { pop true exch } forall astore +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree parenthesis +%% pos -> +/UnfreePar { + /pos exch def ParVectorFree 0 + OpParVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree mul +%% pos -> +/UnfreeMul { + MulVectorFree 0 + MulVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree add +%% pos -> +/UnfreeAdd { + AddVectorFree 0 + AddVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree exp +%% pos -> +/UnfreePow { + PowVectorFree 0 + PowVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree com +%% pos -> +/UnfreeCom { + ComVectorFree 0 + ComVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the condition function +%% -> +/condition { + %% manage the condition + 1 index 1 add 3 index 1 sub FindFirstCom + %% find the test char <,>,=,! + 4 index 1 index 1 sub FindTestChar + 4 index 2 index 1 sub AnalyzeExpr 3 1 roll + 1 add 1 index 1 sub AnalyzeExpr exch + /ExpressionVector ExpressionVector aload length dup 1 add array exch 3 add -1 roll cvx exch astore def + %% manage the then clause + MngClause + %% manage the else clause + MngClause + /ExpressionVector ExpressionVector aload length 1 add /ifelse cvx exch array astore def + mark 8 1 roll cleartomark +} def +/FindTestChar { + 1 exch + { dup ExpressionString exch get + dup 60 eq { pop /lt exit } if%%< + dup 61 eq { pop /eq exit } if%%= + dup 62 eq { pop /gt exit } if%%> + pop pop } for +} def +/MngClause { + 3 1 roll FindFirstCom 4 -1 roll 1 add 1 index 1 sub + /ExpressionVector ExpressionVector exch [] def 3 1 roll AnalyzeExpr + /ExpressionVector exch aload length 1 add ExpressionVector cvx exch array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the sumation function +%% -> +/sumation { + /LoopLevel LoopLevel 1 add def + %% create the accumulator + /ExpressionVector ExpressionVector aload length 1 add 0 exch array astore def + %% read the variable name + 1 index 1 add 3 index 1 sub FindFirstCom + ExpressionString 4 -1 roll 2 index 1 index sub getinterval cvn + /tempvar exch def + %% read the initial value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + %% read the increment value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + %% read the limit value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + /LoopContext LoopContext aload length 1 add ExpressionVector exch array astore def + /ExpressionVector [ tempvar /exch cvx /def cvx ] def + 1 add exch AnalyzeExpr + %% add each term of the sum + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector LoopContext LoopLevel get aload length 2 add + ExpressionVector cvx exch /for cvx exch array astore def pop pop pop pop } def +/GetNextNumber { + exch FindFirstCom ExpressionString 4 -1 roll 1 add 2 index 1 index sub getinterval cvi + /temp exch def } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% METHODS FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% MISC FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/RemoveWS {% + dup length + 0 2 index { 32 ne { 1 add } if } forall + 2 copy ne + { exch pop string 0 2 index + { dup 32 ne { 2 index 2 index 3 -1 roll put 1 add } { pop } ifelse } forall + pop exch pop } { pop pop } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Make a discrete sum +%% var n begin end expr -> +/SUM {} def +%% function arcsine in radians +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup abs 1 eq + { PIdiv2 exch -1 eq { neg } if } + { .1 %% asin(x) + { dup dup PI div 180 mul sin 3 index sub exch PI div 180 mul cos div + dup abs 1e-6 lt { sub exit } if sub + } loop + exch pop } ifelse +} def +%% function arccosine in radians +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup abs 1 eq + { -1 eq { PI } { 0 } ifelse } + { 1.5 %% asin(x) + { dup dup PI div 180 mul cos 3 index sub exch PI div 180 mul sin neg div + dup abs 1e-6 lt { sub exit } if sub + } loop + exch pop } ifelse +} def +%% factorial function +%% n -> n! +/fact { 1 exch 2 exch 1 exch { mul } for } def + +%end + +%% modified exponential funtion for 0 +%% x n -> x^n +/EXP { dup 0 eq { pop pop 1 } { exp } ifelse } def +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /xA ED /yA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end + +% END pst-eqdf.pro + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if 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+CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N +/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} +repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N +/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX +currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.81)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMSY10 +%!PS-AdobeFont-1.1: CMSY10 1.0 +%%CreationDate: 1991 Aug 15 07:20:57 +% Copyright (C) 1997 American Mathematical Society. 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newpath 0.5 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def 28.45274 0 -56.90549 + 0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd exch def xEnd yEnd +L /yStart exch def /xStart exch def 0 setlinecap stroke stroke 3 dup +2 mod 0 eq false and exch 2 lt true and or { /viceversa -56.90549 +28.45274 gt { true }{ false } ifelse def /epsilon 0.01 def /minTickline +-28.45274 def /maxTickline 42.67911 def /dT 1864679 65536 div viceversa +{neg} if def /subTNo 1 def subTNo 0 gt { /dsubT dT subTNo div def}{ +/dsubT 0 def } ifelse -4.0 4.0 /tickend exch def /tickstart exch def +/Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 def /TColor { 0 +setgray } def /subTColor { 0.5 setgray } def /MinValue { xStart +} def /MaxValue { xEnd } def /logLines { false } def /LSstroke { 0 +setlinecap stroke } def /subLSstroke { 0 setlinecap stroke } def 0 +dT MaxValue { /cntTick exch def logLines { gsave 1 10 subTNo div 9.99 +{ /dx exch def /x cntTick dT dx log mul add def x abs MaxValue abs +le { x minTickline moveto x maxTickline lineto } if } for subTwidth +SLW subTColor subLSstroke grestore stroke /dsubT 0 def } if dsubT abs +0 gt { gsave /cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick +abs MaxValue abs le { cntsubTick tickstart STsize mul moveto cntsubTick +tickend STsize mul lineto }{ exit } ifelse /cntsubTick cntsubTick +dsubT add def } repeat subTwidth SLW subTColor subLSstroke grestore +} if gsave cntTick tickstart moveto cntTick tickend lineto Twidth +SLW TColor LSstroke grestore } for /dT dT neg def /dsubT dsubT neg +def 0 dT MinValue epsilon viceversa { add }{ sub } ifelse { /cntTick +exch def logLines { gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick +dT dx log mul add def x abs MinValue abs le { x minTickline moveto +x maxTickline lineto } if } for /dsubT 0 def subTwidth SLW subTColor +subLSstroke grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick +tickstart STsize mul moveto cntsubTick tickend STsize mul lineto +}{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart moveto +cntTick tickend lineto Twidth SLW TColor LSstroke grestore } for } +if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.5 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def 0 42.67911 0 -28.45274 + ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd exch def xEnd yEnd +L /yStart exch def /xStart exch def 0 setlinecap stroke stroke 3 dup +2 mod 0 eq true and exch 2 lt false and or { /viceversa -28.45274 +42.67911 gt { true }{ false } ifelse def /epsilon 0.01 def /minTickline +-56.90549 def /maxTickline 28.45274 def /dT 1864679 65536 div viceversa +{neg} if def /subTNo 1 def subTNo 0 gt { /dsubT dT subTNo div def}{ +/dsubT 0 def } ifelse -4.0 4.0 /tickend exch def /tickstart exch def +/Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 def /TColor { 0 +setgray } def /subTColor { 0.5 setgray } def /MinValue { yStart +} def /MaxValue { yEnd } def /logLines { false } def /LSstroke { 0 +setlinecap stroke } def /subLSstroke { 0 setlinecap stroke } def +0 dT MaxValue { /cntTick exch def logLines { gsave 1 10 subTNo div +9.99 { /dx exch def /x cntTick dT dx log mul add def x abs MaxValue +abs le { x minTickline exch moveto x maxTickline exch lineto } if } +for subTwidth SLW subTColor subLSstroke grestore stroke /dsubT 0 def +} if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def subTNo +1 sub { cntsubTick abs MaxValue abs le { cntsubTick tickstart STsize +mul exch moveto cntsubTick tickend STsize mul exch lineto }{ exit } +ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth SLW +subTColor subLSstroke grestore } if gsave cntTick tickstart exch moveto +cntTick tickend exch lineto Twidth SLW TColor LSstroke grestore } for +/dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon viceversa +{ add }{ sub } ifelse { /cntTick exch def logLines { gsave 1 10 subTNo +div 9.99 { /dx exch def /x cntTick dT dx log mul add def x abs MinValue +abs le { x minTickline exch moveto x maxTickline exch lineto } if } +for /dsubT 0 def subTwidth SLW subTColor subLSstroke grestore } dsubT +abs 0 gt { gsave /cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick +abs MinValue abs le { cntsubTick tickstart STsize mul exch moveto cntsubTick +tickend STsize mul exch lineto }{ exit } ifelse /cntsubTick cntsubTick +dsubT add def } repeat subTwidth SLW subTColor subLSstroke grestore +} if gsave cntTick tickstart exch moveto cntTick tickend exch lineto +Twidth SLW TColor LSstroke grestore } for } if end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray -28.45274 -14.22636 7.11317 0 CLW mul +sub 0 360 arc closepath gsave 0.5 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray 14.22636 -14.22636 7.11317 0 CLW mul sub +0 360 arc closepath gsave 0.5 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray -42.67911 14.22636 7.11317 0 CLW mul sub +0 360 arc closepath gsave 0.5 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0.25 setgray [ -54.06003 34.1432 -2.84544 2.84544 +-54.06003 2.84544 /r 0.71114 def /Lineto { Arcto } def false NArray +n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ n 3 gt +{ CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 ED /xx1 +x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div +def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 1 gt { /Alpha +y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length x12 x11 +sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha cos ArrowPos +mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside known +{ ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos 1. + 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 +sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside +} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 +ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll +2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def +/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath +} ifelse gsave 0.5 SLW 0.25 setgray 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0.25 setgray [ -2.84544 11.38092 -2.84544 42.67911 +-54.06003 42.67911 /r 0.71114 def /Lineto { Arcto } def false NArray +n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ n 3 gt +{ CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 ED /xx1 +x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div +def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 1 gt { /Alpha +y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length x12 x11 +sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha cos ArrowPos +mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside known +{ ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos 1. + 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 +sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside +} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 +ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll +2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def +/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath +} ifelse gsave 0.5 SLW 0.25 setgray 0 setlinecap stroke grestore +end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 14.22636 21.33955 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 14.22636 7.11317 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 21.33955 14.22636 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 7.11317 14.22636 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 20.38658 17.78296 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 17.78296 20.38658 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 20.38658 10.66977 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 17.78296 8.06615 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 8.06615 10.66977 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 10.66977 8.06615 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 8.06615 17.78296 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 10.66977 20.38658 14.22636 14.22636 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -14.22636 38.41138 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -14.22636 24.185 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -21.33955 31.29819 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -7.11317 31.29819 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -8.06615 34.85478 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -10.66977 37.45796 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -8.06615 27.7416 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -10.66977 25.13797 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -20.38658 27.7416 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -17.78296 25.13797 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -20.38658 34.85478 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -17.78296 37.45796 -14.22636 31.29819 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +591 -543 a + tx@Dict begin { -51.21501 36.98865 } PutCoor PutBegin end + 591 -543 a 548 -535 a Fc(b)574 -523 y Fb(11)591 +-543 y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { -5.69046 9.95863 } PutCoor PutBegin end + 591 -543 a 546 -533 a Fc(b)572 +-525 y(r)q(r)591 -543 y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { -42.67911 31.51135 } PutCoor PutBegin end + 591 -543 +a 579 -525 a Fa(\001)591 -543 y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { -35.56592 27.20801 } PutCoor PutBegin end + +591 -543 a 579 -525 a Fa(\001)591 -543 y + tx@Dict begin PutEnd end + 591 -543 a 591 +-543 a + tx@Dict begin { -28.45274 22.90424 } PutCoor PutBegin end + 591 -543 a 579 -525 a Fa(\001)591 -543 y + tx@Dict begin PutEnd end + 591 -543 +a 591 -543 a + tx@Dict begin { -21.33955 18.6009 } PutCoor PutBegin end + 591 -543 a 579 -525 a Fa(\001)591 -543 y + tx@Dict begin PutEnd end + +591 -543 a 591 -543 a + tx@Dict begin { -14.22636 14.29756 } PutCoor PutBegin end + 591 -543 a 579 -525 a Fa(\001)591 +-543 y + tx@Dict begin PutEnd end + 591 -543 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ -56.90549 -34.1432 -62.59595 7.11317 -56.90549 +48.36957 1. 0.1 0. /c ED /b ED /a ED false OpenCurve gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ 28.45274 -34.1432 34.1432 7.11317 28.45274 +48.36957 1. 0.1 0. /c ED /b ED /a ED false OpenCurve gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial 591 -543 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 28.45274 div 2.0 div +def 36.98865 -28.45274 /YA exch 28.45274 div def /XA exch 28.45274 +div def 36.98865 -1.42271 /YB exch 28.45274 div def /XB exch 28.45274 +div def /Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul +XA add def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 +mul def /@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add +def /@yTemp yMid @deltaY 2 mul sub def @xTemp @yTemp 28.45274 mul exch +28.45274 mul exch } false /N@@tempNode 10 {InitPnode } NewNode end +end + 591 +-543 a 591 -543 a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if /rotAngle exch +def end + 591 -543 a 591 -543 a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 1.0 add 28.45274 div Yc 0.0 add 28.45274 div 28.45274 +mul exch 28.45274 mul exch } PutCoor PutBegin end + 591 -543 a 591 +-543 a + tx@Dict begin rotAngle RotBegin end + 591 -543 a 591 -543 a + tx@Dict begin RotEnd end + 591 -543 a 591 -543 a + tx@Dict begin PutEnd end + 591 +-543 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.5 SLW 0 setgray /ArrowA { moveto } def +/ArrowB { } def /ArrowInside { } def 0.5 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /ArrowInside { } def [ tx@NodeDict begin +tx@NodeDict /N@@tempNode known { /N@@tempNode load GetCenter } { 0 +0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY add 28.45274 mul +exch 28.45274 mul exch XA @deltaX add YA @deltaY sub 28.45274 mul +exch 28.45274 mul exch 36.98865 -28.45274 /r 5.69054 def /Lineto { +Arcto } def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () +length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def n { +4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub +x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth +def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def +ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha +sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def +/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { +/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add +y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse +pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat +} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW 0 setgray +0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ 36.98865 -1.42271 XB @deltaX add YB @deltaY +sub 28.45274 mul exch 28.45274 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 28.45274 mul exch 28.45274 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA +x1 y1 /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 + 1 gt { /Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath end + +@endspecial +591 -543 a + tx@Dict begin { 48.36957 -8.5359 } PutCoor PutBegin end + 591 -543 a 11 x Fb(Zeile)19 b Fc(r)c Fb(+)e(1)591 +-543 y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { 48.36957 -15.6491 } PutCoor PutBegin end + 591 -543 a 10 x Fb(bis)19 +b Fc(m)p Fb(\(falls)591 -543 y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { 48.36957 -22.76227 } PutCoor PutBegin end + +591 -543 a 10 x Fc(r)f(<)f(m)p Fb(\))591 -543 y + tx@Dict begin PutEnd end + 591 -543 +a 591 -543 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 28.45274 div 2.0 div +def 36.98865 1.42271 /YA exch 28.45274 div def /XA exch 28.45274 div +def 36.98865 42.67911 /YB exch 28.45274 div def /XB exch 28.45274 div +def /Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul XA +add def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 mul +def /@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add def +/@yTemp yMid @deltaY 2 mul sub def @xTemp @yTemp 28.45274 mul exch +28.45274 mul exch } false /N@@tempNode 10 {InitPnode } NewNode end +end + 591 -543 a 591 -543 a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if /rotAngle exch +def end + 591 -543 a 591 -543 +a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 1.0 add 28.45274 div Yc 0.0 add 28.45274 div 28.45274 +mul exch 28.45274 mul exch } PutCoor PutBegin end + 591 -543 a 591 -543 a + tx@Dict begin rotAngle RotBegin end + 591 -543 a 14 x Fb(Zeile)i(1)h(bis)f +Fc(r)591 -543 y + tx@Dict begin RotEnd end + 591 -543 a 591 -543 a + tx@Dict begin PutEnd end + 591 -543 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.5 SLW 0 setgray /ArrowA { moveto } def +/ArrowB { } def /ArrowInside { } def 0.5 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /ArrowInside { } def [ tx@NodeDict begin +tx@NodeDict /N@@tempNode known { /N@@tempNode load GetCenter } { 0 +0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY add 28.45274 mul +exch 28.45274 mul exch XA @deltaX add YA @deltaY sub 28.45274 mul +exch 28.45274 mul exch 36.98865 1.42271 /r 5.69054 def /Lineto { Arcto +} def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.5 SLW 0 setgray 0 setlinecap +stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ 36.98865 42.67911 XB @deltaX add YB @deltaY +sub 28.45274 mul exch 28.45274 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 28.45274 mul exch 28.45274 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA +x1 y1 /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 + 1 gt { /Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath end + +@endspecial 591 -543 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 28.45274 div 2.0 div +def -54.06003 -31.29819 /YA exch 28.45274 div def /XA exch 28.45274 +div def -1.42271 -31.29819 /YB exch 28.45274 div def /XB exch 28.45274 +div def /Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul +XA add def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 +mul def /@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add +def /@yTemp yMid @deltaY 2 mul sub def @xTemp @yTemp 28.45274 mul exch +28.45274 mul exch } false /N@@tempNode 10 {InitPnode } NewNode end +end + 591 +-543 a 591 -543 a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if 90. add /rotAngle +exch def end + 591 -543 a 591 -543 a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 0.0 add 28.45274 div Yc -4.0 add 28.45274 div 28.45274 +mul exch 28.45274 mul exch } PutCoor PutBegin end + 591 -543 a 591 +-543 a + tx@Dict begin rotAngle RotBegin end + 591 -543 a 420 -533 a Fb(Spalte)h(1)g(bis)f Fc(r)591 +-543 y + tx@Dict begin RotEnd end + 591 -543 a 591 -543 a + tx@Dict begin PutEnd end + 591 -543 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.5 SLW 0 setgray /ArrowA { moveto } def +/ArrowB { } def /ArrowInside { } def 0.5 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /ArrowInside { } def [ tx@NodeDict begin +tx@NodeDict /N@@tempNode known { /N@@tempNode load GetCenter } { 0 +0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY add 28.45274 mul +exch 28.45274 mul exch XA @deltaX add YA @deltaY sub 28.45274 mul +exch 28.45274 mul exch -54.06003 -31.29819 /r 5.69054 def /Lineto +{ Arcto } def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if +() length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def n +{ 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 +sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub +Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add +def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 +Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ -1.42271 -31.29819 XB @deltaX add YB @deltaY +sub 28.45274 mul exch 28.45274 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 28.45274 mul exch 28.45274 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA +x1 y1 /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 + 1 gt { /Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath end + +@endspecial 591 -543 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 28.45274 div 2.0 div +def 1.42271 -31.29819 /YA exch 28.45274 div def /XA exch 28.45274 div +def 28.45274 -31.29819 /YB exch 28.45274 div def /XB exch 28.45274 +div def /Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul +XA add def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 +mul def /@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add +def /@yTemp yMid @deltaY 2 mul sub def @xTemp @yTemp 28.45274 mul exch +28.45274 mul exch } false /N@@tempNode 10 {InitPnode } NewNode end +end + 591 +-543 a 591 -543 a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if 90. add /rotAngle +exch def end + 591 -543 a 591 -543 a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 0.0 add 28.45274 div Yc -4.0 add 28.45274 div 28.45274 +mul exch 28.45274 mul exch } PutCoor PutBegin end + 591 -543 a 591 +-543 a + tx@Dict begin rotAngle RotBegin end + 591 -543 a 440 -533 a Fb(Spalte)h Fc(r)15 b Fb(+)e(1)591 +-543 y + tx@Dict begin RotEnd end + 591 -543 a 591 -543 a + tx@Dict begin PutEnd end + 591 -543 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.5 SLW 0 setgray /ArrowA { moveto } def +/ArrowB { } def /ArrowInside { } def 0.5 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /ArrowInside { } def [ tx@NodeDict begin +tx@NodeDict /N@@tempNode known { /N@@tempNode load GetCenter } { 0 +0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY add 28.45274 mul +exch 28.45274 mul exch XA @deltaX add YA @deltaY sub 28.45274 mul +exch 28.45274 mul exch 1.42271 -31.29819 /r 5.69054 def /Lineto { +Arcto } def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () +length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def n { +4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub +x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth +def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def +ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha +sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def +/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { +/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add +y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse +pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat +} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW 0 setgray +0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.5 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def [ 28.45274 -31.29819 XB @deltaX add YB @deltaY +sub 28.45274 mul exch 28.45274 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 28.45274 mul exch 28.45274 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA +x1 y1 /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 + 1 gt { /Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 setgray 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath end + +@endspecial 591 -543 a + tx@Dict begin { 14.22636 -51.21501 } PutCoor PutBegin end + 591 +-543 a 455 -533 a Fb(bis)19 b Fc(n)g Fb(\(falls)591 -543 +y + tx@Dict begin PutEnd end + 591 -543 a 591 -543 a + tx@Dict begin { 14.22636 -56.90549 } PutCoor PutBegin end + 591 -543 a 507 -533 a Fc(r)f(<)f(n)p +Fb(\))591 -543 y + tx@Dict begin PutEnd end + 591 -543 a eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/06_2.pdf b/06_2.pdf new file mode 100644 index 0000000..5dcad4b Binary files /dev/null and b/06_2.pdf differ diff --git a/2dgrafiken/01_1_1.pst b/2dgrafiken/01_1_1.pst new file mode 100644 index 0000000..f6ede70 --- /dev/null +++ b/2dgrafiken/01_1_1.pst @@ -0,0 +1,33 @@ +\begin{pspicture}(-1,-1)(5,5) + %\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0] + + %%%%%%%%%%%%%%%%%%%%%%%%Koor%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psaxes[Ox=0,Dx=2,Oy=0,Dy=2,linewidth=0.1pt]{->}(0,0)(0,0)(4.5,4.5)%Schnittpunkt, x0, y0 x1,y1 + \rput[l](1.7,-0.8){$1.\ Koordinate$} + \rput[c](4.8,0){$x$} + + \rput[l](0.4,4){$2.\ Koordinate$} + \rput[c](0,4.8){$y$} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Vektor / Gerade%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline[linecolor=red, linewidth=0.1pt](0,0)(3,3) + \rput[c](3.0,-0.4){$a_1$} + \rput[c](-0.4,3){$a_2$} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%Hlfslinien%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline[linecolor=blue, linestyle=dashed, linewidth=0.1pt](3,-0.2)(3,3) + \psline[linecolor=blue, linestyle=dashed, linewidth=0.1pt](-0.2,3)(3,3) + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Pfeil%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline{->}(3.5,2.5)(3.1,2.9) + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Kreuz %%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline[linecolor=green] (2.9,3.1)(3.1,2.9) + \psline[linecolor=green] (2.9,2.9)(3.1,3.1) + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Beschriftung am Pfeil %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \rput[l](3.3,2.3){Punkt} + \rput[l](3.2,1.9){$(a_1, a_2)$} + \end{pspicture} diff --git a/2dgrafiken/01_1_2.pst b/2dgrafiken/01_1_2.pst new file mode 100644 index 0000000..16e8bf4 --- /dev/null +++ b/2dgrafiken/01_1_2.pst @@ -0,0 +1,27 @@ + \begin{pspicture}(-1,-1)(5,5) + %\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0] + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Koordinaten%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psaxes[Ox=0,Dx=2,Oy=0,Dy=2,linewidth=0.1pt]{->}(0,0)(-0.0,-0.0)(4.5,4.5)%Schnittpunkt, x0, y0 x1,y1 + \rput[c](4.8,0){$x$} + \rput[c](0,4.8){$y$} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Vektor%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline[linecolor=red, linewidth=0.1pt]{->}(0,0)(3,3) + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Hilfslinien%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline[linecolor=blue, linestyle=dashed, linewidth=0.1pt](3,-0.2)(3,3) + \psline[linecolor=blue, linestyle=dashed, linewidth=0.1pt](-0.2,3)(3,3) + \rput[c](3.0,-0.4){$a_1$} + \rput[c](-0.4,3){$a_2$} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%Pfeil mit Beschriftung%%%%%%%%%%%%%%%%%%%%%%%%%%% + \psline{->}(3.5,2.5)(3.1,2.9) + \rput[l](1.8,2.3){$Vektor\ ("Pfeil")$} + \rput[l](2.5,1.9){$\vec{a}$} + + + + + \end{pspicture} diff --git a/2dgrafiken/01_1_3.pst b/2dgrafiken/01_1_3.pst new file mode 100644 index 0000000..d67e6db --- /dev/null +++ b/2dgrafiken/01_1_3.pst @@ -0,0 +1,38 @@ +\begin{pspicture}(-1.65,-0.85)(8,5.9) +%\psgrid[griddots=2,gridlabels=0pt, subgriddiv=2] +\psaxes[Ox=0,Dx=3,Oy=0,Dy=3,linewidth=0.1pt]{->}(0,0)(0,0)(7.5,5.5)%Schnittpunkt, x0, y0 x1,y1 + + + + +\psline[linecolor=red, linewidth=0.5pt]{->}(0,0)(5,1) +\psline[linecolor=orange, linewidth=0.5pt, linestyle=dashed]{->}(5,1)(7,5) +\psline[linecolor=orange, linewidth=0.5pt]{->}(0,0)(2,4) +\psline[linecolor=orange,linewidth=0.1pt,linestyle=dashed](2,-0.4)(2,4) 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4)(3.35, 4.5)(3.45,5) +%\psline[linewidth=0.75pt]{->}(4,2)(4.1, 1.75) + +\rput[l](4,2){\color{white}x\rnode{a}x } + +\rput[c](3.5, 5.6){Paralle\Rnode[e]{ae}logramm} + + +\nccurve[nodesep=3pt,angleA=-90,AngleB=90]{->}{ae}{a} + +\end{pspicture} diff --git a/2dgrafiken/04_1_1.pst b/2dgrafiken/04_1_1.pst new file mode 100644 index 0000000..867354f --- /dev/null +++ b/2dgrafiken/04_1_1.pst @@ -0,0 +1,13 @@ +\begin{pspicture}(-0.1,-0.1)(7,1.3) + +%\psgrid(0,0)(7, 1.3) + +\rput[l](0.1,1.1){$\vec a \rnode{a}\times \vec b = \left( {a_2 b_3 - a_3 b_2 ,a_3 b_1 - a_1 b_3 ,a_1 b_2 - a_2 b_1 } \right)$} + + +\rput[l](0.1,0.1){"Kr\Rnode[e]{ae}euz"} + +%\nccurve[angleA=0]{->}{ae}{a} +%\ncbar[nodesep=1pt]{->}{ae}{a} +\ncline[arrows=->,linecolor=red]{ae}{a} +\end{pspicture} diff --git a/2dgrafiken/04_1_1.tex b/2dgrafiken/04_1_1.tex new file mode 100644 index 0000000..d57857b --- /dev/null +++ b/2dgrafiken/04_1_1.tex @@ -0,0 +1,10 @@ +\begin{pspicture}(-0.1,-0.1)(7.5,1.85) + +%\psgrid(0,0)(7.5, 2) + +\rput[l](0.5,1.6){$\vec a \rnode{a}\times \vec b = \left( {a_2 b_3 - a_3 b_2 ,a_3 b_1 - a_1 b_3 ,a_1 b_2 - a_2 b_1 } \right)$} + + +\rput[l](0.5,0.6){"Kr\Rnode[e]{ae}euz"} \rput[l](0.25,0.1){Kreuzprodukt} + +%\nccurve[angleA=0]{->}{ae}{a} %\ncbar[nodesep=1pt]{->}{ae}{a} \ncline[arrows=->,linecolor=red]{ae}{a} \end{pspicture} diff --git a/2dgrafiken/04_2_1.eps b/2dgrafiken/04_2_1.eps new file mode 100644 index 0000000..fe314f0 --- /dev/null +++ b/2dgrafiken/04_2_1.eps @@ -0,0 +1,2762 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software +%%Title: 2dgrafiken.dvi +%%CreationDate: Sun Jun 15 07:29:41 2008 +%%BoundingBox: 76 725 86 737 +%%DocumentFonts: CMMI10 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips -EPSF 2dgrafiken.dvi +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2008.06.15:0729 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub 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2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get +neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr +1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr +2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 +-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S +TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ +Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale +}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState +save N userdict maxlength dict begin/magscale true def normalscale +currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts +/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x +psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx +psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub +TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict +begin/SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ +CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N +/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} +repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N +/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX +currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +%%BeginProcSet: color.pro 0 0 +%! +TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop +setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll +}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def +/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ +setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ +/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch +known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC +/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC +/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 +setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 +setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 +0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC +/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 +setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 +0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ +0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ +0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC +/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 +setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 +setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 +0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC +/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 +setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 +0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ +0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ +0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC +/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 +setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC +/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 +0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 +0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 +0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 +setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 +0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC +/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 +setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 +0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 +1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC +/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 +setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ +0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} +DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 +setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 +setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 +setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /alpha put +dup 97 /a put +dup 98 /b put +dup 126 /vector put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 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rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 6 2007-12-29 21:41:43Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. 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CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 133.7278 0.0 0.0 0.0 /Lineto /lineto load def false 0 +setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 19.91682 56.90549 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 153.64464 56.90549 19.91682 +56.90549 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul +add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 153.64464 56.90549 133.7278 +0.0 /Lineto /lineto load def false 0 setlinejoin NArray n 0 eq not +{ n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup +1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha +cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub +def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha +y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 +y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. 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+\rput[l](1.7,-0.3){\tiny{Zeile $r+1$}} +\rput[l](1.7,-0.55){\tiny{bis $m$\\(falls}} +\rput[l](1.7,-0.8){\tiny{$r + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 6 2007-12-29 21:41:43Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 97 /a put +dup 120 /x put +dup 121 /y put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 +9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 +990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E +6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB +DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 +59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 +D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF +8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 +6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 +1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE +03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 +95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 +74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 +3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 +47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 +AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8 +42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8 +40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837 +B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53 +956017667094CD8DC214A666D7D12CB23EC030318B42DAC7C5B55D30D323720D +18B508F25EC90F4BB39F01A9B5D9FDADCB3F6BF98CBAE558EB843CCBAA498263 +B83BF30467B3249E244947C6FD053CED99A226B8C32894FB029DD305F1374857 +C11C401F455A46F61DF097D8B43AA61FFFF8E9FB7D8BC3C4A3AE7F30EB7A90AA +6D8D7637BB8661D971A06517AD0AEC7BC3ECDA20C75B5D8527BF8154C308BF5F +064B1EC3440E75F0DAB199514994A0E46DDF7F59DEAB0B3DB11CF017A4FDB6CE +FC1BA9BF7B8D27E8A48F437DD7DC3955CFFF805BA63ED962D7281641FF587038 +5DF251D9C0DBCB7BBE9A5C20204AEF774209030E8E87B038D78C17D36805FB7C +AADB49335324F07898B8E6CB7C382967C01FD51DA17A7DB98A1E3339B1EB8AEA +E6FB0FE33D971B21C1A1DD8F01F7E522F857A9C9A1A584C625A5F402EF41749D +9E1F4FC5F19B7FC278EA7B198F4E3D832DC26780A825DF08EDC4FE8B6B7CAC70 +3CB7B7C37451466649360CBBCFDC7C760A3C48ABF01E7BC1E8DF3F3895CEE7AD +7EA124068F2D040CACEA71D0E98B2F296504E4A4B2B3D562B42BC83C17BDB65E +C0E751DD5F2274B8D3F013E42426E1349E0298C2DEAFAD75D6D556C871E6D9C5 +34D1EF8EA00EAAB5084F0629DE55DFE2FD5C204506038E56299437FBF9F9A335 +2A72F41B25A13670C3F8F45882D406D46B2F4BE5F81DF8AE6027EA83F1E8133F +9D7B3E81CC8FEDC08EFE9FCB8DEE761580FE3209D6BCE91BCF5E6278D22B56CF +3EC1FD13D60E957A3DDAE8168814189EBF09C4C3A8CB927A832ED660B1419FE4 +D199D171076868640E3C2541986C6FA403D57D3759E68B46C863D1D0AC6C6669 +17D18F77D838A337FB3F26A50E1F036FCCEEF54BFF6D1A770175F5EB23467D98 +D1C2F8DA9CAC1D739557AA55ECDCDEE692DA3F0CB135036F226DA2790EF30543 +62DBDFDC9E010A29DFAA7407A60F969E54404D8D2E11056EA0D213607AE0CBA2 +55A8B1337DD4568B2CF2ED806C95727600D87BD3EB013944AB47689A9882CB06 +462A23D7885BD62280F3DED49AEA1CF53D886B7C71DD848B78EBBAC2D5EFF289 +A65E3DCCFEAA2DFD0AA9995BFA2C12525838472DE53D781138C2AF79FE32CA2F +34AEF51540D6F8D86C8BD543DF422C8729FC63D21FDFC033272334E8FC +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +%%BeginFont: CMR5 +%!PS-AdobeFont-1.1: CMR5 1.00B +%%CreationDate: 1992 Feb 19 19:55:02 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 40 /parenleft put +dup 41 /parenright put +readonly def +/FontBBox{-341 -250 1304 965}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI5 +%!PS-AdobeFont-1.1: CMMI5 1.100 +%%CreationDate: 1996 Aug 02 08:21:10 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 100 /d put +dup 101 /e put +dup 116 /t put +readonly def +/FontBBox{37 -250 1349 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA06DA87FC7163A5A2A756A598FAB07633 +89DE8BB201D5DB4627484A80A431B6AFDBBBF23D4157D4AFE17E6B1C853DD417 +25F84CD55402AB88AB7EEFDEDBF2C2C731BD25567C53B474CCF739188A930039 +098A197F9C4BE7594D79442B2C8A67447DE44698321145D7689B91EF235EA80E +B600AA8E238064F154284096C4C2554EFE8DDF13AFF8D3CE30E0999375C0FEE6 +F992DEA5FC3897E2CC8B7A90238E61E41622DE80F438DD994C73275CC52249D9 +F6686F87F394FB7BB668138B210BEC9E46415A1B58C990B81E7D7DD301143517 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CLW +mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale +} if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside { +} def 85.35823 0 -5.69046 0 ArrowA CP 4 2 roll ArrowB /yEnd exch +def /xEnd exch def xEnd yEnd L /yStart exch def /xStart exch def 0 +setlinecap stroke stroke 3 dup 2 mod 0 eq false and exch 2 lt true +and or { /viceversa -5.69046 85.35823 gt { true }{ false } ifelse +def /epsilon 0.01 def /minTickline -5.69046 def /maxTickline 62.59595 + def /dT 1864679 abs 65536 div viceversa { neg } if def /subTNo 1 def +subTNo 0 gt { /dsubT dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 +4.0 /tickend exch def /tickstart exch def /Twidth 0.4 def /subTwidth +0.2 def /STsize 0.75 def /TColor { 0 setgray } def /subTColor { +0.5 setgray } def /MinValue { xStart } def /MaxValue { xEnd 1.5 2. + CLW mul add 1.4 mul viceversa { add epsilon sub } { sub epsilon add +} ifelse } def /logLines { false } def /LSstroke { 0 setlinecap stroke +stroke} def /subLSstroke { 0 setlinecap stroke stroke} def 0 dT MaxValue +{ /cntTick exch def logLines { gsave 1 10 subTNo div 9.99 { /dx exch +def /x cntTick dT dx log mul add def x abs MaxValue abs le { x minTickline + moveto x maxTickline lineto } if } for subTwidth SLW subTColor subLSstroke +grestore stroke /dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick +cntTick dsubT add def subTNo 1 sub { cntsubTick abs MaxValue abs le +{ cntsubTick tickstart STsize mul moveto cntsubTick tickend STsize +mul lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } +repeat subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick +tickstart moveto cntTick tickend lineto Twidth SLW TColor LSstroke +grestore } for /dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon +viceversa { add }{ sub } ifelse { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MinValue abs le { x minTickline moveto x maxTickline lineto +} if } for /dsubT 0 def subTwidth SLW subTColor subLSstroke grestore +} dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def subTNo 1 +sub { cntsubTick abs MinValue abs le { cntsubTick tickstart STsize +mul moveto cntsubTick tickend STsize mul lineto }{ exit } ifelse +/cntsubTick cntsubTick dsubT add def } repeat subTwidth SLW subTColor +subLSstroke grestore } if gsave cntTick tickstart moveto cntTick tickend + lineto Twidth SLW TColor LSstroke grestore } for } if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.5 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW +mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale +} if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside { +} def 0 62.59595 0 -5.69046 ArrowA CP 4 2 roll ArrowB /yEnd exch +def /xEnd exch def xEnd yEnd L /yStart exch def /xStart exch def 0 +setlinecap stroke stroke 3 dup 2 mod 0 eq true and exch 2 lt false +and or { /viceversa -5.69046 62.59595 gt { true }{ false } ifelse +def /epsilon 0.01 def /minTickline -5.69046 def /maxTickline 85.35823 + def /dT 1864679 abs 65536 div viceversa { neg } if def /subTNo 1 def +subTNo 0 gt { /dsubT dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 +4.0 /tickend exch def /tickstart exch def /Twidth 0.4 def /subTwidth +0.2 def /STsize 0.75 def /TColor { 0 setgray } def /subTColor { +0.5 setgray } def /MinValue { yStart } def /MaxValue { yEnd 1.5 2. + CLW mul add 1.4 mul viceversa { add epsilon sub } { sub epsilon add +} ifelse } def /logLines { false } def /LSstroke { 0 setlinecap stroke + stroke} def /subLSstroke { 0 setlinecap stroke stroke} def 0 dT MaxValue +{ /cntTick exch def logLines { gsave 1 10 subTNo div 9.99 { /dx exch +def /x cntTick dT dx log mul add def x abs MaxValue abs le { x minTickline +exch moveto x maxTickline exch lineto } if } for subTwidth SLW subTColor +subLSstroke grestore stroke /dsubT 0 def } if dsubT abs 0 gt { gsave +/cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick abs MaxValue +abs le { cntsubTick tickstart STsize mul exch moveto cntsubTick tickend +STsize mul exch lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT +add def } repeat subTwidth SLW subTColor subLSstroke grestore } if +gsave cntTick tickstart exch moveto cntTick tickend exch lineto Twidth +SLW TColor LSstroke grestore } for /dT dT neg def /dsubT dsubT neg +def 0 dT MinValue epsilon viceversa { add }{ sub } ifelse { /cntTick +exch def logLines { gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick +dT dx log mul add def x abs MinValue abs le { x minTickline exch moveto +x maxTickline exch lineto } if } for /dsubT 0 def subTwidth SLW subTColor +subLSstroke grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick +tickstart STsize mul exch moveto cntsubTick tickend STsize mul exch +lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat +subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick tickstart +exch moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke +grestore } for } if end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.5 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 71.13185 14.22636 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.8 SLW +1 0.5 0 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 71.13185 14.22636 71.13185 +-5.69046 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul +add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +1 0.5 0 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 71.13185 14.22636 -5.69046 +14.22636 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul +add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +1 0.5 0 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 14.22636 42.67911 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.8 SLW +1 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 14.22636 42.67911 -5.69046 +42.67911 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. 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def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 6 2007-12-29 21:41:43Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 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Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 6 2007-12-29 21:41:43Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx 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pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 +def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 +rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 +N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop +false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A +length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} +forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ +BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat +{BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch +round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 +rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B +/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} +B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p +-3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ +0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 728 2012-11-19 14:35:21Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 1.15, 2012/10/16 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +% +% +% Define the follwing gs-functions if not known, eg when using distiller +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def % the main PSTricks dictionary +tx@Dict begin +/ADict 25 dict def % The arrow dictionaray +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +/Rand { rand 4294967295 div } def % a real random number +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +% +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +% +/PathLength { + flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } + { /y ED /x ED PathLength@ } + {} + { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if + z +} def +% +/STP { .996264 dup scale } def % BP/PT scaling +/STV { SDict begin normalscale end STP } def % +% +/DashLine { + dup 0 gt + { /a .5 def PathLength exch div } + { pop /a 1 def PathLength } ifelse + /b ED % pattern should fit evenly in b + dup /X ED % pattern array + 0 get /y ED % length of first black segment + /z 0 X {add} forall def % length of the full pattern + %% Computation of the scaling factor as described by van Zandt: + b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div + %%%% scaling factor on stack. + /z ED %% now, z is the scaling factor + false % for the length test below + X { z mul } forall X astore %% modification TN 04-08-07 + %%% Checking whether at least one dash in X has positive length: + {0 gt or} forall + { X 1 a sub y mul } + { [ 1 0 ] 0 } + ifelse + setdash stroke +} def +% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/SymbolLine { % on stack [ x y x y ... + counttomark % number of elements + 2 div cvi /n ED % n pairs + /YA ED /XA ED % the start point + n 1 sub { + /YB ED /XB ED + /XLength XB XA sub def + /YLength YB YA sub def + /PAngle YLength XLength Atan def + /XYLength XLength YLength Pyth def + + %% for negative SymStep we calculate the distance + SymStep 0 lt + { %XYLength SymStep div abs cvi + /nSym SymStep abs cvi def } + { /nSym XYLength SymStep div cvi def } + ifelse + 0.5 setflat + /Shift Symbol stringwidth pop 2 div def + /deltaX XLength nSym div def + /deltaY YLength nSym div def + curveticks + { XA YA moveto } + { XA Shift sub YA Shift sub moveto } + ifelse + nSym { + gsave + curveticks + { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED + currentpoint translate rotAngle rotate + 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto + SymbolLinewidth setlinewidth stroke + } + { + rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if + Symbol show + } + ifelse + grestore + deltaX deltaY rmoveto + } repeat + /YA YB def /XA XB def + } repeat + curveticks + { XA YA moveto } + { XA Shift sub YA Shift sub moveto } + ifelse + gsave + curveticks + { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED + XA YA translate rotAngle rotate + 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto + SymbolLinewidth setlinewidth stroke + } + { + rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if + Symbol show + } + ifelse + grestore + pop % delete the mark symbol +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clipType % must be defined in pstricks.tex: clip -- eoclip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +/DotFill {% on stack: dot radius + /dotRadius ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform + pathbbox % llx lly urx ury of smallest bounding box + /y2 ED /x2 ED /y1 ED /x1 ED + y2 y1 sub a div 2 add cvi /Ny ED + x2 x1 sub a div 2 add cvi /Nx ED + clipType % must be defined in pstricks.tex: clip -- eoclip + newpath + /yA y1 dotRadius add CLW add def + /xA0 x1 dotRadius add CLW add def + Ny { + /xA xA0 def + Nx { + newpath + xA yA dotRadius 0 360 arc + SolidDot { gsave fill grestore } if + stroke + xA a add /xA ED + } repeat + yA a add /yA ED + } repeat + grestore +} def +% +/PenroseFill {% on stack: scaling factor + /Scale ED +% 1 exch div round /penroseFactor ED +% a 0 dtransform round exch round exch +% 2 copy idtransform +% exch Atan rotate +% idtransform pop /a ED +% .25 .25 itransform pathbbox +% /y2 ED +% a Div ceiling cvi /x2 ED /y1 ED +% a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath +gsave + 220 150 translate + Scale dup scale + systemdict /setstrokeadjust known { true setstrokeadjust } if + /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} + { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall + [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto + i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 + mul j l + S rmoveto}F i L j L stroke }F}F}F}F + grestore +% pop pop +} def +% +/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color + /Scale ED + Scale dup scale + /border_colour ED + /kite_colour ED + /dart_colour ED + clip + + newpath + gsave + 100 100 translate + 6 + Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations + 10 %%%% Long side length in millimeters + /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders + /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points + /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio + /l{L f mul}bind def %%%% Short side length l = L*f + /Ll{L l add}bind def %%%% Ll = L + l + /c{36 cos L mul}bind def %%%% c = L*cos(36) + /s{36 sin L mul}bind def %%%% s = L*sin(36) + /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore + 0 setlinewidth stroke grestore border_colour stroke } bind def + /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart + Ll 0 translate 144 rotate kite grestore } + { kite_colour L draw_tile }ifelse + pop } bind def + /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite + -144 rotate Ll neg 0 translate half_dart grestore } + { dart_colour l draw_tile }ifelse + pop } bind def + /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def + border_width setlinewidth 1 setlinejoin 1 setlinecap +% 450 0 translate + dup f exch neg exp dup scale + 5 {kite 72 rotate } repeat stroke + grestore +} def +% +% +/TruchetFill { % on stack: scaling factor + 10 dict begin + dup dup scale + 1 exch div round /penroseFactor ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + systemdict + /setstrokeadjust known { true setstrokeadjust } if + /ma a neg def + /ha a 2 div def + /mha ha neg def + /tile { + rand dup 2 idiv 2 mul eq { 90 rotate } if + mha mha moveto ha mha lineto + ha ha lineto mha ha lineto +% closepath .1 setlinewidth stroke + contents + } def + /contents{ + 0 ha moveto ha 0 lineto + 0 mha moveto mha 0 lineto +% 1 setlinewidth stroke + } def + /dotiling { + f ma mul a f a mul { + /i exch def + f ma mul a f a mul { + /j exch def + gsave i j translate + tile stroke grestore + } for + } for + } def +% + /f 3 def + 5 srand dotiling + end % local user dict +} def +% +/BeginArrow { + ADict begin % hold it local, for end see EndArrow + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse % outer or inner dimen + /b ED % the color definition + 0 z DS SD + b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub + moveto +} def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED % n 2 div on stack + n eq not { exch pop } if % even numbers of points? delete one + ] aload /Points ED + showpoints not { Points aload pop } if +% { ] aload /Points ED } +% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol +} def +% +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +% +/LineToYAxis { + /Ox ED % Save the x origin value + NArray % all x-y pairs on stack + n { 2 copy moveto % go to current point + Ox exch Lineto % line to y-axis + pop % delete old x-value + } repeat +} def +% +/LineToXAxis{ + /Oy ED % Save the y origin value + NArray % all x-y pairs on stack + n 0 eq not + { n 1 eq { 0 0 /n 2 def } if + ArrowA + /n n 2 sub def + CP 2 copy moveto pop Oy Lineto + n { 2 copy moveto pop Oy Lineto } repeat + CP + 4 2 roll + ArrowB + 2 copy moveto pop Oy + L + pop pop } if +} def +% +/Arcto { + /a [ 6 -2 roll ] cvx def + a r + /arcto load stopped { 5 } { 4 } ifelse { pop } repeat + a +} def +% +/CheckClosed { + dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if +} def +% +/Polygon { + NArray n 2 eq { 0 0 /n 3 def } if + n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + n 2 mul -2 roll + /y0 ED /x0 ED /y1 ED /x1 ED + x1 y1 + /x1 x0 x1 add 2 div def + /y1 y0 y1 add 2 div def + x1 y1 moveto + /n n 2 sub def + n { Lineto } repeat + x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse +} def +% +/SymbolPolygon { % on stack [ x y x y ... + counttomark % number of elements + 2 add /m ED + 2 copy m 2 roll % copy last two + m 2 div cvi /n ED % n pairs + /YA ED /XA ED % the start point + n 1 sub { + /YB ED /XB ED + /XLength XB XA sub def + /YLength YB YA sub def + /PAngle YLength XLength Atan def + /XYLength XLength YLength Pyth def + /nSym XYLength SymStep Div cvi def + /Shift Symbol stringwidth pop 2 Div def + /deltaX XLength nSym Div def + /deltaY YLength nSym Div def + XA Shift sub YA Shift sub moveto + nSym { + gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if + Symbol show + grestore + deltaX deltaY rmoveto + } repeat +% XB Shift sub YB Shift sub moveto Symbol show + /YA YB def /XA XB def + } repeat + pop % delete the mark symbol +} def +% +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% +/Triangle { + /mtrx CM def + translate + rotate /h ED 2 div /w ED + dup CLW mul /d ED + /h h d w h Atan sin Div sub def + /w w d h w Atan 2 div dup cos exch sin Div mul sub def + mark + 0 d w neg d 0 h w d 0 d + /ArrowA { moveto } def + /ArrowB { } def + false + Line + closepath + mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def + setmatrix pop +} def +% DG/SR modification end +% +/CCA { + /y ED /x ED + 2 copy y sub /dy1 ED + x sub /dx1 ED + /l1 dx1 dy1 Pyth def +} def +% +/CC { + /l0 l1 def + /x1 x dx sub def + /y1 y dy sub def + /dx0 dx1 def + /dy0 dy1 def + CCA + /dx dx0 l1 c exp mul dx1 l0 c exp mul add def + /dy dy0 l1 c exp mul dy1 l0 c exp mul add def + /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def + /x2 x l0 dx mul m mul sub def + /y2 y l0 dy mul m mul sub def + /dx l1 dx mul m mul neg def + /dy l1 dy mul m mul neg def +} def +% +/IC { + /c c 1 add def + c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse + /a a 2 mul 3 div 45 cos b exp div def + CCA + /dx 0 def + /dy 0 def +} def +% +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +% +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +% +/CurvePath { + %% for negative SymStep we calculate the distance + SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if + 0.5 setflat + flattenpath /z 0 def /z0 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + x1 Shift sub y1 Shift sub moveto + gsave + curveticks + { x1 y1 translate startAngle rotate + 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto + SymbolLinewidth setlinewidth stroke + } + { startAngle rotate Symbol show } + ifelse + grestore /z0 z def } + { /y ED /x ED PathLength@ z z0 sub SymStep ge { + x Shift sub y Shift sub moveto + gsave + curveticks + { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED + x y translate rotAngle rotate + 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto + SymbolLinewidth setlinewidth stroke + } + { + rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if + Symbol show + } + ifelse + grestore /z0 z def } if + /yOld y def /xOld x def } + {} %% the lineto part + { /y y2 def /x x2 def PathLength@ + x Shift sub y Shift sub moveto + gsave + curveticks + { y yOld sub x xOld sub Atan 180 sub /rotAngle ED + x y translate rotAngle rotate + 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto + SymbolLinewidth setlinewidth stroke + } + { + x Shift sub y Shift sub moveto + rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if + Symbol show + } + ifelse + grestore + } + pathforall +% curveticks +% { gsave +% x y translate rotAngle rotate +% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto +% SymbolLinewidth setlinewidth stroke grestore +% } if + z +} def +% +/OpenSymbolCurve { + OpenCurve + 0.1 setflat + /Shift Symbol stringwidth pop 2 div def + CurvePath +} def +% +/AltCurve { + { false NArray n 2 mul 2 roll + [ n 2 mul 3 sub 1 roll ] aload + /Points ED + n 2 mul -2 roll } + { false NArray } ifelse + n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse +} def +% +/AltOpenSymbolCurve { + AltCurve + 0.1 setflat + /Shift Symbol stringwidth pop 2 div def + CurvePath +} def +% +/ClosedCurve { + NArray n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + 6 copy n 2 mul 6 add 6 roll + IC CC x y moveto n { NC } repeat + closepath pop pop + } ifelse +} def +% +/ClosedSymbolCurve { + ClosedCurve + 0.1 setflat + /Shift Symbol stringwidth pop 2 div def + CurvePath +} def +% +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def +% +/FontDot { + DS 2 mul dup + matrix scale matrix concatmatrix exch matrix + rotate matrix concatmatrix exch + findfont exch makefont setfont +} def +% +/Rect { + x1 y1 y2 add 2 div moveto + x1 y2 lineto + x2 y2 lineto + x2 y1 lineto + x1 y1 lineto + closepath +} def +% +/OvalFrame { + x1 x2 eq y1 y2 eq or + { pop pop x1 y1 moveto x2 y2 L } + { y1 y2 sub abs x1 x2 sub abs 2 copy gt + { exch pop } { pop } ifelse + 2 div exch { dup 3 1 roll mul exch } if + 2 copy lt { pop } { exch pop } ifelse + /b ED + x1 y1 y2 add 2 div moveto + x1 y2 x2 y2 b arcto + x2 y2 x2 y1 b arcto + x2 y1 x1 y1 b arcto + x1 y1 x1 y2 b arcto + 16 { pop } repeat + closepath + } ifelse +} def +% +/Frame { + CLW mul /a ED + 3 -1 roll + 2 copy gt { exch } if + a sub /y2 ED + a add /y1 ED + 2 copy gt { exch } if + a sub /x2 ED + a add /x1 ED + 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse +} def +% +/BezierNArray { + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/OpenBezier { + BezierNArray + n 1 eq + { pop pop } + { ArrowA n 4 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + 6 2 roll 4 2 roll ArrowB curveto } ifelse +} def +% +/OpenSymbolBezier { + OpenBezier + 0.1 setflat + /Shift Symbol stringwidth pop 2 div def + CurvePath +} def +% +/ClosedBezier { + BezierNArray + n 1 eq + { pop pop } + { moveto n 1 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + closepath } ifelse +} def +% +/ClosedSymbolBezier { + /f ED % save showpoints value + 2 copy /yEnd ED /xEnd ED + counttomark -2 roll 2 copy /yStart ED /xStart ED + counttomark 2 roll + f + ClosedBezier + 0.1 setflat + /Shift Symbol stringwidth pop 2 div def + CurvePath + [ xEnd yEnd xStart yStart SymbolLine +} def +% +/BezierShowPoints { + gsave + Points aload length 2 div cvi /n ED + moveto + n 1 sub { lineto } repeat + CLW 2 div SLW [ 4 4 ] 0 setdash stroke + grestore +} def +% +/Parab { + /y0 ED /x0 ED /y1 ED /x1 ED + /dx x0 x1 sub 3 div def + /dy y0 y1 sub 3 div def + x0 dx sub y0 dy add x1 y1 ArrowA + x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def +} def +% +/Parab1 { % 1 end | 0 SP + /ySP ED /xSP ED /y1 ED /x1 ED + /dx xSP x1 sub 3 div def + /dy ySP y1 sub 3 div def + newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto + x1 ySP lineto closepath clip + currentpoint + newpath moveto + xSP dx sub ySP dy add x1 y1 ArrowA + xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def +} def +% +/Grid { + newpath + /a 4 string def + /b ED % psk@gridlabels in pt + /c ED % { \pst@usecolor\psgridlabelcolor } + /n ED % psk@griddots + cvi dup 1 lt { pop 1 } if + /s ED % \psk@subgriddiv + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs + /dx ED dy div round dy mul % \pst@number\psxunit abs + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { + /rotAngle ED + /mtrx CM def + T + rotAngle rotate + scale 0 0 1 5 3 roll arc + mtrx setmatrix +} def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { + /TMatrix [ TMatrix setmatrix ] cvx def + /RAngle [ RAngle pop ] cvx def +} def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/Uput { + /a ED + add 2 div /h ED 2 + div /w ED + /s a sin def + /c a cos def + /b s abs c abs 2 copy gt dup + /q ED + { pop } { exch pop } ifelse def + /w1 c b div w mul def + /h1 s b div h mul def + q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse +} def +% +/UUput { + /z ED + abs /y ED + /x ED + q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse + { x x mul y y mul sub z z mul add sqrt z add } + { q { x s div } { x c div } ifelse abs + } ifelse + a PtoC + h1 add exch + w1 add exch +} def +% +/BeginOL { + dup (all) eq exch TheOL eq or + { IfVisible not { Visible /IfVisible true def } if } + { IfVisible { Invisible /IfVisible false def } if } ifelse +} def +% +/InitOL { + /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def + /Visible { CP OLUnit idtransform T moveto } def + /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def + /BOL { BeginOL } def + /IfVisible true def +} def +% +end +%-----------------------------------------------------------------------------% +% +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $ +%% +%% PostScript prologue for PSTricks algorithm parser +%% Version 0.04, 2011/10/21 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%%-----------------------------------------------------------------------------% +% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13 +% +% 09/2011 DR factorial with ! added +% +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF|P! +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P|P! +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { dup 33 eq%% is there a ! DR 09/2011 + { pop 1 add NextNonBlankChar pop EvalFactorial } + { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower } + ifelse + IsEndingFactor { pop exit } if } loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalFactorial {% DR 09/2011 + /ExpressionVector ExpressionVector aload length + /fact cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for factorial ! only cst => null derivative +/EvalFactorial {% DR 09/2011 + 4 index (0) eq + { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll } + { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_EXP {% + PreCommonFunc + { (EXP\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +/! { Fact } bind def +end +% +% END pst-algparser.pro + +%%EndProcSet +%%BeginProcSet: pst-tools.pro 0 0 +% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $ +% +%% PostScript tools prologue for pstricks.tex. +%% Version 0.03, 2012/10/16 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +% +% +/Pi2 1.57079632679489661925640 def +/factorial { % n on stack, returns n! + dup 0 eq { 1 }{ + dup 1 gt { dup 1 sub factorial mul } if } + ifelse } def +% +/MoverN { % m n on stack, returns the binomial coefficient m over n + 2 dict begin + /n exch def /m exch def + n 0 eq { 1 }{ + m n eq { 1 }{ + m factorial n factorial m n sub factorial mul div } ifelse } ifelse + end +} def +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% subroutines for complex numbers, given as an array [a b] +% which is a+bi = Real+i Imag +% +/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2] + dup 0 get % [a1 b1] [a2 b2] a2 + 3 -1 roll % [a2 b2] a2 [a1 b1] + dup 0 get % [a2 b2] a2 [a1 b1] a1 + 3 -1 roll % [a2 b2] [a1 b1] a1 a2 + add % [a2 b2] [a1 b1] a1+a2 + 3 1 roll % a1+a2 [a2 b2] [a1 b1] + 1 get % a1+a2 [a2 b2] b1 + exch 1 get % a1+a2 b1 b2 + add 2 array astore +} def +% +/cxneg { % [a b] + dup 1 get % [a b] b + exch 0 get % b a + neg exch neg % -a -b + 2 array astore +} def +% +/cxsub { cxneg cxadd } def % same as negative addition +% +% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3] +/cxmul { % [a1 b1] [a2 b2] + dup 0 get % [a1 b1] [a2 b2] a2 + exch 1 get % [a1 b1] a2 b2 + 3 -1 roll % a2 b2 [a1 b1] + dup 0 get % a2 b2 [a1 b1] a1 + exch 1 get % a2 b2 a1 b1 + dup % a2 b2 a1 b1 b1 + 5 -1 roll dup % b2 a1 b1 b1 a2 a2 + 3 1 roll mul % b2 a1 b1 a2 b1a2 + 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1 + 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2 + 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2 + 4 -1 roll add % b1 a2 a1 b2 b3 + 4 2 roll mul % b1 b2 b3 a1a2 + 4 2 roll mul sub % b3 a3 + exch 2 array astore +} def +% +% [a b]^2 = [a^2-b^2 2ab] = [a2 b2] +/cxsqr { % [a b] square root + dup 0 get exch 1 get % a b + dup dup mul % a b b^2 + 3 -1 roll % b b^2 a + dup dup mul % b b^2 a a^2 + 3 -1 roll sub % b a a2 + 3 1 roll mul 2 mul % a2 b2 + 2 array astore +} def +% +/cxsqrt { % [a b] +% dup cxnorm sqrt /r exch def +% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2 + cxlog % log[a b] + 2 cxrdiv % log[a b]/2 + aload pop exch % b a + 2.781 exch exp % b exp(a) + exch cxconv exch % [Re +iIm] exp(a) + cxrmul % +} def +% +/cxarg { % [a b] + aload pop % a b + exch atan % arctan b/a + DegtoRad % arg(z)=atan(b/a) +} def +% +% log[a b] = [a^2-b^2 2ab] = [a2 b2] +/cxlog { % [a b] + dup % [a b][a b] + cxnorm % [a b] |z| + log % [a b] log|z| + exch % log|z|[a b] + cxarg % log|z| Theta + cxmake2 % [log|z| Theta] +} def +% +% square of magnitude of complex number +/cxnorm2 { % [a b] + dup 0 get exch 1 get % a b + dup mul % a b^2 + exch dup mul add % a^2+b^2 +} def +% +/cxnorm { % [a b] + cxnorm2 sqrt +} def +% +/cxconj { % conjugent complex + dup 0 get exch 1 get % a b + neg 2 array astore % [a -b] +} def +% +/cxre { 0 get } def % real value +/cxim { 1 get } def % imag value +% +% 1/[a b] = ([a -b]/(a^2+b^2) +/cxrecip { % [a b] + dup cxnorm2 exch % n2 [a b] + dup 0 get exch 1 get % n2 a b + 3 -1 roll % a b n2 + dup % a b n2 n2 + 4 -1 roll exch div % b n2 a/n2 + 3 1 roll div % a/n2 b/n2 + neg 2 array astore +} def +% +/cxmake1 { 0 2 array astore } def % make a complex number, real given +/cxmake2 { 2 array astore } def % dito, both given +% +/cxdiv { cxrecip cxmul } def +% +% multiplikation by a real number +/cxrmul { % [a b] r + exch aload pop % r a b + 3 -1 roll dup % a b r r + 3 1 roll mul % a r b*r + 3 1 roll mul % b*r a*r + exch 2 array astore % [a*r b*r] +} def +% +% division by a real number +/cxrdiv { % [a b] r + 1 exch div % [a b] 1/r + cxrmul +} def +% +% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian +/cxconv { % theta + RadtoDeg dup sin exch cos cxmake2 +} def + +%%%%% ### bubblesort ### +%% syntax : array bubblesort --> array2 trie par ordre croissant +%% code de Bill Casselman +%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ +/bubblesort { % on stack must be an array [ ... ] +4 dict begin + /a exch def + /n a length 1 sub def + n 0 gt { + % at this point only the n+1 items in the bottom of a remain to + % the sorted largest item in that blocks is to be moved up into + % position n + n { + 0 1 n 1 sub { + /i exch def + a i get a i 1 add get gt { + % if a[i] > a[i+1] swap a[i] and a[i+1] + a i 1 add + a i get + a i a i 1 add get + % set new a[i] = old a[i+1] + put + % set new a[i+1] = old a[i] + put + } if + } for + /n n 1 sub def + } repeat + } if + a % return the sorted array +end +} def +% +/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422 + 0 1 index { length add } forall + string + 0 3 2 roll + { 3 copy putinterval length add }forall + pop +} bind def +% +/dot2comma {% on stack a string (...) + 2 dict begin + /Output exch def + 0 1 Output length 1 sub { + /Index exch def + Output Index get 46 eq { Output Index 44 put } if + } for + Output + end +} def +% +/rightTrim { + dup + length 1 sub -1 0 { + /i exch def dup i get 32 ne { exit } if + } for + 0 i 1 add getinterval + dup length string copy +} bind def + +/psStringwidth /stringwidth load def +/psShow /show load def + +%/stringwidth{ rightTrim psStringwidth } bind def + +%/show { rightTrim psShow } bind def +%-----------------------------------------------------------------------------% +% END pst-tools.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.02, 2009/06/16 +%% +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +%% Modified by Herbert Voss (hv) - 2008/04/17 +% +10 dict dup begin % hold local + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def +% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv + /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef + Encoding % replace with given dot names + dup (b) 0 get /Bullet put % get the numerical position of b in ASCII +% % and save /Bullet at this place in Encoding + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put % 67 + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (f) 0 get /Octogon put % 2008-04-18 hv + dup (F) 0 get /BoldOctogon put % 2008-04-18 hv + dup (g) 0 get /SolidOctogon put % 2008-04-18 hv + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put % 65 + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def +CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath { + -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath + } def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath { + 0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath + } def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def +% 2008-04-18 hv + /OctogonPath { + 550 dup 22.5 tan mul dup neg dup add /xMove exch def + exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def + /SolidOctogon { OctogonPath fill } def + /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def + /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def +% + /AsteriskPath { + 20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath + } def + /Asterisk { + AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill + } def +% + /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath { + 50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath + } def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath { + 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath + } def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath + } def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def +end +% +/BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end +} def +% +/BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec +} bind def +% +end +/PSTricksDotFont exch definefont pop +% +%% end + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 707 2012-09-21 14:17:30Z herbert $ +%% +%% PostScript prologue for pst-node.tex. +%% Version 1.14, 2012/09/18. +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +% +tx@Dict begin % from main pstricks dict + /T /translate load def + /CP /currentpoint load def + /startGlobal { true setglobal globaldict begin } bind def + /endGlobal { end false setglobal } bind def +end +/tx@NodeDict 400 dict def tx@NodeDict begin +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + NodeScale % a bugfix for xelatex, it's empty for dvips + /next exch def % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { + Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse + Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse + dx Sin mul abs dy + Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse +} def +% +/InitRnode { + /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED + /NodePos { GetRnodePos } def +} def +% +/DiaNodePos { + w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup + Cos mul exch Sin mul +} def +% +/TriNodePos { + Sin s lt + { d NodeSep sub dup Cos mul Sin Div exch } + { w h mul w Sin mul h Cos abs mul add Div + NodeSep add dup Cos mul exch Sin mul + } ifelse +} def +% +/InitTriNode { + sub 2 div exch + 2 div exch + 2 copy T + 2 copy 4 index index /d ED + pop pop pop pop + -90 mul rotate + /NodeMtrx CM def + /X 0 def /Y 0 def + d sub abs neg /d ED + d add /h ED + 2 div h mul h d sub Div /w ED + /s d w Atan sin def + /NodePos { TriNodePos } def +} def +% +/OvalNodePos { + /ww w NodeSep add def + /hh h NodeSep add def + Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul +} def +% +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { + dup sin exch cos Do + /Cos ED /Sin ED /Dist ED + Cos 0 gt + { Dist Dist Sin mul Cos div } + { Cos 0 lt + { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse + } ifelse + Do +} def +% +/GetEdge { + dup 0 eq + { pop begin 1 0 NodeMtrx dtransform + CM idtransform + exch atan sub + dup + sin /Sin ED + cos /Cos ED + /NodeSep ED + NodePos NodeMtrx dtransform CM idtransform end } + { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse +} def +% +/AddOffset { + 1 index 0 eq + { pop pop } + { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse +} def +% +/GetEdgeA { + NodeSepA AngleA NodeA NodeSepTypeA GetEdge + OffsetA AngleA AddOffset + yA add /yA1 ED + xA add /xA1 ED +} def +% +/GetEdgeB { + NodeSepB AngleB NodeB NodeSepTypeB GetEdge + OffsetB AngleB AddOffset + yB add /yB1 ED + xB add /xB1 ED +} def +% +/GetArmA { + ArmTypeA 0 eq + { /xA2 ArmA AngleA cos mul xA1 add def + /yA2 ArmA AngleA sin mul yA1 add def } + { ArmTypeA 1 eq {{exch}} {{}} ifelse + /Do ED + ArmA AngleA XYPos OffsetA AngleA AddOffset + yA add /yA2 ED + xA add /xA2 ED } ifelse +} def +% +/GetArmB { + ArmTypeB 0 eq + { /xB2 ArmB AngleB cos mul xB1 add def + /yB2 ArmB AngleB sin mul yB1 add def } + { ArmTypeB 1 eq {{exch}} {{}} ifelse + /Do ED + ArmB AngleB XYPos OffsetB AngleB AddOffset + yB add /yB2 ED + xB add /xB2 ED } ifelse +} def +% +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { + 4 copy + 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED + 1 t sub mul + 3 1 roll 1 t sub mul + 4 1 roll t mul add /Y ED + t mul add /X ED +} def +% +/LPutLines { + mark LPutVar counttomark 2 div 1 sub /n ED +% t floor dup n gt + t floor dup n ge % to allow npos<= hv 2008-08-14 + { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse + cvi 2 mul { pop } repeat + LPutLine + cleartomark +} def +% +/BezierMidpoint { + /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED + /cx x1 x0 sub 3 mul def + /cy y1 y0 sub 3 mul def + /bx x2 x1 sub 3 mul cx sub def + /by y2 y1 sub 3 mul cy sub def + /ax x3 x0 sub cx sub bx sub def + /ay y3 y0 sub cy sub by sub def + ax t 3 exp mul bx t t mul mul add + cx t mul add x0 add ay t 3 exp mul + by t t mul mul add cy t mul add + y0 add 3 ay t t mul mul mul 2 + by t mul mul add cy add 3 ax t t mul mul mul + 2 bx t mul mul add cx add atan /NAngle ED + /Y ED /X ED +} def +% +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +% +/NCLine { + NCCoor + tx@Dict begin + ArrowA CP 4 2 roll + ArrowB + lineto pop pop + end +} def +% +/NCLines { + false NArray + n 0 eq + { NCLine } + { 2 copy yA sub exch xA sub Atan /AngleA ED + n 2 mul dup index exch index yB sub exch xB sub + Atan /AngleB ED + GetEdgeA GetEdgeB + /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def + mark LPutVar + tx@Dict begin false Line end + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def + } ifelse +} def +% +/NCCurve { + GetEdgeA + GetEdgeB + xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { + GetEdgeA GetEdgeB GetArmB + /mtrx AngleA matrix rotate def + xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform + /y0 ED /x0 ED + mark + ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA1 yA1 + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def +} def +% +/NCBar { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx itransform pop + xB2 yB2 mtrx itransform pop + sub dup 0 mtrx transform + 3 -1 roll 0 gt + { /yB2 exch yB2 add def /xB2 exch xB2 add def } + { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse + mark + ArmB 0 ne { xB1 yB1 } if + xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def +} def +% +/NCDiag { + /lineAngle ED + GetEdgeA GetEdgeB GetArmA GetArmB mark + lineAngle abs 0 gt { + /xTemp xA2 10 add def + /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def + /dY1 yTemp yA2 sub def + /dX1 xTemp xA2 sub def + /dY2 yB2 yB1 sub def + /dX2 xB2 xB1 sub def + dX1 abs 0.01 lt { + /m2 dY2 dX2 div def + /xB2 xA2 def + /yB2 xA2 xB1 sub m2 mul yB1 add def + }{ + dX2 abs 0.01 lt { + /m1 dY1 dX1 div def + /xB2 xB1 def + /yB2 xB1 xA2 sub m1 mul yA2 add def + }{% + /m1 dY1 dX1 div def + /m2 dY2 dX2 div def + /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def + /yB2 xB2 xA2 sub m1 mul yA2 add def + } ifelse + } ifelse + } if + ArmB 0 ne { xB1 yB1 } if + xB2 yB2 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def +% +% GetEdgeA GetEdgeB GetArmA GetArmB mark +% ArmB 0 ne { xB1 yB1 } if +% xB2 yB2 xA2 yA2 +% ArmA 0 ne { xA1 yA1 } if +% tx@Dict begin false Line end +% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def +% /LPutPos { LPutLines } def +% /HPutPos { HPutLines } def +% /VPutPos { VPutLines } def +} def +% +/NCDiagg { + /lineAngle ED + GetEdgeA GetArmA + lineAngle abs 0 gt + { lineAngle } + { yB yA2 sub xB xA2 sub Atan 180 add } ifelse + /AngleB ED + GetEdgeB mark + lineAngle abs 0 gt { + /dY2 yA2 yA1 sub def + /dX2 xA2 xA1 sub def + lineAngle abs 90 eq { + /m2 dY2 dX2 div def + /yA2 xB xA2 sub m2 mul yA2 add def + /xA2 xB def + }{ + /m1 lineAngle dup sin exch cos div def % tan alpha + dX2 abs 0.01 lt { + /yA2 xA1 xB sub m1 mul yB add def + /xA2 xA1 def + }{% + /m2 dY2 dX2 div def + /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def + /yA2 xA2 xB sub m1 mul yB add def + } ifelse + } ifelse + } if + xB1 yB1 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def +% +% GetEdgeA GetArmA +% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +% GetEdgeB +% mark +% xB1 yB1 xA2 yA2 +% ArmA 0 ne { xA1 yA1 } if +% tx@Dict begin false Line end +% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def +% /LPutPos { LPutLines } def +% /HPutPos { HPutLines } def +% /VPutPos { VPutLines } def +} def +% +/NCLoop { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED + /xB3 xB2 yB2 mtrx transform pop def + xB3 yA3 mtrx itransform /yB3 ED /xB3 ED + xA3 yA3 mtrx itransform /yA3 ED /xA3 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def +} def +% +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% +/NCCircle { + NodeSepA 0 NodeA 0 GetEdge pop + 2 div dup 2 exp r r mul sub abs sqrt + atan 2 mul /a ED + r AngleA 90 add PtoC yA add exch xA add + exch 2 copy + /LPutVar [ 4 2 roll r AngleA ] cvx def + /LPutPos { + LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC + 3 -1 roll add + /Y ED add /X ED /NAngle ED +% DG/SR modification end + } def + /HPutPos { LPutPos } def + /VPutPos { LPutPos } def + r AngleA 90 sub a add AngleA 270 add a sub + tx@Dict begin + /angleB ED /angleA ED /r ED + /c 57.2957 r Div def + /y ED /x ED +} def +% +/NCBox { + /d ED /h ED + /AngleB yB yA sub xB xA sub Atan def + /AngleA AngleB 180 add def + GetEdgeA GetEdgeB + /dx d AngleB sin mul def + /dy d AngleB cos mul neg def + /hx h AngleB sin mul neg def + /hy h AngleB cos mul def + /LPutVar [ + xA1 hx add yA1 hy add xB1 hx add yB1 hy add + xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def + /LPutPos { LPutLines } def + /HPutPos { xB yB xA yA LPutLine } def + /VPutPos { HPutPos } def + mark + LPutVar tx@Dict begin false Polygon end +} def +% +/NCArcBox { + /l ED neg /d ED /h ED /a ED + /AngleA yB yA sub xB xA sub Atan def + /AngleB AngleA 180 add def + /tA AngleA a sub 90 add def + /tB tA a 2 mul add def + /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def + /x0 xA r tA cos mul add def + /y0 yA r tA sin mul add def + /c 57.2958 r div def + /AngleA AngleA a sub 180 add def + /AngleB AngleB a add 180 add def + GetEdgeA GetEdgeB + /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def + /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def + l 0 eq { + x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn + }{ + x0 y0 translate + /tA AngleA l c mul add def + /tB AngleB l c mul sub def + 0 0 r h add tA tB arc r h add + AngleB PtoC r d add + AngleB PtoC 2 copy + 6 2 roll l arcto 4 { pop } repeat + r d add tB PtoC l arcto 4 { pop } repeat + 0 0 r d add tB tA arcn r d add + AngleA PtoC r h add + AngleA PtoC 2 copy 6 2 roll + l arcto 4 { pop } repeat + r h add tA PtoC l arcto 4 { pop } repeat + } ifelse + closepath + /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def + /LPutPos { + LPutVar /d ED /h ED + /AngleB ED /AngleA ED + /r ED /y0 ED /x0 ED + t 1 le { + r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC + }{t 2 lt { + /NAngle AngleB 180 add def r 2 t sub + h mul t 1 sub d mul add add AngleB PtoC + }{ + t 3 lt { + r d add AngleB 3 t sub mul AngleA 2 t sub + mul add dup 90 sub /NAngle ED PtoC + }{ + /NAngle AngleA 180 add def + r 4 t sub d mul t 3 sub h mul add add AngleA PtoC + } ifelse + } ifelse + } ifelse + y0 add /Y ED x0 add /X ED + } def + /HPutPos { LPutPos } def + /VPutPos { LPutPos } def +} def +% +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +% +/LPutCoor { + NAngle + tx@Dict begin /NAngle ED end + gsave + CM STV + CP Y sub neg exch X sub neg exch moveto + setmatrix CP + grestore +} def +% +/LPut { + tx@NodeDict /LPutPos known + { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse + LPutCoor +} def +% +/HPutAdjust { + Sin Cos mul 0 eq + { 0 } + { d Cos mul Sin div flag not { neg } if + h Cos mul Sin div flag { neg } if + 2 copy gt { pop } { exch pop } ifelse + } ifelse + s add flag { r add neg }{ l add } ifelse + X add /X ED +} def +% +/VPutAdjust { + Sin Cos mul + 0 eq + { 0 } + { l Sin mul Cos div flag { neg } if + r Sin mul Cos div flag not { neg } if + 2 copy gt { pop } { exch pop } ifelse + } ifelse + s add flag { d add } { h add neg } ifelse + Y add /Y ED +} def +% +% +end +% +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%!ps +% PostScript prologue for pst-coil.tex. +% Version 1.06, 2011/09/18 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +% +/Sin { + /Func ED + /PointsPerPeriod ED + /ArmB ED + /ArmA ED + /Amplitude ED + /roundValue ED + /relativePeriod ED + /Periods ED + /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + dup /TotalLength ED + ArmA sub ArmB sub /SinLength ED + Atan rotate + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + relativePeriod + {} + { SinLength Periods div + roundValue dup 0 eq { pop cvi } { 1 eq { round } if } ifelse + /Periods ED } ifelse + /dxStep SinLength 360 div def % the default step for x pos + /xStep 360 PointsPerPeriod div def % the step for the for loop + 1 xStep 360 { % PointsPerPeriod times + dup dxStep mul ArmA add exch % x pos and value for the func + Periods mul Func Amplitude mul lineto + } for + mtrx setmatrix TotalLength ArmB sub 0 lineto CP + TotalLength 0 ArrowB lineto + pop pop pop pop +} def +% +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { 15 dict begin + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 + end } def +% + /ZigZagCirc { % x0 y0 x1 y1 bow h w ArmA ArmB on stack + /bow ED + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate % + y0 y1 sub x0 x1 sub 2 copy Pyth 2 div + /HalfLength ED + Atan /ang ED %angle of A relative to B + %rotate % so end B is origin and BA is horizontal, A to right + /theta bow abs HalfLength Atan 2 mul def %halfangular sector for arc + /theta2 theta 2 mul def % full arc + %/psi ang 90 sub theta sub def % angle of B from center if bow>0 + /rho HalfLength theta sin div def % radius of circle + bow 0 gt { /direc 1 def /thetaB ang 90 sub theta sub def } % travel B to A in pos drn + { /direc -1 def /thetaB ang 90 add theta add def } ifelse % travel B to A in neg drn + %thetaB=angle from center to B + rho thetaB 180 add PtoC translate % origin now at center + /h h rho div RadtoDeg def + /ArmA ArmA rho div RadtoDeg def /ArmB ArmB rho div RadtoDeg def + theta2 ArmA sub ArmB sub dup h div cvi /n ED n h mul + %HalfLength 2 mul ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add /ArmB ED + /h h direc mul def % h is now angle increment for half-period + /rhoo rho w add def /rhoi rho w sub def % outer and inner radii + /arg thetaB ArmB direc mul add def % argument for 2nd point +% thetaB = direc = bow = HalfLength = theta = rho = arg = h = n = + mark rho thetaB PtoC rho arg PtoC /arg arg h 2 div add def + n { w 0 gt { rhoo }{ rhoi } ifelse arg PtoC /w w neg def /arg arg h add def } repeat + rho thetaB theta2 ArmA sub direc mul add PtoC rho thetaB theta2 direc mul add PtoC + } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-3d.pro 0 0 +%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $ +% PostScript prologue for pst-3d.tex. +% Version 0.01, 2010/01/01 +% +/tx@3Ddict 300 dict def +tx@3Ddict begin +% +/SetMatrixThreeD { + dup sin /e ED cos /f ED + /p3 ED /p2 ED /p1 ED + p1 0 eq + { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def + p3 p2 abs + } + { p2 0 eq + { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def + p3 p1 abs + } + { p1 dup mul p2 dup mul add sqrt dup + p1 exch div /a ED + p2 exch div neg /b ED + p3 p1 a div + } + ifelse + } + ifelse + atan dup sin /c ED cos /d ED + /Matrix3D + [ + b f mul c a mul e mul sub + a f mul c b mul e mul add + d e mul + b e mul neg c a mul f mul sub + a e mul neg c b mul f mul add + d f mul + ] def +} def +% +/ProjThreeD { + /z ED /y ED /x ED + Matrix3D aload pop + z mul exch y mul add exch x mul add + 4 1 roll + z mul exch y mul add exch x mul add + exch +} def +% +/SetMatrixEmbed { + SetMatrixThreeD + Matrix3D aload pop + /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED + SetMatrixThreeD + [ + Matrix3D aload pop + z3 mul exch z2 mul add exch z1 mul add 4 1 roll + z3 mul exch z2 mul add exch z1 mul add + Matrix3D aload pop + x3 mul exch x2 mul add exch x1 mul add 4 1 roll + x3 mul exch x2 mul add exch x1 mul add + 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy + x3 mul exch x2 mul add exch x1 mul add 4 1 roll + z3 mul exch z2 mul add exch z1 mul add + ] + concat +} def +% +/TMSave { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def +} def +% +/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/TMChange { + TMSave + /cp [ currentpoint ] cvx def % ??? Check this later. + CM + CP T STV + CM matrix invertmatrix % Inv(M') + matrix concatmatrix % M Inv(M') + exch exec + concat cp moveto +} def +% +end % of tx@3Ddict +%% +%% End of file `pst-3d.pro'. + +%%EndProcSet +%%BeginProcSet: pst-math.pro 0 0 +% -*- Mode: Postscript -*- +% pst-math.pro --- PostScript header file pst-math.pro +% +% Author : Christophe JORSSEN +% Author : Herbert Voß +% Created the : Sat 20 March 2004 +% Last Mod : $Date: 2010/10/02 $ +% Version : 0.62 $ +% +/PI 3.14159265359 def +/ENeperian 2.71828182846 def +% +/DegToRad {PI mul 180 div} bind def +/RadToDeg {180 mul PI div} bind def +% +/COS {RadToDeg cos} bind def +/SIN {RadToDeg sin} bind def +/TAN {dup SIN exch COS Div} bind def +/tan {dup sin exch cos Div} bind def +/ATAN {neg -1 atan 180 sub DegToRad} bind def +/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def +/acos {dup dup mul neg 1 add sqrt exch atan} bind def +/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def +/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def +% +/EXP {ENeperian exch exp} bind def +% +/COSH {dup EXP exch neg EXP add 2 div} bind def +/SINH {dup EXP exch neg EXP sub 2 div} bind def +/TANH {dup SINH exch COSH div} bind def +/ACOSH {dup dup mul 1 sub sqrt add ln} bind def +/ASINH {dup dup mul 1 add sqrt add ln} bind def +/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def +% +%/SINC {dup SIN exch Div} bind def +/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def + +/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def +% +/GAMMA { 2 dict begin % hv 2007-08-30 + /z exch def + 1.000000000190015 % p(0) + 0 1 5 { % on stack is 0 1 2 3 4 5 + dup % n-1 n-1 + [ 76.18009172947146 + -86.50532032941677 + 24.0140982483091 + -1.231739572450155 + 0.1208650973866179E-2 + -0.5395239384953E-5 ] exch get exch % p(n) n-1 + 1 add z add div % p(n)/(z+n) + add % build the sum + } for + Pi 2 mul sqrt z div mul + z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul + end } bind def +% +/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015 + 0 1 5 { + [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155 + .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get + 4 -1 roll 1 add dup 5 1 roll div add} for + 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def +/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def +% +/HORNER {aload length + dup 2 add -1 roll + exch 1 sub { + dup 4 1 roll + mul add exch + } repeat + pop +} bind def +% +/BESSEL_J0 {dup abs 8 lt { + dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER + exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER + Div} + {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup + [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER + 3 index COS mul + exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER + 4 -1 roll SIN mul 3 -1 roll mul neg add mul} + ifelse} bind def +% +/BESSEL_Y0 {dup 8 lt { + dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER + exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER + Div exch dup ln exch BESSEL_J0 .636619772 mul mul add} + {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup + [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER + 3 index SIN mul + exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER + 4 -1 roll COS mul 3 -1 roll mul add mul} + ifelse} bind def +% +/BESSEL_J1 {dup abs 8 lt { + dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul + exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER + Div} + {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup + [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER + 3 index COS mul + exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER + 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul} + ifelse} bind def +% +/BESSEL_Y1 {dup 8 lt { + dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER + exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER + Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add} + {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup + [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER + 3 index SIN mul + exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER + 4 -1 roll COS mul 3 -1 roll mul add mul} + ifelse} bind def +% +% En cours... +/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{ + exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div { + mul 3 -1 roll mul 2 index sub pstack} for + } ifelse } ifelse } bind def +% +/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez + 3 index 5 index sub % compute h + 1 % a b var f ierr h n + 4 index 7 index def 3 index exec % a b var f ierr h n f(a) + 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b) + 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2) + exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop + { % a b var f ierr h n old Estim NbLoop + 5 -1 roll 2 div dup 6 1 roll % h<-h/2 + 5 -1 roll 2 mul 5 1 roll % n<-2n + % a b var f ierr h n old Estim NbLoop h + 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul + 5 index { + 1 index 10 index exch def 8 index exec add exch 6 index add exch + } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul + exch pop % a b var f ierr h n old Estim NbLoop New + 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff + 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff + exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff + 5 index 6 div mul abs 6 index lt { exit } if + 1 add dup 9 eq { exit } if + } loop % a b var f ierr h n old Estim NbLoop + exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark +end +} def +% ------------------------------------ math stuff ---------------------------------- +% +% Matrix A in arrays of rows A[[row1][row2]...] +% with [row1]=[a11 a12 ... b1] +% returns on stack solution vector X=[x1 x2 ... xn] +/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b) + 10 dict begin % hold all ocal + /A exch def + /Rows A length def % Rows = number of rows + /Cols A 0 get length def % Cols = number of columns + /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1] + /col 0 def + /row 0 def + /PR Rows array def % PR[c] = pivot row for row row + { % starts the loop, find pivot entry in row r + col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit + /pRow row def % pRow = pivot row + /max A row get col get abs def % get A[row[col]], first A[0,0] + row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1 + /j exch def % index counter + /x A j get col get abs def % get A[j[r]] + x max gt { % x>max, then save position + /pRow j def + /max x def + } if + } for % now we have the row with biggest A[0,1] + % with pRow = the pivot row + max 0 gt { % swap entries pRow and row in i + /tmp Index row get def + Index row Index pRow get put + Index pRow tmp put % and columns pRow and row in A + /tmp A row get def + A row A pRow get put + A pRow tmp put % pivot + /row0 A row get def % the pivoting row + /p0 row0 col get def % the pivot value + row 1 add 1 Rows 1 sub { % start for loop + /j exch def + /c1 A j get def + /p c1 col get p0 div def + c1 col p put % subtract (p1/p0)*row[i] from row[j] + col 1 add 1 Cols 1 sub { % start for loop + /i exch def + c1 dup i exch % c1 i c1 + i get row0 i get p mul sub put + } for + } for + PR row col put + /col col 1 add def + /row row 1 add def + }{ % all zero entries + /row row 1 add def % continue loop with same row + } ifelse + } loop + /X A def % solution vector + A Rows 1 sub get dup + Cols 1 sub get exch + Cols 2 sub get div + X Rows 1 sub 3 -1 roll put % X[n] + Rows 2 sub -1 0 { % for loop to calculate X[i] + /xi exch def % current index + A xi get % i-th row + /Axi exch def + /sum 0 def + Cols 2 sub -1 xi 1 add { + /n exch def + /sum sum Axi n get X n get mul add def + } for + Axi Cols 1 sub get % b=Axi[Cols-1] + sum sub % b-sum + Axi xi get div % b-sum / Axi[xi] + X xi 3 -1 roll put % X[xi] + } for + X + end +} def +% +/c@_0 2.515517 def +/c@_1 0.802853 def +/c@_2 0.010328 def +/d@_1 1.432788 def +/d@_2 0.189269 def +/d@_3 0.001308 def +/norminv { + 5 dict begin + neg 1 add 1 exch div ln 2 mul sqrt + /t exch def + /t2 t dup mul def + /t3 t2 t mul def + c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add + d@_2 t2 mul add d@_3 t3 mul add div neg t add + end +} def +%end{norminv Michael Sharpe} +% +% +% END pst-math.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 692 2012-06-04 06:47:40Z herbert $ +%% +% PostScript prologue for pstricks-add.tex. +% +% Version 0.23, 2009/12/17 +% +/tx@addDict 410 dict def tx@addDict begin +%% +realtime srand % set random generator +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b -> C M Y K + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % on stack c m y k -> gray + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { % on stack r g b -> gray + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToGRAY { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB + Red Green Blue RGBtoGRAY +} def % now the gray color is on the stack +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +%/amplHand {.8} def +%/dtHand 2 def +/varHand { rand sin amplHand mul add } def +/MovetoByHand { moveto } def +%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def +/LinetoByHand { 4 dict begin + /y1 ED /x1 ED + currentpoint /y0 ED /x0 ED + x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED + 0 dtHand dEnd { dup + x1 x0 sub mul dEnd 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CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.1 SLW 0 setgray +/ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 0.0 156.49008 0.0 0.0 /Lineto /lineto load def 0 setlinejoin +false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt +{ 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin +0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.1 SLW 0 setgray +/ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 213.39557 0.0 0.0 0.0 /Lineto /lineto load def 0 setlinejoin +false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt +{ 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin +0 setlinecap stroke grestore end + +@endspecial 266 -169 a Fd(0)266 -877 y(3)366 +-62 y(0)659 b(3)h(6)390 -201 y @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 142.26372 28.45274 0.0 0.0 /Lineto /lineto load def 0 + setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if +() length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg +add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan +def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos +dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.5 SLW 1 0 0 setrgbcolor 1. +.setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 1 0.5 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 199.1692 142.26372 142.26372 28.45274 /Lineto /lineto +load def 0 setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 +mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED +/Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin +ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def +/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { +/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add +y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse +pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat +} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW 1 0.5 0 + setrgbcolor 1. .setopacityalpha 0 setlinecap [ 5.0 3.0 0.0 + 0.0 ] -2 0 add DashLine grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 1 0.5 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 56.90549 113.81097 0.0 0.0 /Lineto /lineto load def 0 + setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if +() length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg +add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan +def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos +dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.5 SLW 1 0.5 0 setrgbcolor +1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 56.90549 113.81097 56.90549 +-11.38092 /Lineto /lineto load def 0 setlinejoin false NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 1 0.5 0 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 56.90549 113.81097 -11.38092 +113.81097 /Lineto /lineto load def 0 setlinejoin false NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 1 0.5 0 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 142.26372 28.45274 142.26372 +-11.38092 /Lineto /lineto load def 0 setlinejoin false NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 1 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 142.26372 28.45274 -11.38092 +28.45274 /Lineto /lineto load def 0 setlinejoin false NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 1 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 199.1692 142.26372 56.90549 113.81097 /Lineto /lineto +load def 0 setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 +mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED +/Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin +ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def +/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { +/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add +y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse +pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat +} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW 1 0 0 setrgbcolor + 1. .setopacityalpha 0 setlinecap [ 5.0 3.0 0.0 0.0 ] -2 0 add + DashLine grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 199.1692 142.26372 -11.38092 +142.26372 /Lineto /lineto load def 0 setlinejoin false NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 199.1692 142.26372 199.1692 +-11.38092 /Lineto /lineto load def 0 setlinejoin false NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos +0.5 abs def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha +cos ArrowPos mul add y1 Alpha sin ArrowPos mul add ArrowInside pop +pop } repeat }{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add +div }{0.5 } ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def +x2 x1 sub ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside +pop pop } repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 +sub def n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } +if gsave 0.1 SLW 0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap +[ 5.0 3.0 0.0 0.0 ] 0 0 add DashLine grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 199.1692 142.26372 0.0 0.0 /Lineto /lineto load def 0 + setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if +() length 0 gt { 1.5 2. 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sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx 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dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. 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CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 1 0 0 setcmykcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 56.90549 113.81097 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 1 0 0 setcmykcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 1 0 0 setcmykcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 56.90549 113.81097 56.90549 +-11.38092 /Lineto /lineto load def false 0 setlinejoin NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 1 0 0 setcmykcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 1 0 0 setcmykcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 56.90549 113.81097 -11.38092 +113.81097 /Lineto /lineto load def false 0 setlinejoin NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 1 0 0 setcmykcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 142.26372 28.45274 142.26372 +-11.38092 /Lineto /lineto load def false 0 setlinejoin NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +1 0 0 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 142.26372 28.45274 -11.38092 +28.45274 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul +add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +1 0 0 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 199.1692 142.26372 56.90549 113.81097 /Lineto /lineto load +def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def +} if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul +neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.5 SLW 1 0 0 setrgbcolor 1. +.setopacityalpha [ 5.0 3.0 ] -2 0 add dup 0 gt { /a .5 def PathLength +exch div } { pop /a 1 def PathLength } ifelse /b ED dup /X ED 0 get +/y ED /z 0 X {add} forall def b a .5 sub 2 mul y mul sub z Div round +z mul a .5 sub 2 mul y mul add b exch Div /z ED false X { z mul } forall +X astore {0 gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse +setdash stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 199.1692 142.26372 -11.38092 +142.26372 /Lineto /lineto load def false 0 setlinejoin NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 0 1 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 199.1692 142.26372 199.1692 +-11.38092 /Lineto /lineto load def false 0 setlinejoin NArray n +0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 0 1 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] 0 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 199.1692 142.26372 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.5 SLW +0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke grestore +end + +@endspecial 354 -177 a + tx@Dict begin { 34.1432 54.06003 } PutCoor PutBegin end + 354 +-177 a 0 1 0 0 TeXcolorcmyk 349 -148 a Fc(~)-37 b(a)p +Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 a + tx@Dict begin { 85.35823 99.5846 } PutCoor PutBegin end + 354 -177 a 0 0 1 +TeXcolorrgb 349 -140 a Fc(~)g(a)19 b Fd(+)491 -162 y +Fc(~)500 -140 y(b)p Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 +a + tx@Dict begin { 113.81097 35.56592 } PutCoor PutBegin end + 354 -177 a 1 0 0 TeXcolorrgb 345 -158 a Fc(~)354 -137 +y(b)p Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 a + tx@Dict begin { 56.90549 -14.22636 } PutCoor PutBegin end + 354 -177 +a 0 1 0 0 TeXcolorcmyk 313 -165 a Fc(a)357 -153 y Fb(1)p +Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 a + tx@Dict begin { -14.22636 113.81097 } PutCoor PutBegin end + 354 -177 a 0 1 0 0 +TeXcolorcmyk 313 -165 a Fc(a)357 -153 y Fb(2)p Black +354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 a + tx@Dict begin { 142.26372 -14.22636 } PutCoor PutBegin end + 354 -177 a 1 0 0 TeXcolorrgb +318 -155 a Fc(b)354 -143 y Fb(1)p Black 354 -177 a + tx@Dict begin PutEnd end + 354 +-177 a 354 -177 a + tx@Dict begin { -14.22636 28.45274 } PutCoor PutBegin end + 354 -177 a 1 0 0 TeXcolorrgb 318 -155 +a Fc(b)354 -143 y Fb(2)p Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a +354 -177 a + tx@Dict begin { 204.85966 -14.22636 } PutCoor PutBegin end + 354 -177 a 0 0 1 TeXcolorrgb 227 -155 a Fc(a)271 +-143 y Fb(1)326 -155 y Fd(+)f Fc(b)445 -143 y Fb(1)p +Black 354 -177 a + tx@Dict begin PutEnd end + 354 -177 a 354 -177 a + tx@Dict begin { -28.45274 142.26372 } PutCoor PutBegin end + 354 -177 a 0 0 1 +TeXcolorrgb 227 -155 a Fc(a)271 -143 y Fb(2)326 -155 +y Fd(+)g Fc(b)445 -143 y Fb(2)p Black 354 -177 a + tx@Dict begin PutEnd end + 354 +-177 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.8 SLW 0 setgray /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 99.5846 156.49008 99.5846 142.26372 +102.43004 106.69778 106.69778 85.35823 113.81097 56.90549 /r 42.67911 +def /Lineto { Arcto } def false 0 setlinejoin NArray n 0 eq not { +n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup +1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha +cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub +def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha +y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 +y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.8 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.75 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 116.65642 49.7923 113.81097 56.90549 /Lineto /lineto load +def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def +} if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul +neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.75 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial 354 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load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ 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w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 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add currentdict /ArrowInside +known { ArrowInside } if pop pop } repeat } ifelse pop pop Lineto } +def n { 4 copy /y11 ED /x11 ED /y12 ED /x12 ED drawArrows } repeat +x1 y1 x0 y0 6 4 roll 2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def +drawArrows /y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows +pop pop closepath } ifelse gsave 1 setgray 1. .setopacityalpha fill + grestore gsave 0.4 SLW 0 setgray 1. .setopacityalpha 0 setlinecap +stroke grestore end + +@endspecial 118 -35 a + tx@Dict begin { 42.67911 99.5846 } PutCoor PutBegin end + 118 -35 a 68 -13 a +Fb(R)131 -1 y Fa(1)118 -35 y + tx@Dict begin PutEnd end + 118 -35 a 118 -35 a + tx@Dict begin { 14.22636 93.89413 } PutCoor PutBegin end + 118 +-35 a 81 -13 a Fb(I)117 -1 y Fa(1)118 -35 y + tx@Dict begin PutEnd end + 118 -35 a +118 -35 a + tx@Dict begin { 156.49008 93.89413 } PutCoor PutBegin end + 118 -35 a 81 -13 a Fb(I)117 -1 y Fa(2)118 -35 +y + tx@Dict begin PutEnd end + 118 -35 a 118 -35 a + tx@Dict begin { 93.89413 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CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 17.07181 85.35823 5.69046 85.35823 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 153.64464 85.35823 165.02599 85.35823 +/Lineto /lineto load def false 0 setlinejoin NArray n 0 eq not { +n 1 eq { 0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add +dup 1.5 mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 +ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 85.35823 68.2864 85.35823 79.66776 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.3 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 0.0 5.69046 0.0 79.66776 /Lineto /lineto +load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 mul exch +0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 +ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.3 SLW 0 setgray 1. .setopacityalpha +[ 5.0 3.0 ] -2 0 add dup 0 gt { /a .5 def PathLength exch div } +{ pop /a 1 def PathLength } ifelse /b ED dup /X ED 0 get /y ED /z 0 +X {add} forall def b a .5 sub 2 mul y mul sub z Div round z mul a .5 +sub 2 mul y mul add b exch Div /z ED false X { z mul } forall X astore +{0 gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke + grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.3 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 170.71646 5.69046 170.71646 79.66776 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.3 SLW +0 setgray 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup 0 gt { +/a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse +/b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub 2 mul +y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div /z +ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub y +mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 113.81097 85.35823 56.90549 85.35823 + /Lineto /lineto load def false 0 setlinejoin NArray n 0 eq not { +n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup +1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha +cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub +def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha +y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 +y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale 0.0 dup 0 eq { pop }{ SLW } ifelse {1 setgray true} +false /DS 2.0 2. CLW mul add 2 div def EndDot EndArrow } def /ArrowInside +{ } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale 0.0 dup 0 eq { pop }{ SLW } ifelse {1 setgray true} +false /DS 2.0 2. CLW mul add 2 div def EndDot EndArrow } def /ArrowInside +{ } def [ 170.71646 85.35823 142.26372 85.35823 /Lineto /lineto load +def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def +} if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul +neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale 0.0 + dup 0 eq { pop }{ SLW } ifelse {1 setgray true} false /DS 2.0 2. +CLW mul add 2 div def EndDot EndArrow moveto } def /ArrowB { BeginArrow +1. 1. scale 0.0 dup 0 eq { pop }{ SLW } ifelse {1 setgray true} +false /DS 2.0 2. CLW mul add 2 div def EndDot EndArrow } def /ArrowInside +{ } def 0.2 SLW 0 setgray /ArrowA { BeginArrow 1. 1. scale 0.0 + dup 0 eq { pop }{ SLW } ifelse {1 setgray true} false /DS 2.0 2. +CLW mul add 2 div def EndDot EndArrow moveto } def /ArrowB { BeginArrow +1. 1. scale 0.0 dup 0 eq { pop }{ SLW } ifelse {1 setgray true} +false /DS 2.0 2. CLW mul add 2 div def EndDot EndArrow } def /ArrowInside +{ } def [ 170.71646 0.0 0.0 0.0 /Lineto /lineto load def false 0 + setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 85.35823 28.45274 85.35823 0.0 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul +exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 +ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 85.35823 85.35823 85.35823 56.90549 + /Lineto /lineto load def false 0 setlinejoin NArray n 0 eq not { +n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup +1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha +cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub +def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha +y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 +y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial eop end 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1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get +neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr +1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr +2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 +-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S +TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ +Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale +}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState +save N userdict maxlength dict begin/magscale true def normalscale +currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts +/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x +psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx +psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub +TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict +begin/SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ +CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N +/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} +repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N +/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX +currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +dup 51 /three put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 73 /I put +dup 82 /R put +dup 85 /U put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 +9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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def /dArrowPos 0.5 abs +def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length gt { exit +} if x11 Alpha cos ArrowPos mul add y11 Alpha sin ArrowPos mul add +currentdict /ArrowInside known { ArrowInside } if pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } +ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x12 x11 sub +ArrowPos mul x11 add y12 y11 sub ArrowPos mul y11 add currentdict /ArrowInside +known { ArrowInside } if pop pop } repeat } ifelse pop pop Lineto } +def n { 4 copy /y11 ED /x11 ED /y12 ED /x12 ED drawArrows } repeat +x1 y1 x0 y0 6 4 roll 2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def +drawArrows /y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows +pop pop closepath } ifelse gsave 1 setgray 1. .setopacityalpha fill + grestore gsave 0.4 SLW 0 setgray 1. .setopacityalpha 0 setlinecap +stroke grestore end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.4 SLW 0 setgray [ 128.03734 5.69046 156.49008 +5.69046 156.49008 -5.69046 128.03734 -5.69046 /Lineto /lineto load +def false 0 setlinejoin NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { +n { pop pop } repeat }{ n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 +ED /x0 ED /y1 ED /x1 ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add +2 div def /y1 y0 y1 add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows +{ x11 y11 0.5 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos +0. def /Length x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs +def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length gt { exit +} if x11 Alpha cos ArrowPos mul add y11 Alpha sin ArrowPos mul add +currentdict /ArrowInside known { ArrowInside } if pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } +ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x12 x11 sub +ArrowPos mul x11 add y12 y11 sub ArrowPos mul y11 add currentdict /ArrowInside +known { ArrowInside } if pop pop } repeat } ifelse pop pop Lineto } +def n { 4 copy /y11 ED /x11 ED /y12 ED /x12 ED drawArrows } repeat +x1 y1 x0 y0 6 4 roll 2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def +drawArrows /y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows +pop pop closepath } ifelse gsave 1 setgray 1. .setopacityalpha fill + grestore gsave 0.4 SLW 0 setgray 1. .setopacityalpha 0 setlinecap +stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.4 SLW 0 setgray [ 79.66776 28.45274 91.04869 +28.45274 91.04869 56.90549 79.66776 56.90549 /Lineto /lineto load +def false 0 setlinejoin NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { +n { pop pop } repeat }{ n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 +ED /x0 ED /y1 ED /x1 ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add +2 div def /y1 y0 y1 add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows +{ x11 y11 0.5 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos +0. def /Length x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs +def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length gt { exit +} if x11 Alpha cos ArrowPos mul add y11 Alpha sin ArrowPos mul add +currentdict /ArrowInside known { ArrowInside } if pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } +ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x12 x11 sub +ArrowPos mul x11 add y12 y11 sub ArrowPos mul y11 add currentdict /ArrowInside +known { ArrowInside } if pop pop } repeat } ifelse pop pop Lineto } +def n { 4 copy /y11 ED /x11 ED /y12 ED /x12 ED drawArrows } repeat +x1 y1 x0 y0 6 4 roll 2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def +drawArrows /y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows +pop pop closepath } ifelse gsave 1 setgray 1. .setopacityalpha fill + grestore gsave 0.4 SLW 0 setgray 1. .setopacityalpha 0 setlinecap +stroke grestore end + +@endspecial 118 -118 a + tx@Dict begin { 28.45274 14.22636 } PutCoor PutBegin end + 118 -118 a 68 -96 +a Fc(R)131 -84 y Fb(3)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 -118 +a + tx@Dict begin { 93.89413 14.22636 } PutCoor PutBegin end + 118 -118 a 81 -96 a Fc(I)117 -84 y Fb(2)118 -118 y + tx@Dict begin PutEnd end + +118 -118 a 118 -118 a + tx@Dict begin { 105.27505 -8.5359 } PutCoor PutBegin end + 118 -118 a 81 -96 a Fc(I)117 -84 +y Fb(1)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 -118 a + tx@Dict begin { 142.26372 14.22636 } PutCoor PutBegin end + 118 -118 a 68 +-96 a Fc(R)131 -84 y Fb(1)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 -118 +a + tx@Dict begin { 99.5846 42.67911 } PutCoor PutBegin end + 118 -118 a 68 -96 a Fc(R)131 -84 y Fb(2)118 -118 y + tx@Dict begin PutEnd end + +118 -118 a 118 -118 a + tx@Dict begin { 179.25237 42.67911 } PutCoor PutBegin end + 118 -118 a 71 -96 a Fc(U)128 -84 +y Fb(2)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 -118 a + tx@Dict begin { -8.5359 42.67911 } PutCoor PutBegin end + 118 -118 a 71 +-96 a Fc(U)128 -84 y Fb(1)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 -118 +a + tx@Dict begin { 85.35823 -8.5359 } PutCoor PutBegin end + 118 -118 a 87 -90 a Fc(A)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a 118 +-118 a + tx@Dict begin { 65.44139 -8.5359 } PutCoor PutBegin end + 118 -118 a 81 -96 a Fc(I)117 -84 y Fb(3)118 -118 +y + tx@Dict begin PutEnd end + 118 -118 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.4 SLW 0 setgray 128.03734 42.67911 8.5359 +0 CLW mul sub 0 360 arc closepath gsave 0.4 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial 118 +-118 a + tx@Dict begin { 128.03734 42.67911 } PutCoor PutBegin end + 118 -118 a 87 -90 a Fa(I)r(I)118 -118 y + tx@Dict begin PutEnd end + 118 -118 +a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.4 SLW 0 setgray 42.67911 42.67911 8.5359 +0 CLW mul sub 0 360 arc closepath gsave 0.4 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial 118 -118 a + tx@Dict begin { 42.67911 42.67911 } PutCoor PutBegin end + 118 +-118 a 103 -90 a Fa(I)118 -118 y + tx@Dict begin PutEnd end + 118 -118 a @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false +0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a +ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a +neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow + moveto } def /ArrowB { } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { BeginArrow 1. 1. scale false 0.3 1.5 4.2679 0. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow moveto } def /ArrowB { } def +/ArrowInside { } def [ 68.2864 0.0 62.59595 0.0 /Lineto /lineto load +def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def +} if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 mul exch 0.3 +mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED +/Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false +0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a +ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a +neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow + moveto } def /ArrowB { } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { BeginArrow 1. 1. scale false 0.3 1.5 4.2679 0. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow moveto } def /ArrowB { } def +/ArrowInside { } def [ 108.1205 0.0 102.43004 0.0 /Lineto /lineto +load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 mul exch +0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 +ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray 1. .setopacityalpha +0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.2 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 85.35823 11.38092 85.35823 17.07181 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 setgray 1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.3 SLW 0 setgray + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 0.0 5.69046 0.0 79.66776 /Lineto /lineto +load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 4.2679 0. 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RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md 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setcmykcolor}DC/LimeGreen{0.50 0 1 0 +setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ +0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} +DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 +setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 +setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 +setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 48 /parenlefttp put +dup 49 /parenrighttp put +dup 64 /parenleftbt put +dup 65 /parenrightbt put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF5B8CAC6A7BEB5D02276E511FFAF2AE11910 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+0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +TeXDict begin 40258437 52099154 1000 600 600 (2dgrafiken.dvi) +@start /Fa 201[42 1[42 42 42 42 42 48[{}6 83.022 /CMR10 +rf /Fb 190[73 73 14[73 73 48[{}4 83.022 /CMEX10 rf +%DVIPSBitmapFont: Fc ecrm1000 10 2 +/Fc 2 46 df<000000300000000000003000000000000030000000000000300000000000 +003000000000000030000000000000300000000000003000000000000030000000000000 +300000000000003000000000000030000000000000300000000000003000000000000030 +000000000000300000000000003000000000000030000000000000300000000000003000 +000000000030000000000000300000000000003000000000000030000000000000300000 +0000000030000000FFFFFFFFFFFFFCFFFFFFFFFFFFFC0000003000000000000030000000 +000000300000000000003000000000000030000000000000300000000000003000000000 +000030000000000000300000000000003000000000000030000000000000300000000000 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CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 73.9773 17.07181 34.1432 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +0 0 1 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 83.9355 17.07181 44.10184 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +0 0 1 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 93.89413 17.07181 54.06003 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +0 0 1 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 34.1432 17.07181 71.13185 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +1 0 0 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 44.10184 17.07181 81.09048 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +1 0 0 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.3 1.5 4.2679 0. CLW mul add dup 2 div /w ED +mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto +0 0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a +sub moveto EndArrow } def /ArrowInside { } def 0.4 SLW 1 0 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.3 +1.5 4.2679 0. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { +0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg +rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow } +def /ArrowInside { } def [ 54.06003 17.07181 91.04869 68.2864 /Lineto +/lineto load def false 0 setlinejoin NArray n 0 eq not { n 1 eq { +0 0 /n 2 def } if () length 0 gt { 4.2679 0. CLW mul add dup 1.5 +mul exch 0.3 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +1 0 0 setrgbcolor 1. .setopacityalpha [ 5.0 3.0 ] -2 0 add dup +0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } +ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} forall def b a .5 sub +2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div +/z ED false X { z mul } forall X astore {0 gt or} forall { X 1 a sub +y mul } { [ 1 0 ] 0 } ifelse setdash stroke grestore end + +@endspecial -236 71 a + tx@Dict begin { 31.29819 71.13185 } PutCoor PutBegin end + -236 71 a 0 0 1 TeXcolorrgb +-268 92 a Fc(+)p Black -236 71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 41.25638 71.13185 } PutCoor PutBegin end + +-236 71 a 0 0 1 TeXcolorrgb -268 92 a Fc(+)p Black -236 +71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 51.21501 71.13185 } PutCoor PutBegin end + -236 71 a 0 0 1 TeXcolorrgb +-268 92 a Fc(+)p Black -236 71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 31.29819 14.22636 } PutCoor PutBegin end + +-236 71 a 1 0 0 TeXcolorrgb -250 89 a Fc(-)p Black -236 +71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 41.25638 14.22636 } PutCoor PutBegin end + -236 71 a 1 0 0 TeXcolorrgb +-250 89 a Fc(-)p Black -236 71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 51.21501 14.22636 } PutCoor PutBegin end + +-236 71 a 1 0 0 TeXcolorrgb -250 89 a Fc(-)p Black -236 +71 a + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 42.67911 42.67911 } PutCoor PutBegin end + -236 71 a -319 -75 a Fb(0)-319 +74 y(@)-236 71 y + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 42.67911 42.67911 } PutCoor PutBegin end + -236 71 a -257 -9 +a Fa(4)-257 91 y(3)-257 190 y(1)-236 71 y + tx@Dict begin PutEnd end + -236 71 a -236 +71 a + tx@Dict begin { 52.63774 42.67911 } PutCoor PutBegin end + -236 71 a -257 -9 a Fa(6)-257 91 y(1)-257 190 y(2)-236 +71 y + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 62.59595 42.67911 } PutCoor PutBegin end + -236 71 a -257 -9 a Fa(3)-257 +91 y(0)-257 190 y(1)-236 71 y + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 62.59595 42.67911 } PutCoor PutBegin end + -236 +71 a -226 -75 a Fb(1)-226 74 y(A)-236 71 y + tx@Dict begin PutEnd end + -236 71 a +-236 71 a + tx@Dict begin { 72.55458 42.67911 } PutCoor PutBegin end + -236 71 a -257 -9 a Fa(4)-257 91 y(3)-257 190 +y(1)-236 71 y + tx@Dict begin PutEnd end + -236 71 a -236 71 a + tx@Dict begin { 82.51277 42.67911 } PutCoor PutBegin end + -236 71 a -257 -9 a +Fa(6)-257 91 y(1)-257 190 y(2)-236 71 y + tx@Dict begin PutEnd end + -236 71 a eop +end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/2dgrafiken/Aufgabe011.pdf b/2dgrafiken/Aufgabe011.pdf new file mode 100644 index 0000000..ae36898 Binary files /dev/null and b/2dgrafiken/Aufgabe011.pdf differ diff --git a/2dgrafiken/Aufgabe011.pst b/2dgrafiken/Aufgabe011.pst new file mode 100644 index 0000000..a93df40 --- /dev/null +++ b/2dgrafiken/Aufgabe011.pst @@ -0,0 +1,73 @@ +\psset{xunit=1cm, yunit=1cm} 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dvips(k) 5.96dev Copyright 2007 Radical Eye Software +%%Title: 2dgrafiken.dvi +%%CreationDate: Mon Jun 09 13:16:28 2008 +%%BoundingBox: 133 744 170 753 +%%DocumentFonts: CMR10 CMMI10 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips -EPSF 2dgrafiken.dvi +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2008.06.09:1316 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 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CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +0.44 0.5 0.565 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke + grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 0.4 SLW 0.44 0.5 0.565 setrgbcolor /ArrowA +{ moveto } def /ArrowB { } def /ArrowInside { } def [ 1.42271 85.35823 +-1.42271 85.35823 /Lineto /lineto load def false 0 setlinejoin NArray +n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW +mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA +x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength mul add /n +n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt +{ /Alpha y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /Length x2 +x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.4 SLW +0.44 0.5 0.565 setrgbcolor 1. .setopacityalpha 0 setlinecap stroke + grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def +/ArrowInside { } def 2.0 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def [ 1.42271 85.35823 1.42271 +28.45274 /Lineto /lineto load def false 0 setlinejoin NArray n 0 +eq not { n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. 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coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 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cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED 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Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.08, 2006/06/17 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2006/06/17 : - changes to the code (hv) +% 2006/04/21 : - Improved parser -> generic with derivative and translator into ps (dr) +% 2006/01/16 : - EXP -> Exp to prevent missmatch with pst-math (hv) +% 2005/09/28 : - rename it to pstricks-add.pro +% - add support for Gouraud shading (hv) +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression (dr) +% 2004/12/16 : addition of Sum and IfTE (dr) +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +% +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { tx@AlgToPs begin AlgToPs end } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end%%%tx@CoreAnalyzerDict +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat } + { tutu 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (ln\() StrConcat 8 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if 90 div 1.57079632680 mul +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan 90 div 1.57079632680 mul +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if 90 div 1.57079632680 mul } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { 2.71828182846 exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +TeXDict begin 40258437 52099154 1000 600 600 (2dgrafiken.dvi) +@start /Fa 134[41 47 15[48 2[39 28[69 72[{}5 83.022 /CMMI10 +rf /Fb 255[65{}1 83.022 /CMSY10 rf end +%%EndProlog +%%BeginSetup +%%Feature: *Resolution 600dpi +TeXDict begin + end +%%EndSetup +TeXDict begin 1 0 bop +-32891 -32891 32891 32891 9323397 0 11933994 + 756 -236 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +85.35825 0 -85.35825 0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 1 dup 2 mod 0 eq false and exch 2 lt true and or { /viceversa +-85.35825 85.35825 gt { true }{ false } ifelse def /epsilon 0.01 +def /minTickline -5.69089 def /maxTickline 113.811 def /dT 3729359 +abs 65536 div viceversa { neg } if def /subTNo 1 def subTNo 0 gt { +/dsubT dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 4.0 /tickend +exch def /tickstart exch def /Twidth 0.4 def /subTwidth 0.2 def /STsize +0.75 def /TColor { 0 setgray } def /subTColor { 0.5 setgray } def +/MinValue { xStart } def /MaxValue { xEnd 1.5 2. CLW mul add 1.4 +mul viceversa { add epsilon sub } { sub epsilon add } ifelse } def +/logLines { false } def /LSstroke { 0 setlinecap stroke } def /subLSstroke +{ 0 setlinecap stroke } def 0 dT MaxValue { /cntTick exch def logLines +{ gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul +add def x abs MaxValue abs le { x minTickline moveto x maxTickline + lineto } if } for subTwidth SLW subTColor subLSstroke grestore stroke +/dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul moveto cntsubTick tickend STsize mul lineto +}{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart moveto +cntTick tickend lineto Twidth SLW TColor LSstroke grestore } for /dT +dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon viceversa { add +}{ sub } ifelse { /cntTick exch def logLines { gsave 1 10 subTNo div +9.99 { /dx exch def /x cntTick dT dx log mul add def x abs MinValue +abs le { x minTickline moveto x maxTickline lineto } if } for /dsubT +0 def subTwidth SLW subTColor subLSstroke grestore } dsubT abs 0 gt +{ gsave /cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick +abs MinValue abs le { cntsubTick tickstart STsize mul moveto cntsubTick +tickend STsize mul lineto }{ exit } ifelse /cntsubTick cntsubTick +dsubT add def } repeat subTwidth SLW subTColor subLSstroke grestore +} if gsave cntTick tickstart moveto cntTick tickend lineto Twidth +SLW TColor LSstroke grestore } for } if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 1 0 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +0 113.811 0 -5.69089 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 1 dup 2 mod 0 eq true and exch 2 lt false and or { /viceversa +-5.69089 113.811 gt { true }{ false } ifelse def /epsilon 0.01 def +/minTickline -85.35825 def /maxTickline 85.35825 def /dT 3729359 +abs 65536 div viceversa { neg } if def /subTNo 1 def subTNo 0 gt { +/dsubT dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 4.0 /tickend +exch def /tickstart exch def /Twidth 0.4 def /subTwidth 0.2 def /STsize +0.75 def /TColor { 0 setgray } def /subTColor { 0.5 setgray } def +/MinValue { yStart } def /MaxValue { yEnd 1.5 2. CLW mul add 1.4 +mul viceversa { add epsilon sub } { sub epsilon add } ifelse } def +/logLines { false } def /LSstroke { 0 setlinecap stroke } def /subLSstroke +{ 0 setlinecap stroke } def 0 dT MaxValue { /cntTick exch def logLines +{ gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul +add def x abs MaxValue abs le { x minTickline exch moveto x maxTickline +exch lineto } if } for subTwidth SLW subTColor subLSstroke grestore +stroke /dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick +dsubT add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul exch moveto cntsubTick tickend STsize mul exch +lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat +subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick tickstart +exch moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke +grestore } for /dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon +viceversa { add }{ sub } ifelse { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MinValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for /dsubT 0 def subTwidth SLW subTColor subLSstroke +grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def +subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick tickstart +STsize mul exch moveto cntsubTick tickend STsize mul exch lineto }{ +exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart exch +moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke grestore +} for } if end + +@endspecial 756 +-236 a + tx@Dict begin { -56.9055 -14.22636 } PutCoor PutBegin end + 756 -236 a 704 -215 a Fb(\000)p Fa(e)756 -236 +y + tx@Dict begin PutEnd end + 756 -236 a 756 -236 a + tx@Dict begin { 56.9055 -14.22636 } PutCoor PutBegin end + 756 -236 a 737 -218 a Fa(e)756 +-236 y + tx@Dict begin PutEnd end + 756 -236 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.2 SLW 0 0 1 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ -56.9055 85.35825 -56.9055 0.0 /Lineto +/lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } +if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg +add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 0 1 setrgbcolor [ 5.0 + 3.0 ] 0 0 add dup 0 gt { /a .5 def PathLength exch div } { pop /a +1 def PathLength } ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} +forall def b a .5 sub 2 mul y mul sub z Div round z mul a .5 sub 2 +mul y mul add b exch Div /z ED false X { z mul } forall X astore {0 +gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke + grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.2 SLW 0 0 1 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 56.9055 85.35825 -56.9055 85.35825 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 +mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED +/Alpha y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos arrowlength +mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 0 1 setrgbcolor [ 5.0 + 3.0 ] 0 0 add dup 0 gt { /a .5 def PathLength exch div } { pop /a +1 def PathLength } ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} +forall def b a .5 sub 2 mul y mul sub z Div round z mul a .5 sub 2 +mul y mul add b exch Div /z ED false X { z mul } forall X astore {0 +gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke + grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.2 SLW 0 0 1 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 56.9055 0.0 56.9055 85.35825 /Lineto +/lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } +if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg +add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 0 1 setrgbcolor [ 5.0 + 3.0 ] 0 0 add dup 0 gt { /a .5 def PathLength exch div } { pop /a +1 def PathLength } ifelse /b ED dup /X ED 0 get /y ED /z 0 X {add} +forall def b a .5 sub 2 mul y mul sub z Div round z mul a .5 sub 2 +mul y mul add b exch Div /z ED false X { z mul } forall X astore {0 +gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke + grestore end + +@endspecial 756 -236 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 56.9055 div 2.0 div +def 62.59639 0.0 /YA exch 56.9055 div def /XA exch 56.9055 div def +62.59639 85.35825 /YB exch 56.9055 div def /XB exch 56.9055 div def +/Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul XA add +def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 mul def +/@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add def /@yTemp +yMid @deltaY 2 mul sub def @xTemp @yTemp 56.9055 mul exch 56.9055 mul +exch } false /N@@tempNode 10 {InitPnode } NewNode end end + 756 -236 a 756 -236 +a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if /rotAngle exch +def end + 756 -236 a 756 -236 a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 5.0 add 56.9055 div Yc 0.0 add 56.9055 div 56.9055 mul +exch 56.9055 mul exch } PutCoor PutBegin end + 756 -236 a 756 -236 a + tx@Dict begin rotAngle RotBegin end + 756 -236 +a 28 x Fa(H)756 -236 y + tx@Dict begin RotEnd end + 756 -236 a 756 -236 a + tx@Dict begin PutEnd end + 756 -236 +a @beginspecial @setspecial + tx@Dict begin STP newpath 0.2 SLW 1 0.5 0 setrgbcolor /ArrowA { +moveto } def /ArrowB { } def /ArrowInside { } def 0.2 SLW 1 0.5 0 + setrgbcolor /ArrowA { moveto } def /ArrowB { } def /ArrowInside { +} def [ tx@NodeDict begin tx@NodeDict /N@@tempNode known { /N@@tempNode +load GetCenter } { 0 0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY +add 56.9055 mul exch 56.9055 mul exch XA @deltaX add YA @deltaY sub +56.9055 mul exch 56.9055 mul exch 62.59639 0.0 /r 5.69054 def /Lineto +{ Arcto } def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if +() length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg +add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha +y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos arrowlength mul add +y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1 +ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub atan +def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def /dArrowPos +0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos Length +gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.2 SLW 1 0.5 0 setrgbcolor 0 +setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.2 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 62.59639 85.35825 XB @deltaX add YB +@deltaY sub 56.9055 mul exch 56.9055 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 56.9055 mul exch 56.9055 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 + mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.8 SLW 1 0.5 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def 0.0 85.35825 /y ED /x ED /r 56.90549 +def /c 57.2957 r Div def /angleA 180. 0.0 c mul 2 div add def /angleB +360. 0.0 c mul 2 div sub def x y r angleA angleB arc gsave 0.8 SLW +1 0.5 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial 756 -236 a + tx@Dict begin tx@NodeDict begin {/bW2 9.95863 56.9055 div 2.0 div +def 2.84544 28.45274 /YA exch 56.9055 div def /XA exch 56.9055 div +def 2.84544 85.35825 /YB exch 56.9055 div def /XB exch 56.9055 div +def /Alpha YB YA sub XB XA sub atan def /xMid XB XA sub 0.5 mul XA +add def /yMid YB YA sub 0.5 mul YA add def /@deltaX Alpha sin bW2 mul +def /@deltaY Alpha cos bW2 mul def /@xTemp xMid @deltaX 2 mul add def +/@yTemp yMid @deltaY 2 mul sub def @xTemp @yTemp 56.9055 mul exch 56.9055 +mul exch } false /N@@tempNode 10 {InitPnode } NewNode end end + 756 +-236 a 756 -236 a + tx@Dict begin Alpha 90 sub 9.95863 0 lt {180 add} if /rotAngle exch +def end + 756 -236 a 756 -236 a + tx@Dict begin { tx@NodeDict begin tx@NodeDict /N@@tempNode known +{ /N@@tempNode load GetCenter } { 0 0 } ifelse end /Yc exch def /Xc +exch def Xc 5.0 add 56.9055 div Yc 0.0 add 56.9055 div 56.9055 mul +exch 56.9055 mul exch } PutCoor PutBegin end + 756 -236 a 756 +-236 a + tx@Dict begin rotAngle RotBegin end + 756 -236 a 29 x Fa(h)756 -236 y + tx@Dict begin RotEnd end + 756 -236 a 756 +-236 a + tx@Dict begin PutEnd end + 756 -236 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.2 SLW 0 1 0 setrgbcolor /ArrowA { moveto +} def /ArrowB { } def /ArrowInside { } def 0.2 SLW 0 1 0 setrgbcolor + /ArrowA { moveto } def /ArrowB { } def /ArrowInside { } def [ tx@NodeDict +begin tx@NodeDict /N@@tempNode known { /N@@tempNode load GetCenter +} { 0 0 } ifelse end @xTemp @deltaX sub @yTemp @deltaY add 56.9055 +mul exch 56.9055 mul exch XA @deltaX add YA @deltaY sub 56.9055 mul +exch 56.9055 mul exch 2.84544 28.45274 /r 5.69054 def /Lineto { Arcto +} def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add /arrowlength +exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 +sub atan def ArrowA x1 Alpha cos arrowlength mul add y1 Alpha sin arrowlength +mul add /n n 1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 +0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length +x2 x1 sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 1 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.2 SLW 0 1 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 2.84544 85.35825 XB @deltaX add YB +@deltaY sub 56.9055 mul exch 56.9055 mul exch @xTemp @deltaX sub @yTemp +@deltaY add 56.9055 mul exch 56.9055 mul exch tx@NodeDict begin tx@NodeDict +/N@@tempNode known { /N@@tempNode load GetCenter } { 0 0 } ifelse end + /r 5.69054 def /Lineto { Arcto } def false NArray n 0 eq not { n 1 +eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 + mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED +/y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub atan def ArrowA x1 Alpha cos +arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW +0 1 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath end + +@endspecial 756 -236 a + tx@Dict begin { 85.35825 -5.69089 } PutCoor PutBegin end + 756 -236 a 732 -218 +a Fa(x)756 -236 y + tx@Dict begin PutEnd end + 756 -236 a 756 -236 a + tx@Dict begin { -11.38092 102.43007 } PutCoor PutBegin end + 756 -236 a 734 +-226 a Fa(y)756 -236 y + tx@Dict begin PutEnd end + 756 -236 a eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/2dgrafiken/Aufgabe122.pst b/2dgrafiken/Aufgabe122.pst new file mode 100644 index 0000000..8c660d6 --- /dev/null +++ b/2dgrafiken/Aufgabe122.pst @@ -0,0 +1,29 @@ +\psset{xunit=2cm, yunit=2cm} +%\psframebox{ +\begin{pspicture}(-1.6,-0.5)(1.6,2) +%\psgrid[%griddots=20, +%gridlabels=0pt, subgriddiv=10](-1.6,-0.5)(1.6,2) +\psset{plotpoints=200} +\psaxes[linecolor=red,%ticks=none, +ticks=x, +labels=none +]{->}(0,0)(-1.5,-0.1)(1.5,2) %Mittelpunkt (linke Seite x,y 3/4 Quad) (rechte Seite x,y) + +\rput[c](-1,-0.25){$-e$} +\rput[c](1,-0.25){$e$} 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p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +%! +% PostScript prologue for pstricks.tex. +% Version 1.00, 2005/09/18 +% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.08, 2006/06/17 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2006/06/17 : - changes to the code (hv) +% 2006/04/21 : - Improved parser -> generic with derivative and translator into ps (dr) +% 2006/01/16 : - EXP -> Exp to prevent missmatch with pst-math (hv) +% 2005/09/28 : - rename it to pstricks-add.pro +% - add support for Gouraud shading (hv) +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression (dr) +% 2004/12/16 : addition of Sum and IfTE (dr) +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +% +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { tx@AlgToPs begin AlgToPs end } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end%%%tx@CoreAnalyzerDict +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat } + { tutu 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (ln\() StrConcat 8 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if 90 div 1.57079632680 mul +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan 90 div 1.57079632680 mul +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if 90 div 1.57079632680 mul } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { 2.71828182846 exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +/PI 3.14159265358 def +end +% END pstricks-add.pro + + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. 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{ ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath 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copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 6 2007-12-29 21:41:43Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get +neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr +1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr +2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 +-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S +TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ +Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale +}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState +save N userdict maxlength dict begin/magscale true def normalscale +currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts +/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x +psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx +psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub +TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict +begin/SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ +CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N +/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} +repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N +/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX +currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +dup 51 /three put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 2 /multiply put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. 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grestore grestore end + +24 -24 a eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/2dgrafiken/Kreuzprodukt.pdf b/2dgrafiken/Kreuzprodukt.pdf new file mode 100644 index 0000000..b9dd4ac Binary files /dev/null and b/2dgrafiken/Kreuzprodukt.pdf differ diff --git a/2dgrafiken/Kreuzprodukt.pst b/2dgrafiken/Kreuzprodukt.pst new file mode 100644 index 0000000..925a005 --- /dev/null +++ b/2dgrafiken/Kreuzprodukt.pst @@ -0,0 +1,14 @@ +\begin{pspicture}(-0.1,-0.1)(7.5,1.85) + +%\psgrid(0,0)(7.5, 2) + +\rput[l](0.5,1.6){$\vec a \rnode{a}\times \vec b = \left( {a_2 b_3 - a_3 b_2 ,a_3 b_1 - a_1 b_3 ,a_1 b_2 - a_2 b_1 } \right)$} + + +\rput[l](0.5,0.6){"Kr\Rnode[e]{ae}euz"} +\rput[l](0.25,0.1){Kreuzprodukt} + +%\nccurve[angleA=0]{->}{ae}{a} +%\ncbar[nodesep=1pt]{->}{ae}{a} +\ncline[arrows=->,linecolor=red]{ae}{a} +\end{pspicture} diff --git a/2dgrafiken/LaengeVektorInEbene.eps b/2dgrafiken/LaengeVektorInEbene.eps new file mode 100644 index 0000000..c1f6844 --- /dev/null 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dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- 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L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx 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setcmykcolor}DC/LimeGreen{0.50 0 1 0 +setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ +0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} +DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 +setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 +setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 +setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 7{currentfile token not{stop}if 65781.76 div })) +pop + +userdict begin/bop-hook{preview-bop-level 0 le{7{currentfile token +not{stop}if 65781.76 div DVImag mul}repeat 72 add 72 2 copy gt{exch}if +4 2 roll neg 2 copy lt{exch}if dup 0 gt{pop 0 exch}{exch dup 0 lt{pop +0}if}ifelse 720 add exch 720 add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat +<>setpagedevice}if//bop-hook +exec}bind def end + +@fedspecial end +%%BeginFont: CMR8 +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 43 /plus put +readonly def +/FontBBox{-36 -250 1070 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR6 +%!PS-AdobeFont-1.1: CMR6 1.0 +%%CreationDate: 1991 Aug 20 16:39:02 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +readonly def +/FontBBox{-20 -250 1193 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI8 +%!PS-AdobeFont-1.1: CMMI8 1.100 +%%CreationDate: 1996 Jul 23 07:53:54 +% Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def +/FullName (CMMI8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 97 /a put +readonly def +/FontBBox{-24 -250 1110 750}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMEX10 +%!PS-AdobeFont-1.1: CMEX10 1.00 +%%CreationDate: 1992 Jul 23 21:22:48 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 113 /radicalBig put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D +E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 +47AEDE4191CCDB8B61345FD070FD30C4F375D8418DDD454729A251B3F61DAE7C +8882384282FDD6102AE8EEFEDE6447576AFA181F27A48216A9CAD730561469E4 +78B286F22328F2AE84EF183DE4119C402771A249AAC1FA5435690A28D1B47486 +1060C8000D3FE1BF45133CF847A24B4F8464A63CEA01EC84AA22FD005E74847E +01426B6890951A7DD1F50A5F3285E1F958F11FC7F00EE26FEE7C63998EA1328B +C9841C57C80946D2C2FC81346249A664ECFB08A2CE075036CEA7359FCA1E90C0 +F686C3BB27EEFA45D548F7BD074CE60E626A4F83C69FE93A5324133A78362F30 +8E8DCC80DD0C49E137CDC9AC08BAE39282E26A7A4D8C159B95F227BDA2A281AF +A9DAEBF31F504380B20812A211CF9FEB112EC29A3FB3BD3E81809FC6293487A7 +455EB3B879D2B4BD46942BB1243896264722CB59146C3F65BD59B96A74B12BB2 +9A1354AF174932210C6E19FE584B1B14C00E746089CBB17E68845D7B3EA05105 +EEE461E3697FCF835CBE6D46C75523478E766832751CF6D96EC338BDAD57D53B +52F5340FAC9FE0456AD13101824234B262AC0CABA43B62EBDA39795BAE6CFE97 +563A50AAE1F195888739F2676086A9811E5C9A4A7E0BF34F3E25568930ADF80F +0BDDAC3B634AD4BA6A59720EA4749236CF0F79ABA4716C340F98517F6F06D9AB +7ED8F46FC1868B5F3D3678DF71AA772CF1F7DD222C6BF19D8EF0CFB7A76FC6D1 +0AD323C176134907AB375F20CFCD667AB094E2C7CB2179C4283329C9E435E7A4 +1E042AD0BAA059B3F862236180B34D3FCED833472577BACD472A4CD5C7347D2E +1D0D6630F446F3708FCB29A85F40B4DAB4D60AA8F5B2DBD67F2E45D80C7A7E86 +144669F75F8FA14609F8E4246FEC475ED262E03D30393C78C7828206842B565A +DBE20EA52EE9C4C3862B2F5F12CF89D935B89B84A45CEFCEAEE8EC8806339364 +56FF1FE2E5112803E3E40162D5188D2210A54816AA9960611721C23A292AE80A +8F8C0FB114D71C111700B0FEA8804F37C5D31ECD7006603C53F4BDF7208286AF +3A25CEE58E88BF81A4800B68C2A19EBDADF9B1074702E779A7DD915EFE09D35E +BD176D7346D859D0944520171C4E97696AE0502C43C391FCE5E8FB1789065E18 +BE3AF62200D57912360411CE848B4550D1B0A3BA576F9B41CED3A23E753631A7 +25375ABE8A4B55BC65AE2EAFAE452766961965093084D218637FB447795CC991 +EB1EF26BF82B7A81FA847ABD3B559D35828AD7DDC5FC7B43C6C14E6ADEDD7663 +F272AA9A121630C5263D58773BCB1437EC2FC54C4AF90E677A8E7D1738D003D4 +18998C03CC9AE182E7758767FEB5E1B03C6CC32AD30D0ABAE6552290771E2CB1 +A23F469A8447C1868C6DEC2C3C2BCFC691867E +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +%%BeginFont: CMMI10 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 97 /a put +dup 120 /x put +dup 121 /y put +dup 126 /vector put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 +9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 +990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E +6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB +DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 +59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 +D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF +8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 +6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 +1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE +03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 +95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 +74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 +3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 +47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 +AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8 +42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8 +40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837 +B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53 +9560176671A33FC55340CD04C2DE46FD812FC2711A85F70616E4B2F7C0EFA18D +28C25F2510A63A3C55C2EEC5CAD04051CCE773EC997373A7B72E99B1C581B9D6 +F945B833780834A8A81AC913CD0390BE72A97E66AA9DBBCC4547C3E48FB55E97 +0FCD36A15C764735DCC35D6AFE72FA07AC862F705D3836DEFE836EBB286E0B5E +DB9AD3E936F8850A7A0726CE409780A458A3269A7647BF7D4F3A207F2228BD5E +856D37106F4FBAFB0BAE752A491EF3B250840A2CC66035A1E8DFB435F0525F3B +13C37EA9D2C9BDE25A0C0E03252CFFDFBBC06B239255218247AE43B1CAF3EA34 +7972BA332161355DF8EBA2F1315CDAC872EA06721730931CAEBBAA963BC9949B +F9E162156673618678B5F76DDAD4DD7970155F8BFE1C6609F6A2FF2147DB60C4 +89E435F5D9496BFD328A20B1CF794B0BA02D6C3289093FC68D635305FCB0E143 +DDB2E07B63E6F4D3A15EF00A0E411E7F85CC83697CB7F7DCB89CAAADD722CB49 +165F8F4674AEAA92CD18F51E463318438E59DA2A0108074544C7B724DCAB810B +B674927B5F4259D6C733E00F1946ECAD42AC01AFF42B94F8606DF64E20F88EAE +8F13E2680CE34EDF0EE029A78F22D62099E405C64D76648055B496CB417011EA +A3037B0FA8B91629E7A42B6D535E5966EB536A06481849493C239DF109AE296A +70E8A3DC7D426639895D96E5EE5C4AD5B2C32366A62D595A629BBF994D6F4F8C +9DFEC30866671E3966980F8CC98E40A8ACDAA599986064FAB145878A0B311DED +6A022B07E7678F0A05D260757D0FF361866AD230750A2604D28D02E01180BA4F +2C77DB23664952822EB1CD1A6A2CC70F6323C05DCCBCCD5E5819896D6A8B9B62 +12296FB1CECC0B9E4F09E50C39ACF97E0649A3B4A827C1A363C38288A0A54647 +39CAAD96469B2829FB7AF562421DCBEE4E4FE3FF73739E502A1957AB532B9935 +09BD85D21181A066BC46A913DA782B4F283CAAAF0008A068438C481003D91162 +7BB3128722E98304F512DA617F0D79BF19CBE85A338B6B98FD3477A70D8CC79C +061A2C930F08DE6483C1F85F93616BA460577ED9C4DC02813E3C2DEE1E08506B +F48BD0A79AB6F9A804941B03DB3F8BE763C1B5BD81D2AAD18D56DC75B639CB9A +1EBF6701AAD5E0D4B2A23A5F2D745827D67643D3D899924C49A91A4E134757A0 +3E9A40451A0DE5936E4234BEC5EC50B717D6CEC5561783E6A192F66D52FA729A +8738748A6F3A6131F873E7636862F4BEB924B0D437FF096BE7FC0EF7C78664B0 +37EE8D5B1C3CC3EB048F4BCA7B38909F5A07EB3C3B1FC0AF089ACE54C401DE47 +79B843C54991FA30EA1196D8076D109859CA6550DA8127A4878D85 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +dup 51 /three put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +99.5846 0 -5.69046 0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 0 dup 2 mod 0 eq false and exch 2 lt true and or { /viceversa +-5.69046 99.5846 gt { true }{ false } ifelse def /epsilon 0.01 def +/minTickline -5.69046 def /maxTickline 99.5846 def /dT 1864679 abs +65536 div viceversa { neg } if def /subTNo 1 def subTNo 0 gt { /dsubT +dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 4.0 /tickend exch def +/tickstart exch def /Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 +def /TColor { 0 setgray } def /subTColor { 0.5 setgray } def /MinValue +{ xStart } def /MaxValue { xEnd 1.5 2. CLW mul add 1.4 mul viceversa +{ add epsilon sub } { sub epsilon add } ifelse } def /logLines { false +} def /LSstroke { 0 setlinecap stroke stroke} def /subLSstroke { 0 +setlinecap stroke stroke} def 0 dT MaxValue { /cntTick exch def logLines +{ gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul +add def x abs MaxValue abs le { x minTickline moveto x maxTickline + lineto } if } for subTwidth SLW subTColor subLSstroke grestore stroke +/dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul moveto cntsubTick tickend STsize mul lineto +}{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart moveto +cntTick tickend lineto Twidth SLW TColor LSstroke grestore } for /dT +dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon viceversa { add +}{ sub } ifelse { /cntTick exch def logLines { gsave 1 10 subTNo div +9.99 { /dx exch def /x cntTick dT dx log mul add def x abs MinValue +abs le { x minTickline moveto x maxTickline lineto } if } for /dsubT +0 def subTwidth SLW subTColor subLSstroke grestore } dsubT abs 0 gt +{ gsave /cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick +abs MinValue abs le { cntsubTick tickstart STsize mul moveto cntsubTick +tickend STsize mul lineto }{ exit } ifelse /cntsubTick cntsubTick +dsubT add def } repeat subTwidth SLW subTColor subLSstroke grestore +} if gsave cntTick tickstart moveto cntTick tickend lineto Twidth +SLW TColor LSstroke grestore } for } if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.1 SLW 0 setgray /ArrowA { moveto } +def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +0 99.5846 0 -5.69046 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 0 dup 2 mod 0 eq true and exch 2 lt false and or { /viceversa +-5.69046 99.5846 gt { true }{ false } ifelse def /epsilon 0.01 def +/minTickline -5.69046 def /maxTickline 99.5846 def /dT 1864679 abs +65536 div viceversa { neg } if def /subTNo 1 def subTNo 0 gt { /dsubT +dT subTNo div def}{ /dsubT 0 def } ifelse -4.0 4.0 /tickend exch def +/tickstart exch def /Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 +def /TColor { 0 setgray } def /subTColor { 0.5 setgray } def /MinValue +{ yStart } def /MaxValue { yEnd 1.5 2. CLW mul add 1.4 mul viceversa +{ add epsilon sub } { sub epsilon add } ifelse } def /logLines { false +} def /LSstroke { 0 setlinecap stroke stroke} def /subLSstroke { 0 +setlinecap stroke stroke} def 0 dT MaxValue { /cntTick exch def logLines +{ gsave 1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul +add def x abs MaxValue abs le { x minTickline exch moveto x maxTickline +exch lineto } if } for subTwidth SLW subTColor subLSstroke grestore +stroke /dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick +dsubT add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul exch moveto cntsubTick tickend STsize mul exch +lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat +subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick tickstart +exch moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke +grestore } for /dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon +viceversa { add }{ sub } ifelse { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MinValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for /dsubT 0 def subTwidth SLW subTColor subLSstroke +grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def +subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick tickstart +STsize mul exch moveto cntsubTick tickend STsize mul exch lineto }{ +exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart exch +moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke grestore +} for } if end + +@endspecial 26 +-398 a Fh(1)26 -635 y(2)26 -871 y(3)357 -61 y(1)194 b(2)h(3)142 +-189 y + tx@Dict begin { 108.1205 0.0 } PutCoor PutBegin end + 142 -189 a 118 -171 a Fg(x)142 -189 y + tx@Dict begin PutEnd end + 142 -189 +a 142 -189 a + tx@Dict begin { 0.0 108.1205 } PutCoor PutBegin end + 142 -189 a 120 -179 a Fg(y)142 -189 y + tx@Dict begin PutEnd end + 142 +-189 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.5 SLW 0 0 1 setrgbcolor + /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 85.35823 85.35823 0.0 0.0 /Lineto /lineto load def false +0 setlinejoin NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 1.5 2. 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+% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +/pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def + x1 0 gt y1 0 gt x 0 gt y 0 gt and { [ y x y1 x1 ] 1 a sub y mul} + { [ 1 0] 0 } ifelse setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch +2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +% DG/SR modification end +Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def + n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop 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mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def 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dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y 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exch dup mul add sqrt } def % Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z 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2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.08, 2006/06/17 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2006/06/17 : - changes to the code (hv) +% 2006/04/21 : - Improved parser -> generic with derivative and translator into ps (dr) +% 2006/01/16 : - EXP -> Exp to prevent missmatch with pst-math (hv) +% 2005/09/28 : - rename it to pstricks-add.pro +% - add support for Gouraud shading (hv) +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression (dr) +% 2004/12/16 : addition of Sum and IfTE (dr) +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +% +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { tx@AlgToPs begin AlgToPs end } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end%%%tx@CoreAnalyzerDict +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat } + { tutu 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (ln\() StrConcat 8 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub 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scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: alt-rule.pro 0 0 +%! +% Patch by TVZ +% Makes dvips files draw rules with stroke rather than fill. +% Makes narrow rules more predictable at low resolutions +% after distilling to PDF. +% May have unknown consequences for very thick rules. +% Tested only with dvips 5.85(k). +TeXDict begin +/QV { + gsave newpath /ruleY X /ruleX X + Rx Ry gt + { ruleX ruleY Ry 2 div sub moveto Rx 0 rlineto Ry } + { ruleX Rx 2 div add ruleY moveto 0 Ry neg rlineto Rx } + ifelse + setlinewidth 0 setlinecap stroke grestore +} bind def +end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +%! +% PostScript prologue for pstricks.tex. +% Version 1.00, 2005/09/18 +% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.01, 2005/09/27 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2005/09/28 : - rename it to pstricks-add.pro +% - agg support for Gouraud shading +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression +% 2004/12/16 : addition of SUM and IFTE +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { InitParser SetExpr LexStr 0 exch AnalyzeListOfE ExpressionVector /ExpressionVector [] def} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/SetExpr { RemoveWS /ExpressionString exch def } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/InitParser { + /ExpressionVector [] def /AddVector [] def + /AddVectorfree [] def /MulVector [] def + /MulVectorfree [] def /PowVector [] def + /PowVectorfree [] def /OpParVector [] def + /ClParVector [] def /ParVectorFree [] def + %%/CompVector [] def /CompVectorFree [] def + /BraVector [] def /SemVector [] def + /ComVector [] def /ExpressionVector [] def + /LoopLevel -1 def /LoopContext [] def %%% NEW for SUM function +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/FLbreak { tst not {/L exch def /F exch def 2 copy L eq exch F eq and /tst exch def} {pop pop} ifelse} def +/Negbreak { tst not { dup 0 lt /tst exch def } if } def +/STOP { tst {TOUF} if} def +/tst false def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List +%% first last +/AnalyzeListOfE { + exch SemVector { + exch 1 index 1 sub AnalyzeExpr 1 add + } forall%%last_char + exch AnalyzeExpr +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expr +%% first last +/AnalyzeExpr { + FindFirstAdd%% first last pos+ + 2 copy abs 1 sub ne + { 3 -1 roll 1 index abs 1 sub AnalyzeExpr dup abs 1 add 3 -1 roll AnalyzeTerm EvalAdd } + { pop AnalyzeTerm } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Term +%% first last +/AnalyzeTerm {%%19 28 FLbreak STOP + FindFirstMul%% first last pos* + 2 copy abs 1 sub ne + { 3 -1 roll 1 index abs 1 sub AnalyzeTerm dup abs 1 add 3 -1 roll AnalyzeSignedFactor EvalMul }%%% NEW 2004/11/14 + { pop AnalyzeSignedFactor } ifelse%%% NEW 2004/11/14 +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NEW 2004/11/14 +%% analyze Signed Factor +%% first last -> +/AnalyzeSignedFactor { + ExpressionString 2 index get + dup 45 eq%% a - sign + { pop exch 1 add exch AnalyzeSignedFactor EvalNeg } + { 43 eq%%a + sign + { exch 1 add exch AnalyzeSignedFactor } + { AnalyzeFactor } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Factor +%% first last -> +/AnalyzeFactor { + FindFirstPow%% first last pos* + 2 copy abs 1 sub ne +% { 3 -1 roll 1 index abs 1 sub AnalyzeFactor dup abs 1 add 3 -1 roll AnalyzePower EvalPow } + { 3 -1 roll 1 index abs 1 sub AnalyzeFactor dup abs 1 add 3 -1 roll AnalyzeSignedFactor EvalPow }% NEW 2004/11/14 + { pop AnalyzePower } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Power +%% first last -> +/compteur 0 def +/AnalyzePower { + ExpressionString 2 index get + dup 40 eq%% an open parenthesis + { pop 1 index UnfreePar 1 sub exch 1 add exch AnalyzeExpr } + { dup 45 eq%% a - sign + { pop exch 1 add exch AnalyzePower EvalNeg } + { dup 43 eq%%a + sign + { pop exch 1 add exch AnalyzePower } + { dup 46 eq 1 index 48 ge 2 index 57 le and or%%a digit or a dot + { pop AnalyzeNumber } + { pop AnalyzeLiteral } ifelse } ifelse } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze parameters list +%% first last +/AnalyzeParam { + { FindFirstCom%% first last pos, + 3 -1 roll 1 index 1 sub AnalyzeExpr + 2 copy 1 sub ne { 1 add exch } { pop pop exit } ifelse + } loop +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual addition at this level +%% first last -> position +/FindFirstAdd { + 2 copy /Last exch def /First exch def false 0 + AddVector { + AddVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos abs First gt pos abs Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeAdd} %% find one mul + { Last 1 add } ifelse +} def +%% { +%% 2 copy /Last exch def /First exch def false 0 +%% AddVector { +%% AddVectorFree 2 index get +%% { /pos exch def +%% true 0 1 ClParVector length 1 sub +%% { ParVectorFree 1 index get +%% { OpParVector 1 index get pos abs le +%% ClParVector 2 index get pos abs ge and +%% pos abs First lt pos abs Last gt or or +%% { pop pop false exit } if +%% } if +%% pop +%% } for +%% { pop pop true dup exit } if +%% } +%% { pop } ifelse +%% 1 add +%% } forall +%% pop +%% { pos UnfreeAdd}%% find one add +%% { Last 1 add } ifelse +%% } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual multiplication at this level +%% first last -> first last position +/FindFirstMul { + 2 copy /Last exch def /First exch def false 0 + MulVector { + MulVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos abs First gt pos abs Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeMul} %% find one mul + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual power at this level +%% first last -> first last position +/FindFirstPow { + 2 copy /Last exch def /First exch def false 0 + PowVector { + PowVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos First gt pos Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesis + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreePow} %% find one ^ + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the eventual comma at this level +%% first last -> first last position +/FindFirstCom { + 2 copy /Last exch def /First exch def false 0 + ComVector { + ComVectorFree 2 index get + { /pos exch def + %% if it is in the current part of the analysed expr + pos First gt pos Last lt and + { true 0 1 ClParVector length + dup 0 eq%% no parenthesisSTOP + { pop pop pop pop exch not exch exit } + { 1 sub + { ParVectorFree 1 index get + { OpParVector 1 index get pos abs lt%% in this parenthesis level + ClParVector 2 index get pos abs gt and + { pop pop false exit } if%%then exit loop + } if + pop } for + { pop pop true dup exit } if } ifelse } if + } { pop } ifelse + 1 add + } forall + pop + { pos UnfreeCom} %% find one comma + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the first opened parenthesis (only for func call) +%% first last -> first last position +/FindFirstPar { + 2 copy /Last exch def /First exch def false 0 + OpParVector { + ParVectorFree 2 index get + { /pos exch def + pos First gt pos Last lt and + { exch not exch exit } if + } { pop } ifelse + 1 add + } forall + pop + { pos dup UnfreePar }%% find one par + { Last 1 add } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Find the first opening bracket +%% first last -> first last position +/FindFirstBra { + 2 copy /Last exch def /First exch def + BraVector { + /pos exch def + pos First gt pos Last lt and + { exit } if + } forall + pos dup UnfreePar%% finding it is mandatory +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Read the number and push it in the vector +%% first last -> +/AnalyzeNumber { + 1 index sub 1 add ExpressionString 3 1 roll getinterval cvr /n exch def + /ExpressionVector ExpressionVector aload length n exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Read the literal and push it in the vector +%% first last -> +/AnalyzeLiteral { + ExpressionString 1 index get dup 41 eq %%close par at the end => function call + { pop FindFirstPar%%first last parpos + ExpressionString 3 index dup 3 index exch sub getinterval + dup (SUM) eq { sumation } + { dup (IFTE) eq { condition } + { 1 index 1 add 3 index 1 sub AnalyzeParam + dup cvn /n exch def TrigoFunc + /ExpressionVector ExpressionVector aload length + /tx@addDict cvx /begin cvx n cvx /end cvx 5 -1 roll 4 add array astore def + %%n cvx exch 1 add array astore def + pop pop pop } ifelse } ifelse } + { 93 eq%%close bracket => vector element + { FindFirstBra%%first last brapos + ExpressionString 3 index dup 3 index exch sub getinterval cvn /n exch def + /ExpressionVector ExpressionVector aload length n cvx exch 1 add array astore def + 2 copy 1 add exch 1 sub AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def + pop pop pop + } + { 1 index sub 1 add ExpressionString 3 1 roll getinterval cvn /n exch def + /ExpressionVector ExpressionVector aload length n cvx exch 1 add array astore def } ifelse } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push add in the vector +%% kind -> +%% if kind>0 then add else sub +/EvalAdd { + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll + 0 gt { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push mul in the vector +%% -> +/EvalMul { + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll + 0 gt { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push exp in the vector +%% -> +/EvalPow { + pop /ExpressionVector ExpressionVector aload length + /tx@addDict cvx exch /begin cvx exch /EXP cvx exch /end cvx exch 4 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% push neg in the vector +%% -> +/EvalNeg { + /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Lexical Analyzis of the string +%% -> +/LexStr { + /freepar 0 def /lastpar 0 def /lastchar 0 def + 0 ExpressionString + { dup 40 eq 1 index 91 eq or %% open parenthesis + { /OpParVector OpParVector aload length dup 3 add index exch 1 add array astore def + /ClParVector ClParVector aload length -1 exch 1 add array astore def + /lastpar freepar def /freepar freepar 1 add def /NoPar false def} if + dup 41 eq 1 index 93 eq or %% close parenthesis + { ClParVector lastpar 3 index put lastpar + dup 0 eq + { pop } + { { 1 sub dup ClParVector exch get -1 eq { /lastpar exch def exit } { dup 0 eq { pop exit} if } ifelse } loop } + ifelse } if + dup 42 eq %% * operator + %%{ /MulVector MulVector aload length dup 3 add index exch 1 add array astore def } if + { /MulVector 2 index MulVector aload length 1 add array astore def } if + dup 43 eq %% + operator + { %%test if it is a real operator and not the unary operator + lastchar dup 40 ne %% open parenthesis + 1 index 59 ne and %% ; + 1 index 42 ne and %% * + 1 index 43 ne and %% + + 1 index 44 ne and %% , + 1 index 45 ne and %% - + 1 index 47 ne and %% / + 1 index 0 ne and %% first char + 1 index 94 ne and %% ^%%2004/11/14 + exch 124 ne and %% | + %%{/AddVector AddVector aload length dup 3 add index exch 1 add array astore def } if} + {/AddVector 2 index AddVector aload length 1 add array astore def } if} + if + dup 44 eq %% , separator + { /ComVector ComVector aload length dup 3 add index exch 1 add array astore def } + if + dup 45 eq %% - operator + { %%test if it is a real operator and not the unary operator + lastchar dup 40 ne %% open parenthesis + 1 index 59 ne and %% ; + 1 index 42 ne and %% * + 1 index 43 ne and %% + + 1 index 44 ne and %% , + 1 index 45 ne and %% - + 1 index 47 ne and %% / + 1 index 0 ne and %% first char + 1 index 94 ne and %% ^%%2004/11/14 + exch 124 ne and %% | + %%{/AddVector AddVector aload length dup 3 add index neg exch 1 add array astore def } if} + {/AddVector 2 index neg AddVector aload length 1 add array astore def } if} + if + dup 47 eq %% / operator + %%{ /MulVector MulVector aload length dup 3 add index neg exch 1 add array astore def } + { /MulVector 2 index neg MulVector aload length 1 add array astore def } + if + dup 59 eq 1 index 124 eq or%% ; separator | + { /SemVector SemVector aload length dup 3 add index exch 1 add array astore def } + if + dup 91 eq %% open bracket + { /BraVector BraVector aload length dup 3 add index exch 1 add array astore def } + if + dup 94 eq %% ^ operator + %%{ /PowVector PowVector aload length dup 3 add index exch 1 add array astore def } + { /PowVector 2 index PowVector aload length 1 add array astore def }%%2004/11/14 + if + /lastchar exch def 1 add + } forall + /AddVectorFree AddVector CreateFree def + /MulVectorFree MulVector CreateFree def + /ParVectorFree OpParVector CreateFree def + /PowVectorFree PowVector CreateFree def + /ComVectorFree ComVector CreateFree def + 1 sub +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Create Free vector +%% -> +/CreateFree { + dup length array exch + { pop true exch } forall astore +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree parenthesis +%% pos -> +/UnfreePar { + /pos exch def ParVectorFree 0 + OpParVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree mul +%% pos -> +/UnfreeMul { + MulVectorFree 0 + MulVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree add +%% pos -> +/UnfreeAdd { + AddVectorFree 0 + AddVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree exp +%% pos -> +/UnfreePow { + PowVectorFree 0 + PowVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Unfree com +%% pos -> +/UnfreeCom { + ComVectorFree 0 + ComVector { pos eq { exit } if 1 add } forall + false put +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the condition function +%% -> +/condition { + %% manage the condition + 1 index 1 add 3 index 1 sub FindFirstCom + %% find the test char <,>,=,! + 4 index 1 index 1 sub FindTestChar + 4 index 2 index 1 sub AnalyzeExpr 3 1 roll + 1 add 1 index 1 sub AnalyzeExpr exch + /ExpressionVector ExpressionVector aload length dup 1 add array exch 3 add -1 roll cvx exch astore def + %% manage the then clause + MngClause + %% manage the else clause + MngClause + /ExpressionVector ExpressionVector aload length 1 add /ifelse cvx exch array astore def + mark 8 1 roll cleartomark +} def +/FindTestChar { + 1 exch + { dup ExpressionString exch get + dup 60 eq { pop /lt exit } if%%< + dup 61 eq { pop /eq exit } if%%= + dup 62 eq { pop /gt exit } if%%> + pop pop } for +} def +/MngClause { + 3 1 roll FindFirstCom 4 -1 roll 1 add 1 index 1 sub + /ExpressionVector ExpressionVector exch [] def 3 1 roll AnalyzeExpr + /ExpressionVector exch aload length 1 add ExpressionVector cvx exch array astore def +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the sumation function +%% -> +/sumation { + /LoopLevel LoopLevel 1 add def + %% create the accumulator + /ExpressionVector ExpressionVector aload length 1 add 0 exch array astore def + %% read the variable name + 1 index 1 add 3 index 1 sub FindFirstCom + ExpressionString 4 -1 roll 2 index 1 index sub getinterval cvn + /tempvar exch def + %% read the initial value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + %% read the increment value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + %% read the limit value + GetNextNumber + /ExpressionVector ExpressionVector aload length 1 add temp exch array astore def + /LoopContext LoopContext aload length 1 add ExpressionVector exch array astore def + /ExpressionVector [ tempvar /exch cvx /def cvx ] def + 1 add exch AnalyzeExpr + %% add each term of the sum + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector LoopContext LoopLevel get aload length 2 add + ExpressionVector cvx exch /for cvx exch array astore def pop pop pop pop } def +/GetNextNumber { + exch FindFirstCom ExpressionString 4 -1 roll 1 add 2 index 1 index sub getinterval cvi + /temp exch def } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% METHODS FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% MISC FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/RemoveWS {% + dup length + 0 2 index { 32 ne { 1 add } if } forall + 2 copy ne + { exch pop string 0 2 index + { dup 32 ne { 2 index 2 index 3 -1 roll put 1 add } { pop } ifelse } forall + pop exch pop } { pop pop } ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Make a discrete sum +%% var n begin end expr -> +/SUM {} def +%% function arcsine in radians +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup abs 1 eq + { PIdiv2 exch -1 eq { neg } if } + { .1 %% asin(x) + { dup dup PI div 180 mul sin 3 index sub exch PI div 180 mul cos div + dup abs 1e-6 lt { sub exit } if sub + } loop + exch pop } ifelse +} def +%% function arccosine in radians +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup abs 1 eq + { -1 eq { PI } { 0 } ifelse } + { 1.5 %% asin(x) + { dup dup PI div 180 mul cos 3 index sub exch PI div 180 mul sin neg div + dup abs 1e-6 lt { sub exit } if sub + } loop + exch pop } ifelse +} def +%% factorial function +%% n -> n! +/fact { 1 exch 2 exch 1 exch { mul } for } def + +%end + +%% modified exponential funtion for 0 +%% x n -> x^n +/EXP { dup 0 eq { pop pop 1 } { exp } ifelse } def +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /xA ED /yA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end + +% END pst-eqdf.pro + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne 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+CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N +/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} +repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N +/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX +currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.81)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 40 /parenleft put +dup 41 /parenright put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 52 /four put +dup 80 /P put +dup 107 /k put +dup 110 /n put +dup 116 /t put +dup 117 /u put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +/UniqueID 5000793 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 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CLW mul add +dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave +w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +128.03734 0 0.0 0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 0 dup 2 mod 0 eq false and exch 2 lt true and or { /viceversa +0.0 128.03734 gt { true }{ false } ifelse def /epsilon 0.01 def /minTickline +0.0 def /maxTickline 128.03734 def /dT 3729358 65536 div viceversa +{neg} if def /subTNo 1 def subTNo 0 gt { /dsubT dT subTNo div def}{ +/dsubT 0 def } ifelse -4.0 4.0 /tickend exch def /tickstart exch def +/Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 def /TColor { 0 +setgray } def /subTColor { 0.5 setgray } def /MinValue { xStart +} def /MaxValue { xEnd 1.5 2. CLW mul add 1.4 mul viceversa { add +epsilon sub } { sub epsilon add } ifelse } def /logLines { false } +def /LSstroke { 0 setlinecap stroke } def /subLSstroke { 0 setlinecap +stroke } def 0 dT MaxValue { /cntTick exch def logLines { gsave 1 10 +subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def x abs +MaxValue abs le { x minTickline moveto x maxTickline lineto } if +} for subTwidth SLW subTColor subLSstroke grestore stroke /dsubT 0 +def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def subTNo +1 sub { cntsubTick abs MaxValue abs le { cntsubTick tickstart STsize +mul moveto cntsubTick tickend STsize mul lineto }{ exit } ifelse +/cntsubTick cntsubTick dsubT add def } repeat subTwidth SLW subTColor +subLSstroke grestore } if gsave cntTick tickstart moveto cntTick tickend + lineto Twidth SLW TColor LSstroke grestore } for /dT dT neg def /dsubT +dsubT neg def 0 dT MinValue epsilon viceversa { add }{ sub } ifelse +{ /cntTick exch def logLines { gsave 1 10 subTNo div 9.99 { /dx exch +def /x cntTick dT dx log mul add def x abs MinValue abs le { x minTickline + moveto x maxTickline lineto } if } for /dsubT 0 def subTwidth SLW +subTColor subLSstroke grestore } dsubT abs 0 gt { gsave /cntsubTick +cntTick dsubT add def subTNo 1 sub { cntsubTick abs MinValue abs le +{ cntsubTick tickstart STsize mul moveto cntsubTick tickend STsize +mul lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } +repeat subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick +tickstart moveto cntTick tickend lineto Twidth SLW TColor LSstroke +grestore } for } if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.1 SLW 0 setgray /ArrowA { moveto } def +/ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW mul add +dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave +w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +0 128.03734 0 0.0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 0 dup 2 mod 0 eq true and exch 2 lt false and or { /viceversa +0.0 128.03734 gt { true }{ false } ifelse def /epsilon 0.01 def /minTickline +0.0 def /maxTickline 128.03734 def /dT 3729358 65536 div viceversa +{neg} if def /subTNo 1 def subTNo 0 gt { /dsubT dT subTNo div def}{ +/dsubT 0 def } ifelse -4.0 4.0 /tickend exch def /tickstart exch def +/Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 def /TColor { 0 +setgray } def /subTColor { 0.5 setgray } def /MinValue { yStart +} def /MaxValue { yEnd 1.5 2. CLW mul add 1.4 mul viceversa { add +epsilon sub } { sub epsilon add } ifelse } def /logLines { false } +def /LSstroke { 0 setlinecap stroke } def /subLSstroke { 0 setlinecap +stroke } def 0 dT MaxValue { /cntTick exch def logLines { gsave 1 +10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MaxValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for subTwidth SLW subTColor subLSstroke grestore stroke +/dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul exch moveto cntsubTick tickend STsize mul exch +lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat +subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick tickstart +exch moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke +grestore } for /dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon +viceversa { add }{ sub } ifelse { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MinValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for /dsubT 0 def subTwidth SLW subTColor subLSstroke +grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def +subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick tickstart +STsize mul exch moveto cntsubTick tickend STsize mul exch lineto }{ +exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart exch +moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke grestore +} for } if end + +@endspecial 1600 +-2793 a Fc(0)1600 -9092 y(2)1600 -15391 y(4)2873 -1440 +y(0)5746 b(2)g(4)3150 -3150 y + tx@Dict begin { 48.36957 -22.76227 } PutCoor PutBegin end + 3150 -3150 a 385 x Fc(1)p +Fb(:)370 b(K)79 b(oor)31 b(dinate)3150 -3150 y + tx@Dict begin PutEnd end + 3150 -3150 +a 3150 -3150 a + tx@Dict begin { 136.57324 0.0 } PutCoor PutBegin end + 3150 -3150 a 2834 -2911 a Fb(x)3150 -3150 +y + tx@Dict begin PutEnd end + 3150 -3150 a 3150 -3150 a + tx@Dict begin { 11.38092 113.81097 } PutCoor PutBegin end + 3150 -3150 a 385 x Fc(2)p +Fb(:)370 b(K)79 b(oor)31 b(dinate)3150 -3150 y + tx@Dict begin PutEnd end + 3150 -3150 +a 3150 -3150 a + tx@Dict begin { 0.0 136.57324 } PutCoor PutBegin end + 3150 -3150 a 2859 -3019 a Fb(y)3150 -3150 +y + tx@Dict begin PutEnd end + 3150 -3150 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.1 SLW 1 0 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 85.35823 85.35823 0.0 0.0 /Lineto +/lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } +if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def +n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 +y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 +sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos +add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos mul add +y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ /ArrowPos +0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. + cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul +x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } +ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +1 0 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial +3150 -3150 a + tx@Dict begin { 85.35823 -8.5359 } PutCoor PutBegin end + 3150 -3150 a 2609 -2995 a Fb(a)3194 -2829 +y Fa(1)3150 -3150 y + tx@Dict begin PutEnd end + 3150 -3150 a 3150 -3150 a + tx@Dict begin { -8.5359 85.35823 } PutCoor PutBegin end + 3150 -3150 +a 2609 -2995 a Fb(a)3194 -2829 y Fa(2)3150 -3150 y + tx@Dict begin PutEnd end + 3150 +-3150 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 85.35823 85.35823 85.35823 -5.69046 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 0 1 setrgbcolor [ 5.0 3.0 ] 0 0 add dup 0 gt { /a .5 def PathLength +exch div } { pop /a 1 def PathLength } ifelse /b ED dup /X ED 0 get +/y ED /z 0 X {add} forall def b a .5 sub 2 mul y mul sub z Div round +z mul a .5 sub 2 mul y mul add b exch Div /z ED false X { z mul } forall +X astore {0 gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse +setdash stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.1 SLW 0 0 1 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 85.35823 85.35823 -5.69046 85.35823 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.1 SLW +0 0 1 setrgbcolor [ 5.0 3.0 ] 0 0 add dup 0 gt { /a .5 def PathLength +exch div } { pop /a 1 def PathLength } ifelse /b ED dup /X ED 0 get +/y ED /z 0 X {add} forall def b a .5 sub 2 mul y mul sub z Div round +z mul a .5 sub 2 mul y mul add b exch Div /z ED false X { z mul } forall +X astore {0 gt or} forall { X 1 a sub y mul } { [ 1 0 ] 0 } ifelse +setdash stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul +dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 +0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub +moveto EndArrow } def /ArrowInside { } def 0.8 SLW 0 setgray +/ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 +1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 +h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto +gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside +{ } def [ 88.20367 82.51277 99.5846 71.13185 /Lineto /lineto load +def false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if () length +0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n 1 sub def n { 4 copy +/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 +sub atan def /ArrowPos 0. def /Length x2 x1 sub y2 y1 sub Pyth def +/dArrowPos 0.5 abs def { /ArrowPos ArrowPos dArrowPos add def ArrowPos +Length gt { exit } if x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos +mul add ArrowInside pop pop } loop }{ /ArrowPos 0. def /dArrowPos +1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos +ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub +ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto +} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4 +2 roll ArrowB L pop pop } if gsave 0.8 SLW 0 setgray 0 setlinecap +stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.8 SLW 0 1 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 88.20367 82.51277 82.51277 88.20367 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.8 SLW +0 1 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def /ArrowInside +{ } def 0.8 SLW 0 1 0 setrgbcolor /ArrowA { moveto } def /ArrowB +{ } def /ArrowInside { } def [ 88.20367 88.20367 82.51277 82.51277 + /Lineto /lineto load def false NArray n 0 eq not { n 1 eq { 0 0 /n +2 def } if () length 0 gt { 2 copy /y1 ED /x1 ED ArrowA x1 y1 /n n +1 sub def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { +/Alpha y2 y1 sub x2 x1 sub atan def /ArrowPos 0. def /Length x2 x1 +sub y2 y1 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos ArrowPos +dArrowPos add def ArrowPos Length gt { exit } if x1 Alpha cos ArrowPos +mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } loop }{ +/ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse +def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos +mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat +} ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto +} repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.8 SLW +0 1 0 setrgbcolor 0 setlinecap stroke grestore end + +@endspecial 3150 -3150 a + tx@Dict begin { 93.89413 65.44139 } PutCoor PutBegin end + 3150 -3150 a 385 +x Fc(Punkt)3150 -3150 y + tx@Dict begin PutEnd end + 3150 -3150 a 3150 -3150 a + tx@Dict begin { 91.04869 54.06003 } PutCoor PutBegin end + 3150 +-3150 a 277 x Fc(\()p Fb(a)4165 -2707 y Fa(1)4662 -2873 +y Fb(;)184 b(a)5738 -2707 y Fa(2)6236 -2873 y Fc(\))3150 +-3150 y + tx@Dict begin PutEnd end + 3150 -3150 a eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/2dgrafiken/VektorenInEbeneVeranschaulichung01.pdf 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/setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale CirclePath eofill + 45 rotate .775 .775 scale CrossPath fill} def + /BOtimes {CirclePath .8 .8 scale CirclePath eofill + 45 rotate .775 .775 scale BoldCrossPath fill } def + /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def + /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto + closepath} def + /Bar {BarPath fill} def + /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto + closepath} def + /BoldBar {BoldBarPath fill} def + /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath} def + /SolidDiamond {DiamondPath fill} def + /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def + /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def +%%% + /.notdef { } def + end + /BuildGlyph { + exch + begin +% Metrics 1 index get exec 0 + 0 0 +% BBoxes 3 index get exec + -1000 -1000 1000 1000 +% -571.5 -742.5 571.5 742.5 + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop + + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +% $Id: pst-node.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for pst-node.tex. +% Version 1.00, 2008/01/01. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin + /T /translate load def +end +/NewNode { % on stack: { x y } boolean N@name type InitXnode + gsave + /next ED % { x y } boolean N@name type + dict dup % { x y } boolean N@name dict dict + 3 1 roll def % { x y } boolean dict N@name dict def + exch { dup 3 1 roll def } if % { x y } dict boolean + begin % { x y } dict begin + tx@Dict begin + STV CP T exec % set scaling + end + /NodeMtrx CM def % save CM + next % InitXNode + end + grestore +} def +% +/InitPnode { + /Y ED /X ED + /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +% +/InitCnode { + /r ED /Y ED /X ED + /NodePos { NodeSep r add dup Cos mul exch Sin mul } def +} def +% +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +% +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist + Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } + { 0 Dist Sin mul } ifelse } ifelse Do +} def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform + exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx + dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop + XYPos } ifelse +} def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { + /b ED /a ED % second and first node + /NodeSepTypeB ED /NodeSepTypeA ED + /NodeSepB ED /NodeSepA ED + /OffsetB ED /OffsetA ED + tx@NodeDict a known tx@NodeDict b known and dup { + /NodeA a load def + /NodeB b load def + NodeA GetCenter /yA ED /xA ED + NodeB GetCenter /yB ED /xB ED } if +} def +% +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +% +/NCAngles { + GetEdgeA GetEdgeB GetArmA GetArmB + /mtrx AngleA matrix rotate def + xA2 yA2 mtrx transform pop + xB2 yB2 mtrx transform exch pop + mtrx itransform + /y0 ED /x0 ED + mark ArmB 0 ne { xB1 yB1 } if + xB2 yB2 x0 y0 xA2 yA2 + ArmA 0 ne { xA1 yA1 } if + tx@Dict begin false Line end + /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def + /LPutPos { LPutLines } def + /HPutPos { HPutLines } def + /VPutPos { VPutLines } def } def +% +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def + +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def + +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.05, 2006/11/04 +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + /ifCMYK exch def % do we have rgb or cmyk? hv 1.06 + rotate + /MidPoint ED + /NumLines ED + ifCMYK { + /LastBlack ED % 1.06 + /LastYellow ED % 1.06 + /LastMagenta ED % 1.06 + /LastCyan ED % 1.06 + /FirstBlack ED % 1.06 + /FirstYellow ED % 1.06 + /FirstMagenta ED % 1.06 + /FirstCyan ED % 1.06 + }{ /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED + /FirstRed ED + } ifelse + /GradientPosY ED + /GradientPosX ED + /GradientScale ED + /ifGradientCircle ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + 4 copy /ury ED /urx ED /lly ED /llx ED + /y ED /x ED + ifGradientCircle + { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if } + {2 copy translate} ifelse + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + ifCMYK { % 1.06 + LastCyan FirstCyan add 2 div % 1.06 + LastMagenta FirstMagenta add 2 div % 1.06 + LastYellow FirstYellow add 2 div % 1.06 + LastBlack FirstBlack add 2 div % 1.06 + setcmykcolor % 1.06 + }{ + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor + } ifelse + ifGradientCircle + { /YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def + }{ + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + } ifelse + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } ifelse + MidLine 0 gt { + ifCMYK { + /Cyan FirstCyan def + /Magenta FirstMagenta def + /Yellow FirstYellow def + /Black FirstBlack def + /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def + /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def + /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def + /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def + }{ + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + } ifelse + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt { + ifCMYK { + /Cyan LastCyan def + /Magenta LastMagenta def + /Yellow LastYellow def + /Black LastBlack def + /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def + /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def + /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def + /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def + }{ + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + } ifelse + NumLines MidLine sub { GradientLoop } repeat + } if +} def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine sub def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } if } { 0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + ifCMYK { Cyan Magenta Yellow Black setcmykcolor } + { Red Green Blue setrgbcolor } ifelse + fill + /CurrentY CurrentY YSizePerLine add def + ifCMYK { + /Cyan Cyan CyanIncrement add def + /Magenta Magenta MagentaIncrement add def + /Yellow Yellow YellowIncrement add def + /Black Black BlackIncrement add def + }{ + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def + } ifelse + } ifelse% D.G. modification end + }def +% +/GradientFillHSB { % hv 2006-11-04 + rotate + /MidPoint ED + /NumLines ED + /LastBrightness ED + /LastSaturation ED + /LastHue ED + /FirstBrightness ED + /FirstSaturation ED + /FirstHue ED + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack + /y ED /x ED + 2 copy translate + y sub neg /y ED + x sub neg /x ED + % This avoids gaps due to rounding errors: + LastHue FirstHue add 2 div + LastSaturation FirstSaturation add 2 div + LastBrightness FirstBrightness add 2 div + sethsbcolor + fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Hue FirstHue def + /Saturation FirstSaturation def + /Brightness FirstBrightness def + /HueIncrement LastHue FirstHue sub MidLine 1 sub div def + /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub + div def + /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub + div def + MidLine { GradientLoopHSB } repeat + } if + MidLine NumLines lt + { + /Hue LastHue def + /Saturation LastSaturation def + /Brightness LastBrightness def + /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def + /SaturationIncrement FirstSaturation LastSaturation sub + NumLines MidLine sub 1 sub div def + /BrightnessIncrement FirstBrightness LastBrightness sub + NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoopHSB } repeat + } if +} def +/GradientLoopHSB { + 0 CurrentY moveto + x 0 rlineto + 0 YSizePerLine rlineto + x neg 0 rlineto + closepath + Hue Saturation Brightness sethsbcolor fill + /CurrentY CurrentY YSizePerLine add def + /Brightness Brightness BrightnessIncrement add def + /Saturation Saturation SaturationIncrement add def + /Hue Hue HueIncrement add def +} def +% +end +% +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 1.00, 2006/11/05 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { + /t ED + t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def +/Coil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED + /ArmB ED + /ArmA ED + /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED + x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth + /TotalLength ED + Atan rotate + /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def + /EndAngle TotalLength ArmB sub AspectCos Div + w h mul Div 360 mul def + 1 0 0 0 ArrowA ArmA 0 lineto + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle Inc + EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def + TotalLength 0 ArrowB lineto + pop pop pop pop } def +% DG/SR modification end +/AltCoil { + /Inc ED + dup sin /AspectSin ED + cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED + /mtrx CM def + w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul + BeginAngle 180 div AspectCos mul add BeginAngle cos + /lineto load stopped { moveto } if + BeginAngle Inc EndAngle { CoilLoop } for + EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { + /ArmB ED /ArmA ED + 2 div /w ED + w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED + x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth + /TotalLength ED + Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul + sub 2 div dup ArmA add + /ArmA ED ArmB add + /ArmB ED + /x ArmB h 2 div add def + mark 0 0 ArmB 0 + n { x w /w w neg def /x x h add def } repeat + TotalLength ArmA sub 0 TotalLength 0 } def +% +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.0, 2005-11-29 (hv) +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc { + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow { + /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar { + /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def +% +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%% $Id: pstricks-add.pro 23 2008-05-15 21:51:18Z herbert $ +% PostScript prologue for pstricks-add.tex. +% Version 0.20, 2008/01/01 +% For distribution, see pstricks.tex. +% +% HISTORY -> see file Changes +% +/tx@addDict 410 dict def tx@addDict begin +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +/RGBtoCMYK { % on stack r g b + 3 dict begin + /Blue ED /Green ED /Red ED + 1 Red sub % Cyan + 1 Green sub % Magenta + 1 Blue sub % Yellow + 0 % Black + end +} def +% +/CMYKtoGRAY { % c m y k on stack + exch 0.11 mul add + exch 0.59 mul add + exch 0.3 mul add + dup 1 gt { pop 1 } if + neg 1 add +} def +% +/RGBtoGRAY { + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add +} def +% +/HSBtoGRAY { + 6 dict begin + /b exch def + /s exch def 6 mul dup cvi dup + /i exch def sub + /f exch def + /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def + F i get { s mul neg 1 add b mul} forall + 0.11 mul + exch 0.59 mul add + exch 0.3 mul add + end +} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanometres +%% lambda min=380 nanometres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def +% +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + calculateRGB +} def % now the colors are saved in Red Green Blue +% +/wavelengthToCMYK { % the wavelength in nm must be on top of the stack + cvi /lambda exch def % no floating point here + gsave + calculateRGB Red Green Blue RGBtoCMYK + /Black ED /Yellow ED /Magenta ED /Cyan ED + grestore +} def % now the colors are saved in Cyan Magenta Yellow Black +% +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def +% +end +% +% END pstricks-add.pro + + + +%%EndProcSet +%%BeginProcSet: texps.pro 0 0 +%! +TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 +index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ +dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 +roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def +dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} +if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} +def end + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N +/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N +/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N +/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ +/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho +X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B +/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ +/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known +{userdict/md get type/dicttype eq{userdict begin md length 10 add md +maxlength ge{/md md dup length 20 add dict copy def}if end md begin +/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S +atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ +itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll +transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll +curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf +pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} +if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 +-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 +get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip +yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub +neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ +noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop +90 rotate 1 -1 scale ppr 3 get ppr 1 get neg 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newpath}N/st{stroke SaveX SaveY +moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X +/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 +1 startangle endangle arc savematrix setmatrix}N end + +%%EndProcSet +TeXDict begin @defspecial + +/preview@version(11.84)def + +userdict begin/preview-bop-level 0 def/bop-hook{/preview-bop-level +dup load dup 0 le{/isls false def/vsize 792 def/hsize 612 def}if 1 +add store}bind def/eop-hook{/preview-bop-level dup load dup 0 gt{1 +sub}if store}bind def end + +/preview@tightpage true def (compatibility PostScript comment for dvipng<=1.5 + +userdict begin/bop-hook{7{currentfile token not{stop}if 65781.76 div +DVImag mul}repeat 72 add 72 2 copy gt{exch}if 4 2 roll neg 2 copy lt{exch}if +dup 0 gt{pop 0 exch}{exch dup 0 lt{pop 0}if}ifelse 720 add exch 720 +add 3 1 roll 4{5 -1 roll add 4 1 roll}repeat <>setpagedevice//bop-hook exec}bind def +end + +userdict (some extra code to avoid dvipng>=1.6 unknown special: 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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CLW mul add 1.4 mul viceversa { add +epsilon sub } { sub epsilon add } ifelse } def /logLines { false } +def /LSstroke { 0 setlinecap stroke stroke} def /subLSstroke { 0 setlinecap +stroke stroke} def 0 dT MaxValue { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MaxValue abs le { x minTickline moveto x maxTickline lineto +} if } for subTwidth SLW subTColor subLSstroke grestore stroke /dsubT +0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def +subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick tickstart +STsize mul moveto cntsubTick tickend STsize mul lineto }{ exit } +ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth SLW +subTColor subLSstroke grestore } if gsave cntTick tickstart moveto +cntTick tickend lineto Twidth SLW TColor LSstroke grestore } for /dT +dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon viceversa { add +}{ sub } ifelse { /cntTick exch def logLines { gsave 1 10 subTNo div +9.99 { /dx exch def /x cntTick dT dx log mul add def x abs MinValue +abs le { x minTickline moveto x maxTickline lineto } if } for /dsubT +0 def subTwidth SLW subTColor subLSstroke grestore } dsubT abs 0 gt +{ gsave /cntsubTick cntTick dsubT add def subTNo 1 sub { cntsubTick +abs MinValue abs le { cntsubTick tickstart STsize mul moveto cntsubTick +tickend STsize mul lineto }{ exit } ifelse /cntsubTick cntsubTick +dsubT add def } repeat subTwidth SLW subTColor subLSstroke grestore +} if gsave cntTick tickstart moveto cntTick tickend lineto Twidth +SLW TColor LSstroke grestore } for } if end + + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.1 SLW 0 setgray /ArrowA { moveto } +def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 2. CLW mul +add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if +gsave w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore +grestore 0 h a sub moveto EndArrow } def /ArrowInside { } def +0 128.03734 0 0.0 ArrowA CP 4 2 roll ArrowB /yEnd exch def /xEnd +exch def xEnd yEnd L /yStart exch def /xStart exch def 0 setlinecap +stroke stroke 0 dup 2 mod 0 eq true and exch 2 lt false and or { /viceversa +0.0 128.03734 gt { true }{ false } ifelse def /epsilon 0.01 def /minTickline +0.0 def /maxTickline 128.03734 def /dT 3729358 abs 65536 div viceversa +{ neg } if def /subTNo 1 def subTNo 0 gt { /dsubT dT subTNo div def}{ +/dsubT 0 def } ifelse -4.0 4.0 /tickend exch def /tickstart exch def +/Twidth 0.4 def /subTwidth 0.2 def /STsize 0.75 def /TColor { 0 +setgray } def /subTColor { 0.5 setgray } def /MinValue { yStart +} def /MaxValue { yEnd 1.5 2. CLW mul add 1.4 mul viceversa { add +epsilon sub } { sub epsilon add } ifelse } def /logLines { false } +def /LSstroke { 0 setlinecap stroke stroke} def /subLSstroke { 0 setlinecap +stroke stroke} def 0 dT MaxValue { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MaxValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for subTwidth SLW subTColor subLSstroke grestore stroke +/dsubT 0 def } if dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT +add def subTNo 1 sub { cntsubTick abs MaxValue abs le { cntsubTick +tickstart STsize mul exch moveto cntsubTick tickend STsize mul exch +lineto }{ exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat +subTwidth SLW subTColor subLSstroke grestore } if gsave cntTick tickstart +exch moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke +grestore } for /dT dT neg def /dsubT dsubT neg def 0 dT MinValue epsilon +viceversa { add }{ sub } ifelse { /cntTick exch def logLines { gsave +1 10 subTNo div 9.99 { /dx exch def /x cntTick dT dx log mul add def +x abs MinValue abs le { x minTickline exch moveto x maxTickline exch +lineto } if } for /dsubT 0 def subTwidth SLW subTColor subLSstroke +grestore } dsubT abs 0 gt { gsave /cntsubTick cntTick dsubT add def +subTNo 1 sub { cntsubTick abs MinValue abs le { cntsubTick tickstart +STsize mul exch moveto cntsubTick tickend STsize mul exch lineto }{ +exit } ifelse /cntsubTick cntsubTick dsubT add def } repeat subTwidth +SLW subTColor subLSstroke grestore } if gsave cntTick tickstart exch +moveto cntTick tickend exch lineto Twidth SLW TColor LSstroke grestore +} for } if end + +@endspecial 120 +-209 a Fc(0)120 -682 y(2)120 -1154 y(4)215 -108 y(0)431 +b(2)f(4)236 -236 y + tx@Dict begin { 136.57324 0.0 } PutCoor PutBegin end + 236 -236 a 212 -218 a Fb(x)236 -236 +y + tx@Dict begin PutEnd end + 236 -236 a 236 -236 a + tx@Dict begin { 0.0 136.57324 } PutCoor PutBegin end + 236 -236 a 214 -226 a Fb(y)236 +-236 y + tx@Dict begin PutEnd end + 236 -236 a @beginspecial @setspecial + tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. 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/atan load stopped { pop pop 0 } if } def +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, epects 2 parameter +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +/RadtoDeg { 180 mul Pi div } def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.08, 2006/06/17 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2006/06/17 : - changes to the code (hv) +% 2006/04/21 : - Improved parser -> generic with derivative and translator into ps (dr) +% 2006/01/16 : - EXP -> Exp to prevent missmatch with pst-math (hv) +% 2005/09/28 : - rename it to pstricks-add.pro +% - add support for Gouraud shading (hv) +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression (dr) +% 2004/12/16 : addition of Sum and IfTE (dr) +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +% +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { tx@AlgToPs begin AlgToPs end } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end%%%tx@CoreAnalyzerDict +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat } + { tutu 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (ln\() StrConcat 8 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if 90 div 1.57079632680 mul +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan 90 div 1.57079632680 mul +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if 90 div 1.57079632680 mul } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { 2.71828182846 exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +/PI 3.14159265358 def +end +% END pstricks-add.pro + + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% These are /dotlessj /ff /ffi /ffl. +% +% (4) hyphen appears twice for compatibility with both ASCII and Windows. +% +% (5) /Euro was assigned to 128, as in Windows ANSI +% +% (6) Missing characters from MacRoman encoding incorporated as follows: +% +% PostScript MacRoman TeXBase1 +% -------------- -------------- -------------- +% /notequal 173 0x16 +% /infinity 176 0x17 +% 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CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d +% maximum number of times to iterate the iterative procedure: + 30 +% iterative procedure: takes an angle t on top of stack, computes a better angle (an put it on top of stack) + { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +%after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +} def +% +/EllipticArcArrow { + /d ED % add/sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul x add + a2 sin ry mul y add + a1 cos rx mul x add + a1 sin ry mul y add +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-grad.pro 0 0 +%! +% PostScript prologue for pst-grad.tex. +% Version 1.04, 2004/06/23 (adding %GradientCircle style - D.G.) +% prepared by Herbert Voss +% For copying restrictions, see pstricks.tex. +% +% For the PSTricks gradient fillstyle.% +% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).% +% Syntax:% D.G. modification begin - Apr. 9, %1998 +%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill +% ifGradientCircle GradientScale %GradientPosX GradientPosY +% R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill +% D.G. modification end +% +/tx@GradientDict 40 dict def +tx@GradientDict begin +/GradientFill { + rotate + /MidPoint ED + /NumLines ED + /LastBlue ED + /LastGreen ED + /LastRed ED + /FirstBlue ED + /FirstGreen ED +/FirstRed ED +% D.G. modification begin - Apr. 9, 1998 +/GradientPosY ED +/GradientPosX ED + /GradientScale ED + /ifGradientCircle ED +% D.G. modification end + % This avoids gaps due to rounding errors: + clip + pathbbox %leave llx,lly,urx,ury on stack +% D.G. modification begin - Apr. 10, 1998 + 4 copy /ury ED /urx ED /lly ED /llx ED +% D.G. modification end + /y ED /x ED +% D.G. modification begin - Apr. 10, 1998 +ifGradientCircle + {0 GradientPosX eq + {0 GradientPosX eq {2 copy translate} if} if} + {2 copy translate} ifelse +% D.G. modification end + y sub neg /y ED + x sub neg /x ED % This avoids gaps due to rounding errors: + LastRed FirstRed add 2 div + LastGreen FirstGreen add 2 div + LastBlue FirstBlue add 2 div + setrgbcolor +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {/YSizePerLine y NumLines div def + /CurrentY y 2 div def + /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def} + {fill + /YSizePerLine y NumLines div def + /CurrentY 0 def + /MidLine NumLines 1 MidPoint sub mul abs cvi def} ifelse +% DG modification end + MidLine NumLines 2 sub gt + { /MidLine NumLines def } + { MidLine 2 lt { /MidLine 0 def } if } + ifelse + MidLine 0 gt + { + /Red FirstRed def + /Green FirstGreen def + /Blue FirstBlue def + /RedIncrement LastRed FirstRed sub MidLine 1 sub div def + /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def + /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def + MidLine { GradientLoop } repeat + } if + MidLine NumLines lt + { + /Red LastRed def + /Green LastGreen def + /Blue LastBlue def + /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def + /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def + /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def + NumLines MidLine sub { GradientLoop } repeat } + if + } def/GradientLoop { +% D.G. modification begin - Jul. 23, 1997 / Apr. 9, 1998 + ifGradientCircle + {CurrentY 0 gt { +% The default center used is the center of the bounding box of the object + 0 GradientPosX eq {0 GradientPosX eq + {/GradientPosX urx llx sub 2 div def + /GradientPosY ury lly sub 2 div def} if} if + GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc + Red Green Blue setrgbcolor fill + /CurrentY CurrentY YSizePerLine sub def + /Blue Blue BlueIncrement add def + /Green Green GreenIncrement add def + /Red Red RedIncrement add def} if} {0 CurrentY moveto x 0 rlineto + 0 YSizePerLine rlineto x neg 0 rlineto closepath + Red Green Blue setrgbcolor fill /CurrentY CurrentY YSizePerLine add def + /Blue Blue BlueIncrement add def /Green Green GreenIncrement add def + /Red Red RedIncrement add def} ifelse% D.G. modification end + }def + end +% END pst-grad.pro + +%%EndProcSet +%%BeginProcSet: pst-coil.pro 0 0 +%! +% PostScript prologue for pst-coil.tex. +% Version 97 patch 1, 98/06/02 +% For distribution, see pstricks.tex. +% +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis) +% TotalLength 0 ArrowB lineto } def +TotalLength 0 ArrowB lineto +pop pop pop pop } def +% DG/SR modification end +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +% END pst-coil.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 1.00, 2005/12/15 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def +% hv begin 2005-11-29 1.00 +% String length +% { String CharCount 1 getinterval ShowChar +% /CharCount CharCount 1 add def + /CharSize 1 def + currentfont /FontType get 0 eq + { currentfont /FMapType get dup 2 eq exch dup 5 eq exch 9 eq or or + { /CharSize 2 def} if + } if + String length CharSize idiv + { String CharCount CharSize getinterval ShowChar + /CharCount CharCount CharSize add def +% hv end 2005-11-29 1.00 + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pstricks-add.pro 0 0 +%! +% PostScript prologue for pstricks-add.tex. +% Version 0.08, 2006/06/17 +% For distribution, see pstricks.tex. +% +% HISTORY +% 2006/06/17 : - changes to the code (hv) +% 2006/04/21 : - Improved parser -> generic with derivative and translator into ps (dr) +% 2006/01/16 : - EXP -> Exp to prevent missmatch with pst-math (hv) +% 2005/09/28 : - rename it to pstricks-add.pro +% - add support for Gouraud shading (hv) +% 2005/05/20 : small (unimportant) changes (hv) +% 2005/02/25 : white space removal from expression (dr) +% 2004/12/16 : addition of Sum and IfTE (dr) +% 2004/11/14 : correction of a priority problem +% ^ before unary - (new rule FS) +% +/tx@addDict 410 dict def tx@addDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Pi and Euler are defined in pstricks.pro +/PIdiv2 1.57079632680 def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS %%% NEW 2004/11/14 +% FS -> F | +SF | -SF %%% NEW 2004/11/14 +% F->P|F^P %%% OLD +% F->P|F^SF %%% NEW 2004/11/14 ???? ^FS +% P->(E)|literal +% literal->number|var|var[E]|func(params)%%|-P|+P%%% OLD +% params->E|E,param +% +% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%% str -> [ LIFO vector ] +/AlgParser { tx@AlgToPs begin AlgToPs end } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/GTriangle { + gsave + /mtrx CM def + /colorA ED /colorB ED /colorC ED % save the colors + /yA ED /xA ED % save the origin + xA yA translate + rotate % \psk@gangle + /yB ED /xB ED /yC ED /xC ED % save other coordinates + /ds [ % save data in a array + 0 0 0 colorA aload pop % fd x y xr xg xb + 0 xB xA sub yB yA sub colorB aload pop + 0 xC xA sub yC yA sub colorC aload pop +% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD + ] def + newpath + << + /ShadingType 4 % single Gouraud + /ColorSpace [ /DeviceRGB ] + /DataSource ds + >> + shfill + closepath + mtrx + setmatrix grestore} def +% +%% convertisseur longueur d'onde ->R,G,B Manuel Luque +%% lambda max=780 nanomètres +%% lambda min=380 nanomètres +%% adaptation de : +%% http://www.physics.sfasu.edu/astro/color.html +%% www.efg2.com/lab +% +/Gamma 0.8 def +/calculateRGB { + lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if + lambda 380 ge {lambda 439 le { + /R {lambda 440 sub neg 440 380 sub div} def + /Red R factor mul Gamma exp def + /G 0 def + /Green G factor mul Gamma exp def + /B 1 def + /Blue B factor mul Gamma exp def} if + } if + lambda 440 ge { lambda 489 le { + /G {lambda 440 sub 490 440 sub div} def + /Green G factor mul Gamma exp def + /R 0 def /Red 0 def + /B 1 def + /Blue B factor mul Gamma exp def } if + } if + lambda 490 ge {lambda 509 le { + /B {lambda 510 sub neg 510 490 sub div} def + /Blue B factor mul Gamma exp def + /R 0 def /Red 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 510 ge {lambda 579 le { + /R {lambda 510 sub 580 510 sub div } def + /Red R factor mul Gamma exp def + /Blue 0 def + /G 1 def + /Green G factor mul Gamma exp def } if + } if + lambda 580 ge {lambda 644 le { + /G {lambda 645 sub neg 645 580 sub div } def + /Green G factor mul Gamma exp def + /Blue 0 def + /R 1 def + /Red R factor mul Gamma exp def } if + } if + lambda 645 ge { lambda 780 le { + /Red 1 factor mul Gamma exp def + /Blue 0 def + /Green 0 def } if + } if +} def +% +/factor { + lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if + lambda 420 ge {lambda 700 le { 1 } if } if + lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if +} def + +/wavelengthToRGB { % the wavelength in nm must be on top of the stack + /lambda exch def + calculateRGB +} def + + +/axfill { + 8 dict begin + /xw exch def /nl exch def + /C1 exch def /y1 exch def/x1 exch def + /C0 exch def /y0 exch def/x0 exch def + << /ShadingType 2 + /ColorSpace /DeviceRGB + /Coords [ x0 y0 x1 y1 ] + /EmulatorHints [ xw 2 div dup ] + /Function << + /FunctionType 2 + /Domain [0 1] + /C0 C0 + /C1 C1 + /N 1 + >> + >> shfill + end +} bind def + +systemdict /shfill known not { + +/Emulate_shfill 32 dict def Emulate_shfill begin + +/NumberOfLayers 128 def + +/assert { not { (assert) /typecheck signalerror} if } bind def +/assert /pop load def + +% generic interpolation +% takes two n-arrays, returns a hopefully optimized procedure taking one +% argument, and returning a correct blend of the two arrays (hence an +% n-array) +/interpolating_function { + 10 dict begin /a1 exch def /a0 exch def + a0 length a1 length eq assert + [ /mark load /exch load + 0 1 a0 length 1 sub { /i exch def /dup load a1 i get a0 i get sub /mul load a0 i get /add load /exch load } for /pop load (]) cvn load ] cvx end +} bind def + +% Emulates (rather poorly) a radial or axial fill. +% For radial fills, we _require_ that the inner circle be specified +% first. +% For axial fills, the ``Extend'' behaviour is ignored, and we _require_ +% an additional parameters in the dictionary, named EmulatorHints. It's a +% 2-array denoting the left and right extent of the area to paint. These +% are taken as multiples of the vector orthogonal to the direction vector. +/xshfill { begin gsave + % do some checks. + Function begin FunctionType 2 eq assert + Domain 0 get 0 eq Domain 1 get 1 eq and assert end + ColorSpace setcolorspace + % we assume ll2 at least, so that dicts can be extended. anyway + % the syntax we request is ll2 only. + /mkcol Function begin C0 C1 end interpolating_function bind def + ShadingType 3 eq { + /mkcoords + [ Coords cvx exec 7 3 roll ] [ 5 -3 roll ] + interpolating_function + bind def + /one { newpath mkcoords cvx dup exec 3 -1 roll add exch moveto + exec 0 360 arc fill } bind def + } if + ShadingType 2 eq { + /dv [ Coords cvx exec exch 4 1 roll exch sub 3 1 roll sub exch + ] cvx def % normal vector + /nv [ dv neg exch ] cvx def + /mkcoords + [ Coords cvx exec 5 2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + [ 4 -2 roll nv + exch 4 -1 roll exch EmulatorHints 0 get mul add + 3 1 roll EmulatorHints 0 get mul add ] + interpolating_function + % rescale to adapt to our reverse scan behaviour. + /dv [ dv neg NumberOfLayers div exch neg NumberOfLayers div exch ] cvx def + /bnv [ nv EmulatorHints cvx exec add mul exch + EmulatorHints cvx exec add mul exch ] cvx def + /nv [ bnv neg exch neg exch ] cvx def + bind def + /one { newpath mkcoords cvx exec moveto + nv rlineto + dv rlineto + bnv rlineto + closepath fill } bind def + } if + % The space is traversed backwards, since it is more customary + % for me at least to put the inner circle first for radial fills. + % For axial fills, this does not matter afaict. + 1 1 NumberOfLayers div neg 0 + { dup Function /N get exp mkcol cvx exec setcolor one } + for + grestore end +} bind def + +end +userdict /shfill { Emulate_shfill begin xshfill end } bind put } if + +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E expression, T term, SF signed factor, F factor, P power +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% parser +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end%%%tx@CoreAnalyzerDict +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat } + { tutu 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (ln\() StrConcat 8 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length 3.14159265359 /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if 90 div 1.57079632680 mul +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan 90 div 1.57079632680 mul +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if 90 div 1.57079632680 mul } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { 2.71828182846 exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +/PI 3.14159265358 def +end +% END pstricks-add.pro + + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% These are /dotlessj /ff /ffi /ffl. +% +% (4) hyphen appears twice for compatibility with both ASCII and Windows. +% +% (5) /Euro was assigned to 128, as in Windows ANSI +% +% (6) Missing characters from MacRoman encoding incorporated as follows: +% +% PostScript MacRoman TeXBase1 +% -------------- -------------- -------------- +% /notequal 173 0x16 +% /infinity 176 0x17 +% 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+%275252A8FD25FF27F852FD74FFA8F8F87DFD74FFA8F8F8FD76FF7DA8FD2F +%FFFF +%%EndData +%%EndComments +%%BeginDefaults +%%ViewingOrientation: 1 0 0 1 +%%EndDefaults +%%BeginProlog +%%BeginResource: procset Adobe_AGM_Utils 1.0 0 +%%Version: 1.0 0 +%%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. +systemdict /setpacking known +{ + currentpacking + true setpacking +} if +userdict /Adobe_AGM_Utils 68 dict dup begin put +/bdf +{ + bind def +} bind def +/nd{ + null def +}bdf +/xdf +{ + exch def +}bdf +/ldf +{ + load def +}bdf +/ddf +{ + put +}bdf +/xddf +{ + 3 -1 roll put +}bdf +/xpt +{ + exch put +}bdf +/ndf +{ + exch dup where{ + pop pop pop + }{ + xdf + }ifelse +}def +/cdndf +{ + exch dup currentdict exch known{ + pop pop + }{ + exch def + }ifelse +}def +/bdict +{ + mark +}bdf +/edict +{ + counttomark 2 idiv dup dict begin {def} repeat pop currentdict end +}def +/ps_level + /languagelevel where{ + pop systemdict /languagelevel get exec + }{ + 1 + }ifelse +def +/level2 + ps_level 2 ge +def +/level3 + ps_level 3 ge +def +/ps_version + {version cvr} stopped { + -1 + }if +def +/makereadonlyarray +{ + /packedarray where{ + pop packedarray + }{ + array astore readonly + }ifelse +}bdf +/map_reserved_ink_name +{ + dup type /stringtype eq{ + dup /Red eq{ + pop (_Red_) + }{ + dup /Green eq{ + pop (_Green_) + }{ + dup /Blue eq{ + pop (_Blue_) + }{ + dup () cvn eq{ + pop (Process) + }if + }ifelse + }ifelse + }ifelse + }if +}bdf +/AGMUTIL_GSTATE 22 dict def +/get_gstate +{ + AGMUTIL_GSTATE begin + /AGMUTIL_GSTATE_clr_spc currentcolorspace def + /AGMUTIL_GSTATE_clr_indx 0 def + /AGMUTIL_GSTATE_clr_comps 12 array def + mark currentcolor counttomark + {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 3 -1 roll put + /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 add def} repeat pop + /AGMUTIL_GSTATE_fnt rootfont def + /AGMUTIL_GSTATE_lw currentlinewidth def + /AGMUTIL_GSTATE_lc currentlinecap def + /AGMUTIL_GSTATE_lj currentlinejoin def + /AGMUTIL_GSTATE_ml currentmiterlimit def + currentdash /AGMUTIL_GSTATE_do xdf /AGMUTIL_GSTATE_da xdf + /AGMUTIL_GSTATE_sa currentstrokeadjust def + /AGMUTIL_GSTATE_clr_rnd currentcolorrendering def + /AGMUTIL_GSTATE_op currentoverprint def + /AGMUTIL_GSTATE_bg currentblackgeneration cvlit def + /AGMUTIL_GSTATE_ucr currentundercolorremoval cvlit def + currentcolortransfer cvlit /AGMUTIL_GSTATE_gy_xfer xdf cvlit /AGMUTIL_GSTATE_b_xfer xdf + cvlit /AGMUTIL_GSTATE_g_xfer xdf cvlit /AGMUTIL_GSTATE_r_xfer xdf + /AGMUTIL_GSTATE_ht currenthalftone def + /AGMUTIL_GSTATE_flt currentflat def + end +}def +/set_gstate +{ + AGMUTIL_GSTATE begin + AGMUTIL_GSTATE_clr_spc setcolorspace + AGMUTIL_GSTATE_clr_indx {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 1 sub get + /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 sub def} repeat setcolor + AGMUTIL_GSTATE_fnt setfont + AGMUTIL_GSTATE_lw setlinewidth + AGMUTIL_GSTATE_lc setlinecap + AGMUTIL_GSTATE_lj setlinejoin + AGMUTIL_GSTATE_ml setmiterlimit + AGMUTIL_GSTATE_da AGMUTIL_GSTATE_do setdash + AGMUTIL_GSTATE_sa setstrokeadjust + AGMUTIL_GSTATE_clr_rnd setcolorrendering + AGMUTIL_GSTATE_op setoverprint + AGMUTIL_GSTATE_bg cvx setblackgeneration + AGMUTIL_GSTATE_ucr cvx setundercolorremoval + AGMUTIL_GSTATE_r_xfer cvx AGMUTIL_GSTATE_g_xfer cvx AGMUTIL_GSTATE_b_xfer cvx + AGMUTIL_GSTATE_gy_xfer cvx setcolortransfer + AGMUTIL_GSTATE_ht /HalftoneType get dup 9 eq exch 100 eq or + { + currenthalftone /HalftoneType get AGMUTIL_GSTATE_ht /HalftoneType get ne + { + mark AGMUTIL_GSTATE_ht {sethalftone} stopped cleartomark + } if + }{ + AGMUTIL_GSTATE_ht sethalftone + } ifelse + AGMUTIL_GSTATE_flt setflat + end +}def +/get_gstate_and_matrix +{ + AGMUTIL_GSTATE begin + /AGMUTIL_GSTATE_ctm matrix currentmatrix def + end + get_gstate +}def +/set_gstate_and_matrix +{ + set_gstate + AGMUTIL_GSTATE begin + AGMUTIL_GSTATE_ctm setmatrix + end +}def +/AGMUTIL_str256 256 string def +/AGMUTIL_src256 256 string def +/AGMUTIL_dst64 64 string def +/AGMUTIL_srcLen nd +/AGMUTIL_ndx nd +/agm_sethalftone +{ + dup + begin + /_Data load + /Thresholds xdf + end + level3 + { sethalftone }{ + dup /HalftoneType get 3 eq { + sethalftone + } {pop} ifelse + }ifelse +} def +/rdcmntline +{ + currentfile AGMUTIL_str256 readline pop + (%) anchorsearch {pop} if +} bdf +/filter_cmyk +{ + dup type /filetype ne{ + exch () /SubFileDecode filter + } + { + exch pop + } + ifelse + [ + exch + { + AGMUTIL_src256 readstring pop + dup length /AGMUTIL_srcLen exch def + /AGMUTIL_ndx 0 def + AGMCORE_plate_ndx 4 AGMUTIL_srcLen 1 sub{ + 1 index exch get + AGMUTIL_dst64 AGMUTIL_ndx 3 -1 roll put + /AGMUTIL_ndx AGMUTIL_ndx 1 add def + }for + pop + AGMUTIL_dst64 0 AGMUTIL_ndx getinterval + } + bind + /exec cvx + ] cvx +} bdf +/filter_indexed_devn +{ + cvi Names length mul names_index add Lookup exch get +} bdf +/filter_devn +{ + 4 dict begin + /srcStr xdf + /dstStr xdf + dup type /filetype ne{ + 0 () /SubFileDecode filter + }if + [ + exch + [ + /devicen_colorspace_dict /AGMCORE_gget cvx /begin cvx + currentdict /srcStr get /readstring cvx /pop cvx + /dup cvx /length cvx 0 /gt cvx [ + Adobe_AGM_Utils /AGMUTIL_ndx 0 /ddf cvx + names_index Names length currentdict /srcStr get length 1 sub { + 1 /index cvx /exch cvx /get cvx + currentdict /dstStr get /AGMUTIL_ndx /load cvx 3 -1 /roll cvx /put cvx + Adobe_AGM_Utils /AGMUTIL_ndx /AGMUTIL_ndx /load cvx 1 /add cvx /ddf cvx + } for + currentdict /dstStr get 0 /AGMUTIL_ndx /load cvx /getinterval cvx + ] cvx /if cvx + /end cvx + ] cvx + bind + /exec cvx + ] cvx + end +} bdf +/AGMUTIL_imagefile nd +/read_image_file +{ + AGMUTIL_imagefile 0 setfileposition + 10 dict begin + /imageDict xdf + /imbufLen Width BitsPerComponent mul 7 add 8 idiv def + /imbufIdx 0 def + /origDataSource imageDict /DataSource get def + /origMultipleDataSources imageDict /MultipleDataSources get def + /origDecode imageDict /Decode get def + /dstDataStr imageDict /Width get colorSpaceElemCnt mul string def + /srcDataStrs [ imageDict begin + currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse + { + Width Decode length 2 div mul cvi string + } repeat + end ] def + imageDict /MultipleDataSources known {MultipleDataSources}{false} ifelse + { + /imbufCnt imageDict /DataSource get length def + /imbufs imbufCnt array def + 0 1 imbufCnt 1 sub { + /imbufIdx xdf + imbufs imbufIdx imbufLen string put + imageDict /DataSource get imbufIdx [ AGMUTIL_imagefile imbufs imbufIdx get /readstring cvx /pop cvx ] cvx put + } for + DeviceN_PS2 { + imageDict begin + /DataSource [ DataSource /devn_sep_datasource cvx ] cvx def + /MultipleDataSources false def + /Decode [0 1] def + end + } if + }{ + /imbuf imbufLen string def + Indexed_DeviceN level3 not and DeviceN_NoneName or { + imageDict begin + /DataSource [AGMUTIL_imagefile Decode BitsPerComponent false 1 /filter_indexed_devn load dstDataStr srcDataStrs devn_alt_datasource /exec cvx] cvx def + /Decode [0 1] def + end + }{ + imageDict /DataSource {AGMUTIL_imagefile imbuf readstring pop} put + } ifelse + } ifelse + imageDict exch + load exec + imageDict /DataSource origDataSource put + imageDict /MultipleDataSources origMultipleDataSources put + imageDict /Decode origDecode put + end +} bdf +/write_image_file +{ + begin + { (AGMUTIL_imagefile) (w+) file } stopped{ + false + }{ + Adobe_AGM_Utils/AGMUTIL_imagefile xddf + 2 dict begin + /imbufLen Width BitsPerComponent mul 7 add 8 idiv def + MultipleDataSources {DataSource 0 get}{DataSource}ifelse type /filetype eq { + /imbuf imbufLen string def + }if + 1 1 Height { + pop + MultipleDataSources { + 0 1 DataSource length 1 sub { + DataSource type dup + /arraytype eq { + pop DataSource exch get exec + }{ + /filetype eq { + DataSource exch get imbuf readstring pop + }{ + DataSource exch get + } ifelse + } ifelse + AGMUTIL_imagefile exch writestring + } for + }{ + DataSource type dup + /arraytype eq { + pop DataSource exec + }{ + /filetype eq { + DataSource imbuf readstring pop + }{ + DataSource + } ifelse + } ifelse + AGMUTIL_imagefile exch writestring + } ifelse + }for + end + true + }ifelse + end +} bdf +/close_image_file +{ + AGMUTIL_imagefile closefile (AGMUTIL_imagefile) deletefile +}def +statusdict /product known userdict /AGMP_current_show known not and{ + /pstr statusdict /product get def + pstr (HP LaserJet 2200) eq + pstr (HP LaserJet 4000 Series) eq or + pstr (HP LaserJet 4050 Series ) eq or + pstr (HP LaserJet 8000 Series) eq or + pstr (HP LaserJet 8100 Series) eq or + pstr (HP LaserJet 8150 Series) eq or + pstr (HP LaserJet 5000 Series) eq or + pstr (HP LaserJet 5100 Series) eq or + pstr (HP Color LaserJet 4500) eq or + pstr (HP Color LaserJet 4600) eq or + pstr (HP LaserJet 5Si) eq or + pstr (HP LaserJet 1200 Series) eq or + pstr (HP LaserJet 1300 Series) eq or + pstr (HP LaserJet 4100 Series) eq or + { + userdict /AGMP_current_show /show load put + userdict /show { + currentcolorspace 0 get + /Pattern eq + {false charpath f} + {AGMP_current_show} ifelse + } put + }if + currentdict /pstr undef +} if +/consumeimagedata +{ + begin + currentdict /MultipleDataSources known not + {/MultipleDataSources false def} if + MultipleDataSources + { + 1 dict begin + /flushbuffer Width cvi string def + 1 1 Height cvi + { + pop + 0 1 DataSource length 1 sub + { + DataSource exch get + dup type dup + /filetype eq + { + exch flushbuffer readstring pop pop + }if + /arraytype eq + { + exec pop + }if + }for + }for + end + } + { + /DataSource load type dup + /filetype eq + { + 1 dict begin + /flushbuffer Width Decode length 2 div mul cvi string def + 1 1 Height { pop DataSource flushbuffer readstring pop pop} for + end + }if + /arraytype eq + { + 1 1 Height { pop DataSource pop } for + }if + }ifelse + end +}bdf +/addprocs +{ + 2{/exec load}repeat + 3 1 roll + [ 5 1 roll ] bind cvx +}def +/modify_halftone_xfer +{ + currenthalftone dup length dict copy begin + currentdict 2 index known{ + 1 index load dup length dict copy begin + currentdict/TransferFunction known{ + /TransferFunction load + }{ + currenttransfer + }ifelse + addprocs /TransferFunction xdf + currentdict end def + currentdict end sethalftone + }{ + currentdict/TransferFunction known{ + /TransferFunction load + }{ + currenttransfer + }ifelse + addprocs /TransferFunction xdf + currentdict end sethalftone + pop + }ifelse +}def +/clonearray +{ + dup xcheck exch + dup length array exch + Adobe_AGM_Core/AGMCORE_tmp -1 ddf + { + Adobe_AGM_Core/AGMCORE_tmp AGMCORE_tmp 1 add ddf + dup type /dicttype eq + { + AGMCORE_tmp + exch + clonedict + Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf + } if + dup type /arraytype eq + { + AGMCORE_tmp exch + clonearray + Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf + } if + exch dup + AGMCORE_tmp 4 -1 roll put + }forall + exch {cvx} if +}bdf +/clonedict +{ + dup length dict + begin + { + dup type /dicttype eq + { + clonedict + } if + dup type /arraytype eq + { + clonearray + } if + def + }forall + currentdict + end +}bdf +/DeviceN_PS2 +{ + /currentcolorspace AGMCORE_gget 0 get /DeviceN eq level3 not and +} bdf +/Indexed_DeviceN +{ + /indexed_colorspace_dict AGMCORE_gget dup null ne { + /CSD known + }{ + pop false + } ifelse +} bdf +/DeviceN_NoneName +{ + /Names where { + pop + false Names + { + (None) eq or + } forall + }{ + false + }ifelse +} bdf +/DeviceN_PS2_inRip_seps +{ + /AGMCORE_in_rip_sep where + { + pop dup type dup /arraytype eq exch /packedarraytype eq or + { + dup 0 get /DeviceN eq level3 not and AGMCORE_in_rip_sep and + { + /currentcolorspace exch AGMCORE_gput + false + } + { + true + }ifelse + } + { + true + } ifelse + } + { + true + } ifelse +} bdf +/base_colorspace_type +{ + dup type /arraytype eq {0 get} if +} bdf +/doc_setup{ + Adobe_AGM_Utils begin +}bdf +/doc_trailer{ + currentdict Adobe_AGM_Utils eq{ + end + }if +}bdf +systemdict /setpacking known +{ + setpacking +} if +%%EndResource +%%BeginResource: procset Adobe_AGM_Core 2.0 0 +%%Version: 2.0 0 +%%Copyright: Copyright (C) 1997-2003 Adobe Systems, Inc. All Rights Reserved. +systemdict /setpacking known +{ + currentpacking + true setpacking +} if +userdict /Adobe_AGM_Core 216 dict dup begin put +/nd{ + null def +}bind def +/Adobe_AGM_Core_Id /Adobe_AGM_Core_2.0_0 def +/AGMCORE_str256 256 string def +/AGMCORE_save nd +/AGMCORE_graphicsave nd +/AGMCORE_c 0 def +/AGMCORE_m 0 def +/AGMCORE_y 0 def +/AGMCORE_k 0 def +/AGMCORE_cmykbuf 4 array def +/AGMCORE_screen [currentscreen] cvx def +/AGMCORE_tmp 0 def +/AGMCORE_&setgray nd +/AGMCORE_&setcolor nd +/AGMCORE_&setcolorspace nd +/AGMCORE_&setcmykcolor nd +/AGMCORE_cyan_plate nd +/AGMCORE_magenta_plate nd +/AGMCORE_yellow_plate nd +/AGMCORE_black_plate nd +/AGMCORE_plate_ndx nd +/AGMCORE_get_ink_data nd +/AGMCORE_is_cmyk_sep nd +/AGMCORE_host_sep nd +/AGMCORE_avoid_L2_sep_space nd +/AGMCORE_distilling nd +/AGMCORE_composite_job nd +/AGMCORE_producing_seps nd +/AGMCORE_ps_level -1 def +/AGMCORE_ps_version -1 def +/AGMCORE_environ_ok nd +/AGMCORE_CSA_cache 0 dict def +/AGMCORE_CSD_cache 0 dict def +/AGMCORE_pattern_cache 0 dict def +/AGMCORE_currentoverprint false def +/AGMCORE_deltaX nd +/AGMCORE_deltaY nd +/AGMCORE_name nd +/AGMCORE_sep_special nd +/AGMCORE_err_strings 4 dict def +/AGMCORE_cur_err nd +/AGMCORE_ovp nd +/AGMCORE_current_spot_alias false def +/AGMCORE_inverting false def +/AGMCORE_feature_dictCount nd +/AGMCORE_feature_opCount nd +/AGMCORE_feature_ctm nd +/AGMCORE_ConvertToProcess false def +/AGMCORE_Default_CTM matrix def +/AGMCORE_Default_PageSize nd +/AGMCORE_currentbg nd +/AGMCORE_currentucr nd +/AGMCORE_gradientcache 32 dict def +/AGMCORE_in_pattern false def +/knockout_unitsq nd +/AGMCORE_CRD_cache where{ + pop +}{ + /AGMCORE_CRD_cache 0 dict def +}ifelse +/AGMCORE_key_known +{ + where{ + /Adobe_AGM_Core_Id known + }{ + false + }ifelse +}ndf +/flushinput +{ + save + 2 dict begin + /CompareBuffer 3 -1 roll def + /readbuffer 256 string def + mark + { + currentfile readbuffer {readline} stopped + {cleartomark mark} + { + not + {pop exit} + if + CompareBuffer eq + {exit} + if + }ifelse + }loop + cleartomark + end + restore +}bdf +/getspotfunction +{ + AGMCORE_screen exch pop exch pop + dup type /dicttype eq{ + dup /HalftoneType get 1 eq{ + /SpotFunction get + }{ + dup /HalftoneType get 2 eq{ + /GraySpotFunction get + }{ + pop + { + abs exch abs 2 copy add 1 gt{ + 1 sub dup mul exch 1 sub dup mul add 1 sub + }{ + dup mul exch dup mul add 1 exch sub + }ifelse + }bind + }ifelse + }ifelse + }if +} def +/clp_npth +{ + clip newpath +} def +/eoclp_npth +{ + eoclip newpath +} def +/npth_clp +{ + newpath clip +} def +/add_grad +{ + AGMCORE_gradientcache 3 1 roll put +}bdf +/exec_grad +{ + AGMCORE_gradientcache exch get exec +}bdf +/graphic_setup +{ + /AGMCORE_graphicsave save def + concat + 0 setgray + 0 setlinecap + 0 setlinejoin + 1 setlinewidth + [] 0 setdash + 10 setmiterlimit + newpath + false setoverprint + false setstrokeadjust + Adobe_AGM_Core/spot_alias get exec + /Adobe_AGM_Image where { + pop + Adobe_AGM_Image/spot_alias 2 copy known{ + get exec + }{ + pop pop + }ifelse + } if + 100 dict begin + /dictstackcount countdictstack def + /showpage {} def + mark +} def +/graphic_cleanup +{ + cleartomark + dictstackcount 1 countdictstack 1 sub {end}for + end + AGMCORE_graphicsave restore +} def +/compose_error_msg +{ + grestoreall initgraphics + /Helvetica findfont 10 scalefont setfont + /AGMCORE_deltaY 100 def + /AGMCORE_deltaX 310 def + clippath pathbbox newpath pop pop 36 add exch 36 add exch moveto + 0 AGMCORE_deltaY rlineto AGMCORE_deltaX 0 rlineto + 0 AGMCORE_deltaY neg rlineto AGMCORE_deltaX neg 0 rlineto closepath + 0 AGMCORE_&setgray + gsave 1 AGMCORE_&setgray fill grestore + 1 setlinewidth gsave stroke grestore + currentpoint AGMCORE_deltaY 15 sub add exch 8 add exch moveto + /AGMCORE_deltaY 12 def + /AGMCORE_tmp 0 def + AGMCORE_err_strings exch get + { + dup 32 eq + { + pop + AGMCORE_str256 0 AGMCORE_tmp getinterval + stringwidth pop currentpoint pop add AGMCORE_deltaX 28 add gt + { + currentpoint AGMCORE_deltaY sub exch pop + clippath pathbbox pop pop pop 44 add exch moveto + } if + AGMCORE_str256 0 AGMCORE_tmp getinterval show ( ) show + 0 1 AGMCORE_str256 length 1 sub + { + AGMCORE_str256 exch 0 put + }for + /AGMCORE_tmp 0 def + } + { + AGMCORE_str256 exch AGMCORE_tmp xpt + /AGMCORE_tmp AGMCORE_tmp 1 add def + } ifelse + } forall +} bdf +/doc_setup{ + Adobe_AGM_Core begin + /AGMCORE_ps_version xdf + /AGMCORE_ps_level xdf + errordict /AGM_handleerror known not{ + errordict /AGM_handleerror errordict /handleerror get put + errordict /handleerror { + Adobe_AGM_Core begin + $error /newerror get AGMCORE_cur_err null ne and{ + $error /newerror false put + AGMCORE_cur_err compose_error_msg + }if + $error /newerror true put + end + errordict /AGM_handleerror get exec + } bind put + }if + /AGMCORE_environ_ok + ps_level AGMCORE_ps_level ge + ps_version AGMCORE_ps_version ge and + AGMCORE_ps_level -1 eq or + def + AGMCORE_environ_ok not + {/AGMCORE_cur_err /AGMCORE_bad_environ def} if + /AGMCORE_&setgray systemdict/setgray get def + level2{ + /AGMCORE_&setcolor systemdict/setcolor get def + /AGMCORE_&setcolorspace systemdict/setcolorspace get def + }if + /AGMCORE_currentbg currentblackgeneration def + /AGMCORE_currentucr currentundercolorremoval def + /AGMCORE_distilling + /product where{ + pop systemdict/setdistillerparams known product (Adobe PostScript Parser) ne and + }{ + false + }ifelse + def + level2 not{ + /xput{ + dup load dup length exch maxlength eq{ + dup dup load dup + length dup 0 eq {pop 1} if 2 mul dict copy def + }if + load begin + def + end + }def + }{ + /xput{ + load 3 1 roll put + }def + }ifelse + /AGMCORE_GSTATE AGMCORE_key_known not{ + /AGMCORE_GSTATE 21 dict def + /AGMCORE_tmpmatrix matrix def + /AGMCORE_gstack 32 array def + /AGMCORE_gstackptr 0 def + /AGMCORE_gstacksaveptr 0 def + /AGMCORE_gstackframekeys 10 def + /AGMCORE_&gsave /gsave ldf + /AGMCORE_&grestore /grestore ldf + /AGMCORE_&grestoreall /grestoreall ldf + /AGMCORE_&save /save ldf + /AGMCORE_gdictcopy { + begin + { def } forall + end + }def + /AGMCORE_gput { + AGMCORE_gstack AGMCORE_gstackptr get + 3 1 roll + put + }def + /AGMCORE_gget { + AGMCORE_gstack AGMCORE_gstackptr get + exch + get + }def + /gsave { + AGMCORE_&gsave + AGMCORE_gstack AGMCORE_gstackptr get + AGMCORE_gstackptr 1 add + dup 32 ge {limitcheck} if + Adobe_AGM_Core exch + /AGMCORE_gstackptr xpt + AGMCORE_gstack AGMCORE_gstackptr get + AGMCORE_gdictcopy + }def + /grestore { + AGMCORE_&grestore + AGMCORE_gstackptr 1 sub + dup AGMCORE_gstacksaveptr lt {1 add} if + Adobe_AGM_Core exch + /AGMCORE_gstackptr xpt + }def + /grestoreall { + AGMCORE_&grestoreall + Adobe_AGM_Core + /AGMCORE_gstackptr AGMCORE_gstacksaveptr put + }def + /save { + AGMCORE_&save + AGMCORE_gstack AGMCORE_gstackptr get + AGMCORE_gstackptr 1 add + dup 32 ge {limitcheck} if + Adobe_AGM_Core begin + /AGMCORE_gstackptr exch def + /AGMCORE_gstacksaveptr AGMCORE_gstackptr def + end + AGMCORE_gstack AGMCORE_gstackptr get + AGMCORE_gdictcopy + }def + 0 1 AGMCORE_gstack length 1 sub { + AGMCORE_gstack exch AGMCORE_gstackframekeys dict put + } for + }if + level3 /AGMCORE_&sysshfill AGMCORE_key_known not and + { + /AGMCORE_&sysshfill systemdict/shfill get def + /AGMCORE_&usrshfill /shfill load def + /AGMCORE_&sysmakepattern systemdict/makepattern get def + /AGMCORE_&usrmakepattern /makepattern load def + }if + /currentcmykcolor [0 0 0 0] AGMCORE_gput + /currentstrokeadjust false AGMCORE_gput + /currentcolorspace [/DeviceGray] AGMCORE_gput + /sep_tint 0 AGMCORE_gput + /devicen_tints [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] AGMCORE_gput + /sep_colorspace_dict null AGMCORE_gput + /devicen_colorspace_dict null AGMCORE_gput + /indexed_colorspace_dict null AGMCORE_gput + /currentcolor_intent () AGMCORE_gput + /customcolor_tint 1 AGMCORE_gput + << + /MaxPatternItem currentsystemparams /MaxPatternCache get + >> + setuserparams + end +}def +/page_setup +{ + /setcmykcolor where{ + pop + Adobe_AGM_Core/AGMCORE_&setcmykcolor /setcmykcolor load put + }if + Adobe_AGM_Core begin + /setcmykcolor + { + 4 copy AGMCORE_cmykbuf astore /currentcmykcolor exch AGMCORE_gput + 1 sub 4 1 roll + 3 { + 3 index add neg dup 0 lt { + pop 0 + } if + 3 1 roll + } repeat + setrgbcolor pop + }ndf + /currentcmykcolor + { + /currentcmykcolor AGMCORE_gget aload pop + }ndf + /setoverprint + { + pop + }ndf + /currentoverprint + { + false + }ndf + /AGMCORE_deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt def + /AGMCORE_cyan_plate 1 0 0 0 test_cmyk_color_plate def + /AGMCORE_magenta_plate 0 1 0 0 test_cmyk_color_plate def + /AGMCORE_yellow_plate 0 0 1 0 test_cmyk_color_plate def + /AGMCORE_black_plate 0 0 0 1 test_cmyk_color_plate def + /AGMCORE_plate_ndx + AGMCORE_cyan_plate{ + 0 + }{ + AGMCORE_magenta_plate{ + 1 + }{ + AGMCORE_yellow_plate{ + 2 + }{ + AGMCORE_black_plate{ + 3 + }{ + 4 + }ifelse + }ifelse + }ifelse + }ifelse + def + /AGMCORE_have_reported_unsupported_color_space false def + /AGMCORE_report_unsupported_color_space + { + AGMCORE_have_reported_unsupported_color_space false eq + { + (Warning: Job contains content that cannot be separated with on-host methods. This content appears on the black plate, and knocks out all other plates.) == + Adobe_AGM_Core /AGMCORE_have_reported_unsupported_color_space true ddf + } if + }def + /AGMCORE_composite_job + AGMCORE_cyan_plate AGMCORE_magenta_plate and AGMCORE_yellow_plate and AGMCORE_black_plate and def + /AGMCORE_in_rip_sep + /AGMCORE_in_rip_sep where{ + pop AGMCORE_in_rip_sep + }{ + AGMCORE_distilling + { + false + }{ + userdict/Adobe_AGM_OnHost_Seps known{ + false + }{ + level2{ + currentpagedevice/Separations 2 copy known{ + get + }{ + pop pop false + }ifelse + }{ + false + }ifelse + }ifelse + }ifelse + }ifelse + def + /AGMCORE_producing_seps AGMCORE_composite_job not AGMCORE_in_rip_sep or def + /AGMCORE_host_sep AGMCORE_producing_seps AGMCORE_in_rip_sep not and def + /AGM_preserve_spots + /AGM_preserve_spots where{ + pop AGM_preserve_spots + }{ + AGMCORE_distilling AGMCORE_producing_seps or + }ifelse + def + /AGM_is_distiller_preserving_spotimages + { + currentdistillerparams/PreserveOverprintSettings known + { + currentdistillerparams/PreserveOverprintSettings get + { + currentdistillerparams/ColorConversionStrategy known + { + currentdistillerparams/ColorConversionStrategy get + /LeaveColorUnchanged eq + }{ + true + }ifelse + }{ + false + }ifelse + }{ + false + }ifelse + }def + /convert_spot_to_process where {pop}{ + /convert_spot_to_process + { + dup map_alias { + /Name get exch pop + } if + dup dup (None) eq exch (All) eq or + { + pop false + }{ + AGMCORE_host_sep + { + gsave + 1 0 0 0 setcmykcolor currentgray 1 exch sub + 0 1 0 0 setcmykcolor currentgray 1 exch sub + 0 0 1 0 setcmykcolor currentgray 1 exch sub + 0 0 0 1 setcmykcolor currentgray 1 exch sub + add add add 0 eq + { + pop false + }{ + false setoverprint + 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor + currentgray 0 eq + }ifelse + grestore + }{ + AGMCORE_distilling + { + pop AGM_is_distiller_preserving_spotimages not + }{ + Adobe_AGM_Core/AGMCORE_name xddf + false + Adobe_AGM_Core/AGMCORE_in_pattern known {Adobe_AGM_Core/AGMCORE_in_pattern get}{false} ifelse + not currentpagedevice/OverrideSeparations known and + { + currentpagedevice/OverrideSeparations get + { + /HqnSpots /ProcSet resourcestatus + { + pop pop pop true + }if + }if + }if + { + AGMCORE_name /HqnSpots /ProcSet findresource /TestSpot get exec not + }{ + gsave + [/Separation AGMCORE_name /DeviceGray {}]setcolorspace + false + currentpagedevice/SeparationColorNames 2 copy known + { + get + { AGMCORE_name eq or}forall + not + }{ + pop pop pop true + }ifelse + grestore + }ifelse + }ifelse + }ifelse + }ifelse + }def + }ifelse + /convert_to_process where {pop}{ + /convert_to_process + { + dup length 0 eq + { + pop false + }{ + AGMCORE_host_sep + { + dup true exch + { + dup (Cyan) eq exch + dup (Magenta) eq 3 -1 roll or exch + dup (Yellow) eq 3 -1 roll or exch + dup (Black) eq 3 -1 roll or + {pop} + {convert_spot_to_process and}ifelse + } + forall + { + true exch + { + dup (Cyan) eq exch + dup (Magenta) eq 3 -1 roll or exch + dup (Yellow) eq 3 -1 roll or exch + (Black) eq or and + }forall + not + }{pop false}ifelse + }{ + false exch + { + dup (Cyan) eq exch + dup (Magenta) eq 3 -1 roll or exch + dup (Yellow) eq 3 -1 roll or exch + dup (Black) eq 3 -1 roll or + {pop} + {convert_spot_to_process or}ifelse + } + forall + }ifelse + }ifelse + }def + }ifelse + /AGMCORE_avoid_L2_sep_space + version cvr 2012 lt + level2 and + AGMCORE_producing_seps not and + def + /AGMCORE_is_cmyk_sep + AGMCORE_cyan_plate AGMCORE_magenta_plate or AGMCORE_yellow_plate or AGMCORE_black_plate or + def + /AGM_avoid_0_cmyk where{ + pop AGM_avoid_0_cmyk + }{ + AGM_preserve_spots + userdict/Adobe_AGM_OnHost_Seps known + userdict/Adobe_AGM_InRip_Seps known or + not and + }ifelse + { + /setcmykcolor[ + { + 4 copy add add add 0 eq currentoverprint and{ + pop 0.0005 + }if + }/exec cvx + /AGMCORE_&setcmykcolor load dup type/operatortype ne{ + /exec cvx + }if + ]cvx def + }if + AGMCORE_host_sep{ + /setcolortransfer + { + AGMCORE_cyan_plate{ + pop pop pop + }{ + AGMCORE_magenta_plate{ + 4 3 roll pop pop pop + }{ + AGMCORE_yellow_plate{ + 4 2 roll pop pop pop + }{ + 4 1 roll pop pop pop + }ifelse + }ifelse + }ifelse + settransfer + } + def + /AGMCORE_get_ink_data + AGMCORE_cyan_plate{ + {pop pop pop} + }{ + AGMCORE_magenta_plate{ + {4 3 roll pop pop pop} + }{ + AGMCORE_yellow_plate{ + {4 2 roll pop pop pop} + }{ + {4 1 roll pop pop pop} + }ifelse + }ifelse + }ifelse + def + /AGMCORE_RemoveProcessColorNames + { + 1 dict begin + /filtername + { + dup /Cyan eq 1 index (Cyan) eq or + {pop (_cyan_)}if + dup /Magenta eq 1 index (Magenta) eq or + {pop (_magenta_)}if + dup /Yellow eq 1 index (Yellow) eq or + {pop (_yellow_)}if + dup /Black eq 1 index (Black) eq or + {pop (_black_)}if + }def + dup type /arraytype eq + {[exch {filtername}forall]} + {filtername}ifelse + end + }def + /AGMCORE_IsSeparationAProcessColor + { + dup (Cyan) eq exch dup (Magenta) eq exch dup (Yellow) eq exch (Black) eq or or or + }def + level3 { + /AGMCORE_IsCurrentColor + { + gsave + false setoverprint + 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor + currentgray 0 eq + grestore + }def + /AGMCORE_filter_functiondatasource + { + 5 dict begin + /data_in xdf + data_in type /stringtype eq + { + /ncomp xdf + /comp xdf + /string_out data_in length ncomp idiv string def + 0 ncomp data_in length 1 sub + { + string_out exch dup ncomp idiv exch data_in exch ncomp getinterval comp get 255 exch sub put + }for + string_out + }{ + string /string_in xdf + /string_out 1 string def + /component xdf + [ + data_in string_in /readstring cvx + [component /get cvx 255 /exch cvx /sub cvx string_out /exch cvx 0 /exch cvx /put cvx string_out]cvx + [/pop cvx ()]cvx /ifelse cvx + ]cvx /ReusableStreamDecode filter + }ifelse + end + }def + /AGMCORE_separateShadingFunction + { + 2 dict begin + /paint? xdf + /channel xdf + begin + FunctionType 0 eq + { + /DataSource channel Range length 2 idiv DataSource AGMCORE_filter_functiondatasource def + currentdict /Decode known + {/Decode Decode channel 2 mul 2 getinterval def}if + paint? not + {/Decode [1 1]def}if + }if + FunctionType 2 eq + { + paint? + { + /C0 [C0 channel get 1 exch sub] def + /C1 [C1 channel get 1 exch sub] def + }{ + /C0 [1] def + /C1 [1] def + }ifelse + }if + FunctionType 3 eq + { + /Functions [Functions {channel paint? AGMCORE_separateShadingFunction} forall] def + }if + currentdict /Range known + {/Range [0 1] def}if + currentdict + end + end + }def + /AGMCORE_separateShading + { + 3 -1 roll begin + currentdict /Function known + { + currentdict /Background known + {[1 index{Background 3 index get 1 exch sub}{1}ifelse]/Background xdf}if + Function 3 1 roll AGMCORE_separateShadingFunction /Function xdf + /ColorSpace [/DeviceGray] def + }{ + ColorSpace dup type /arraytype eq {0 get}if /DeviceCMYK eq + { + /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ /_black_] /DeviceCMYK {}] def + }{ + ColorSpace dup 1 get AGMCORE_RemoveProcessColorNames 1 exch put + }ifelse + ColorSpace 0 get /Separation eq + { + { + [1 /exch cvx /sub cvx]cvx + }{ + [/pop cvx 1]cvx + }ifelse + ColorSpace 3 3 -1 roll put + pop + }{ + { + [exch ColorSpace 1 get length 1 sub exch sub /index cvx 1 /exch cvx /sub cvx ColorSpace 1 get length 1 add 1 /roll cvx ColorSpace 1 get length{/pop cvx} repeat]cvx + }{ + pop [ColorSpace 1 get length {/pop cvx} repeat cvx 1]cvx + }ifelse + ColorSpace 3 3 -1 roll bind put + }ifelse + ColorSpace 2 /DeviceGray put + }ifelse + end + }def + /AGMCORE_separateShadingDict + { + dup /ColorSpace get + dup type /arraytype ne + {[exch]}if + dup 0 get /DeviceCMYK eq + { + exch begin + currentdict + AGMCORE_cyan_plate + {0 true}if + AGMCORE_magenta_plate + {1 true}if + AGMCORE_yellow_plate + {2 true}if + AGMCORE_black_plate + {3 true}if + AGMCORE_plate_ndx 4 eq + {0 false}if + dup not currentoverprint and + {/AGMCORE_ignoreshade true def}if + AGMCORE_separateShading + currentdict + end exch + }if + dup 0 get /Separation eq + { + exch begin + ColorSpace 1 get dup /None ne exch /All ne and + { + ColorSpace 1 get AGMCORE_IsCurrentColor AGMCORE_plate_ndx 4 lt and ColorSpace 1 get AGMCORE_IsSeparationAProcessColor not and + { + ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq + { + /ColorSpace + [ + /Separation + ColorSpace 1 get + /DeviceGray + [ + ColorSpace 3 get /exec cvx + 4 AGMCORE_plate_ndx sub -1 /roll cvx + 4 1 /roll cvx + 3 [/pop cvx]cvx /repeat cvx + 1 /exch cvx /sub cvx + ]cvx + ]def + }{ + AGMCORE_report_unsupported_color_space + AGMCORE_black_plate not + { + currentdict 0 false AGMCORE_separateShading + }if + }ifelse + }{ + currentdict ColorSpace 1 get AGMCORE_IsCurrentColor + 0 exch + dup not currentoverprint and + {/AGMCORE_ignoreshade true def}if + AGMCORE_separateShading + }ifelse + }if + currentdict + end exch + }if + dup 0 get /DeviceN eq + { + exch begin + ColorSpace 1 get convert_to_process + { + ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq + { + /ColorSpace + [ + /DeviceN + ColorSpace 1 get + /DeviceGray + [ + ColorSpace 3 get /exec cvx + 4 AGMCORE_plate_ndx sub -1 /roll cvx + 4 1 /roll cvx + 3 [/pop cvx]cvx /repeat cvx + 1 /exch cvx /sub cvx + ]cvx + ]def + }{ + AGMCORE_report_unsupported_color_space + AGMCORE_black_plate not + { + currentdict 0 false AGMCORE_separateShading + /ColorSpace [/DeviceGray] def + }if + }ifelse + }{ + currentdict + false -1 ColorSpace 1 get + { + AGMCORE_IsCurrentColor + { + 1 add + exch pop true exch exit + }if + 1 add + }forall + exch + dup not currentoverprint and + {/AGMCORE_ignoreshade true def}if + AGMCORE_separateShading + }ifelse + currentdict + end exch + }if + dup 0 get dup /DeviceCMYK eq exch dup /Separation eq exch /DeviceN eq or or not + { + exch begin + ColorSpace dup type /arraytype eq + {0 get}if + /DeviceGray ne + { + AGMCORE_report_unsupported_color_space + AGMCORE_black_plate not + { + ColorSpace 0 get /CIEBasedA eq + { + /ColorSpace [/Separation /_ciebaseda_ /DeviceGray {}] def + }if + ColorSpace 0 get dup /CIEBasedABC eq exch dup /CIEBasedDEF eq exch /DeviceRGB eq or or + { + /ColorSpace [/DeviceN [/_red_ /_green_ /_blue_] /DeviceRGB {}] def + }if + ColorSpace 0 get /CIEBasedDEFG eq + { + /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ /_black_] /DeviceCMYK {}] + }if + currentdict 0 false AGMCORE_separateShading + }if + }if + currentdict + end exch + }if + pop + dup /AGMCORE_ignoreshade known + { + begin + /ColorSpace [/Separation (None) /DeviceGray {}] def + currentdict end + }if + }def + /shfill + { + clonedict + AGMCORE_separateShadingDict + dup /AGMCORE_ignoreshade known + {pop} + {AGMCORE_&sysshfill}ifelse + }def + /makepattern + { + exch + dup /PatternType get 2 eq + { + clonedict + begin + /Shading Shading AGMCORE_separateShadingDict def + currentdict end + exch AGMCORE_&sysmakepattern + }{ + exch AGMCORE_&usrmakepattern + }ifelse + }def + }if + }if + AGMCORE_in_rip_sep{ + /setcustomcolor + { + exch aload pop + dup 7 1 roll inRip_spot_has_ink not { + 4 {4 index mul 4 1 roll} + repeat + /DeviceCMYK setcolorspace + 6 -2 roll pop pop + }{ + Adobe_AGM_Core begin + /AGMCORE_k xdf /AGMCORE_y xdf /AGMCORE_m xdf /AGMCORE_c xdf + end + [/Separation 4 -1 roll /DeviceCMYK + {dup AGMCORE_c mul exch dup AGMCORE_m mul exch dup AGMCORE_y mul exch AGMCORE_k mul} + ] + setcolorspace + }ifelse + setcolor + }ndf + /setseparationgray + { + [/Separation (All) /DeviceGray {}] setcolorspace_opt + 1 exch sub setcolor + }ndf + }{ + /setseparationgray + { + AGMCORE_&setgray + }ndf + }ifelse + /findcmykcustomcolor + { + 5 makereadonlyarray + }ndf + /setcustomcolor + { + exch aload pop pop + 4 {4 index mul 4 1 roll} repeat + setcmykcolor pop + }ndf + /has_color + /colorimage where{ + AGMCORE_producing_seps{ + pop true + }{ + systemdict eq + }ifelse + }{ + false + }ifelse + def + /map_index + { + 1 index mul exch getinterval {255 div} forall + } bdf + /map_indexed_devn + { + Lookup Names length 3 -1 roll cvi map_index + } bdf + /n_color_components + { + base_colorspace_type + dup /DeviceGray eq{ + pop 1 + }{ + /DeviceCMYK eq{ + 4 + }{ + 3 + }ifelse + }ifelse + }bdf + level2{ + /mo /moveto ldf + /li /lineto ldf + /cv /curveto ldf + /knockout_unitsq + { + 1 setgray + 0 0 1 1 rectfill + }def + /level2ScreenFreq{ + begin + 60 + HalftoneType 1 eq{ + pop Frequency + }if + HalftoneType 2 eq{ + pop GrayFrequency + }if + HalftoneType 5 eq{ + pop Default level2ScreenFreq + }if + end + }def + /currentScreenFreq{ + currenthalftone level2ScreenFreq + }def + level2 /setcolorspace AGMCORE_key_known not and{ + /AGMCORE_&&&setcolorspace /setcolorspace ldf + /AGMCORE_ReplaceMappedColor + { + dup type dup /arraytype eq exch /packedarraytype eq or + { + dup 0 get dup /Separation eq + { + pop + dup length array copy + dup dup 1 get + current_spot_alias + { + dup map_alias + { + begin + /sep_colorspace_dict currentdict AGMCORE_gput + pop pop pop + [ + /Separation Name + CSA map_csa + dup /MappedCSA xdf + /sep_colorspace_proc load + ] + dup Name + end + }if + }if + map_reserved_ink_name 1 xpt + }{ + /DeviceN eq + { + dup length array copy + dup dup 1 get [ + exch { + current_spot_alias{ + dup map_alias{ + /Name get exch pop + }if + }if + map_reserved_ink_name + } forall + ] 1 xpt + }if + }ifelse + }if + }def + /setcolorspace + { + dup type dup /arraytype eq exch /packedarraytype eq or + { + dup 0 get /Indexed eq + { + AGMCORE_distilling + { + /PhotoshopDuotoneList where + { + pop false + }{ + true + }ifelse + }{ + true + }ifelse + { + aload pop 3 -1 roll + AGMCORE_ReplaceMappedColor + 3 1 roll 4 array astore + }if + }{ + AGMCORE_ReplaceMappedColor + }ifelse + }if + DeviceN_PS2_inRip_seps {AGMCORE_&&&setcolorspace} if + }def + }if + }{ + /adj + { + currentstrokeadjust{ + transform + 0.25 sub round 0.25 add exch + 0.25 sub round 0.25 add exch + itransform + }if + }def + /mo{ + adj moveto + }def + /li{ + adj lineto + }def + /cv{ + 6 2 roll adj + 6 2 roll adj + 6 2 roll adj curveto + }def + /knockout_unitsq + { + 1 setgray + 8 8 1 [8 0 0 8 0 0] {} image + }def + /currentstrokeadjust{ + /currentstrokeadjust AGMCORE_gget + }def + /setstrokeadjust{ + /currentstrokeadjust exch AGMCORE_gput + }def + /currentScreenFreq{ + currentscreen pop pop + }def + /setcolorspace + { + /currentcolorspace exch AGMCORE_gput + } def + /currentcolorspace + { + /currentcolorspace AGMCORE_gget + } def + /setcolor_devicecolor + { + base_colorspace_type + dup /DeviceGray eq{ + pop setgray + }{ + /DeviceCMYK eq{ + setcmykcolor + }{ + setrgbcolor + }ifelse + }ifelse + }def + /setcolor + { + currentcolorspace 0 get + dup /DeviceGray ne{ + dup /DeviceCMYK ne{ + dup /DeviceRGB ne{ + dup /Separation eq{ + pop + currentcolorspace 3 get exec + currentcolorspace 2 get + }{ + dup /Indexed eq{ + pop + currentcolorspace 3 get dup type /stringtype eq{ + currentcolorspace 1 get n_color_components + 3 -1 roll map_index + }{ + exec + }ifelse + currentcolorspace 1 get + }{ + /AGMCORE_cur_err /AGMCORE_invalid_color_space def + AGMCORE_invalid_color_space + }ifelse + }ifelse + }if + }if + }if + setcolor_devicecolor + } def + }ifelse + /sop /setoverprint ldf + /lw /setlinewidth ldf + /lc /setlinecap ldf + /lj /setlinejoin ldf + /ml /setmiterlimit ldf + /dsh /setdash ldf + /sadj /setstrokeadjust ldf + /gry /setgray ldf + /rgb /setrgbcolor ldf + /cmyk /setcmykcolor ldf + /sep /setsepcolor ldf + /devn /setdevicencolor ldf + /idx /setindexedcolor ldf + /colr /setcolor ldf + /csacrd /set_csa_crd ldf + /sepcs /setsepcolorspace ldf + /devncs /setdevicencolorspace ldf + /idxcs /setindexedcolorspace ldf + /cp /closepath ldf + /clp /clp_npth ldf + /eclp /eoclp_npth ldf + /f /fill ldf + /ef /eofill ldf + /@ /stroke ldf + /nclp /npth_clp ldf + /gset /graphic_setup ldf + /gcln /graphic_cleanup ldf + currentdict{ + dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and { + bind + }if + def + }forall + /currentpagedevice currentpagedevice def +/getrampcolor { +/indx exch def +0 1 NumComp 1 sub { +dup +Samples exch get +dup type /stringtype eq { indx get } if +exch +Scaling exch get aload pop +3 1 roll +mul add +} for +ColorSpaceFamily /Separation eq + { + sep + } + { + ColorSpaceFamily /DeviceN eq + { + devn + } + { + setcolor + }ifelse + }ifelse +} bind def +/sssetbackground { aload pop setcolor } bind def +/RadialShade { +40 dict begin +/ColorSpaceFamily exch def +/background exch def +/ext1 exch def +/ext0 exch def +/BBox exch def +/r2 exch def +/c2y exch def +/c2x exch def +/r1 exch def +/c1y exch def +/c1x exch def +/rampdict exch def +/setinkoverprint where {pop /setinkoverprint{pop}def}if +gsave +BBox length 0 gt { +newpath +BBox 0 get BBox 1 get moveto +BBox 2 get BBox 0 get sub 0 rlineto +0 BBox 3 get BBox 1 get sub rlineto +BBox 2 get BBox 0 get sub neg 0 rlineto +closepath +clip +newpath +} if +c1x c2x eq +{ +c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse +} +{ +/slope c2y c1y sub c2x c1x sub div def +/theta slope 1 atan def +c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if +c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if +} +ifelse +gsave +clippath +c1x c1y translate +theta rotate +-90 rotate +{ pathbbox } stopped +{ 0 0 0 0 } if +/yMax exch def +/xMax exch def +/yMin exch def +/xMin exch def +grestore +xMax xMin eq yMax yMin eq or +{ +grestore +end +} +{ +/max { 2 copy gt { pop } {exch pop} ifelse } bind def +/min { 2 copy lt { pop } {exch pop} ifelse } bind def +rampdict begin +40 dict begin +background length 0 gt { background sssetbackground gsave clippath fill grestore } if +gsave +c1x c1y translate +theta rotate +-90 rotate +/c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def +/c1y 0 def +/c1x 0 def +/c2x 0 def +ext0 { +0 getrampcolor +c2y r2 add r1 sub 0.0001 lt +{ +c1x c1y r1 360 0 arcn +pathbbox +/aymax exch def +/axmax exch def +/aymin exch def +/axmin exch def +/bxMin xMin axmin min def +/byMin yMin aymin min def +/bxMax xMax axmax max def +/byMax yMax aymax max def +bxMin byMin moveto +bxMax byMin lineto +bxMax byMax lineto +bxMin byMax lineto +bxMin byMin lineto +eofill +} +{ +c2y r1 add r2 le +{ +c1x c1y r1 0 360 arc +fill +} +{ +c2x c2y r2 0 360 arc fill +r1 r2 eq +{ +/p1x r1 neg def +/p1y c1y def +/p2x r1 def +/p2y c1y def +p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto +fill +} +{ +/AA r2 r1 sub c2y div def +/theta AA 1 AA dup mul sub sqrt div 1 atan def +/SS1 90 theta add dup sin exch cos div def +/p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def +/p1y p1x SS1 div neg def +/SS2 90 theta sub dup sin exch cos div def +/p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def +/p2y p2x SS2 div neg def +r1 r2 gt +{ +/L1maxX p1x yMin p1y sub SS1 div add def +/L2maxX p2x yMin p2y sub SS2 div add def +} +{ +/L1maxX 0 def +/L2maxX 0 def +}ifelse +p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto +L1maxX L1maxX p1x sub SS1 mul p1y add lineto +fill +} +ifelse +} +ifelse +} ifelse +} if +c1x c2x sub dup mul +c1y c2y sub dup mul +add 0.5 exp +0 dtransform +dup mul exch dup mul add 0.5 exp 72 div +0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt +72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt +1 index 1 index lt { exch } if pop +/hires exch def +hires mul +/numpix exch def +/numsteps NumSamples def +/rampIndxInc 1 def +/subsampling false def +numpix 0 ne +{ +NumSamples numpix div 0.5 gt +{ +/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def +/rampIndxInc NumSamples 1 sub numsteps div def +/subsampling true def +} if +} if +/xInc c2x c1x sub numsteps div def +/yInc c2y c1y sub numsteps div def +/rInc r2 r1 sub numsteps div def +/cx c1x def +/cy c1y def +/radius r1 def +newpath +xInc 0 eq yInc 0 eq rInc 0 eq and and +{ +0 getrampcolor +cx cy radius 0 360 arc +stroke +NumSamples 1 sub getrampcolor +cx cy radius 72 hires div add 0 360 arc +0 setlinewidth +stroke +} +{ +0 +numsteps +{ +dup +subsampling { round cvi } if +getrampcolor +cx cy radius 0 360 arc +/cx cx xInc add def +/cy cy yInc add def +/radius radius rInc add def +cx cy radius 360 0 arcn +eofill +rampIndxInc add +} +repeat +pop +} ifelse +ext1 { +c2y r2 add r1 lt +{ +c2x c2y r2 0 360 arc +fill +} +{ +c2y r1 add r2 sub 0.0001 le +{ +c2x c2y r2 360 0 arcn +pathbbox +/aymax exch def +/axmax exch def +/aymin exch def +/axmin exch def +/bxMin xMin axmin min def +/byMin yMin aymin min def +/bxMax xMax axmax max def +/byMax yMax aymax max def +bxMin byMin moveto +bxMax byMin lineto +bxMax byMax lineto +bxMin byMax lineto +bxMin byMin lineto +eofill +} +{ +c2x c2y r2 0 360 arc fill +r1 r2 eq +{ +/p1x r2 neg def +/p1y c2y def +/p2x r2 def +/p2y c2y def +p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto +fill +} +{ +/AA r2 r1 sub c2y div def +/theta AA 1 AA dup mul sub sqrt div 1 atan def +/SS1 90 theta add dup sin exch cos div def +/p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def +/p1y c2y p1x SS1 div sub def +/SS2 90 theta sub dup sin exch cos div def +/p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def +/p2y c2y p2x SS2 div sub def +r1 r2 lt +{ +/L1maxX p1x yMax p1y sub SS1 div add def +/L2maxX p2x yMax p2y sub SS2 div add def +} +{ +/L1maxX 0 def +/L2maxX 0 def +}ifelse +p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto +L1maxX L1maxX p1x sub SS1 mul p1y add lineto +fill +} +ifelse +} +ifelse +} ifelse +} if +grestore +grestore +end +end +end +} ifelse +} bind def +/GenStrips { +40 dict begin +/ColorSpaceFamily exch def +/background exch def +/ext1 exch def +/ext0 exch def +/BBox exch def +/y2 exch def +/x2 exch def +/y1 exch def +/x1 exch def +/rampdict exch def +/setinkoverprint where {pop /setinkoverprint{pop}def}if +gsave +BBox length 0 gt { +newpath +BBox 0 get BBox 1 get moveto +BBox 2 get BBox 0 get sub 0 rlineto +0 BBox 3 get BBox 1 get sub rlineto +BBox 2 get BBox 0 get sub neg 0 rlineto +closepath +clip +newpath +} if +x1 x2 eq +{ +y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse +} +{ +/slope y2 y1 sub x2 x1 sub div def +/theta slope 1 atan def +x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if +x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if +} +ifelse +gsave +clippath +x1 y1 translate +theta rotate +{ pathbbox } stopped +{ 0 0 0 0 } if +/yMax exch def +/xMax exch def +/yMin exch def +/xMin exch def +grestore +xMax xMin eq yMax yMin eq or +{ +grestore +end +} +{ +rampdict begin +20 dict begin +background length 0 gt { background sssetbackground gsave clippath fill grestore } if +gsave +x1 y1 translate +theta rotate +/xStart 0 def +/xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def +/ySpan yMax yMin sub def +/numsteps NumSamples def +/rampIndxInc 1 def +/subsampling false def +xStart 0 transform +xEnd 0 transform +3 -1 roll +sub dup mul +3 1 roll +sub dup mul +add 0.5 exp 72 div +0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt +72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt +1 index 1 index lt { exch } if pop +mul +/numpix exch def +numpix 0 ne +{ +NumSamples numpix div 0.5 gt +{ +/numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def +/rampIndxInc NumSamples 1 sub numsteps div def +/subsampling true def +} if +} if +ext0 { +0 getrampcolor +xMin xStart lt +{ xMin yMin xMin neg ySpan rectfill } if +} if +/xInc xEnd xStart sub numsteps div def +/x xStart def +0 +numsteps +{ +dup +subsampling { round cvi } if +getrampcolor +x yMin xInc ySpan rectfill +/x x xInc add def +rampIndxInc add +} +repeat +pop +ext1 { +xMax xEnd gt +{ xEnd yMin xMax xEnd sub ySpan rectfill } if +} if +grestore +grestore +end +end +end +} ifelse +} bind def +}def +/page_trailer +{ + end +}def +/doc_trailer{ +}def +systemdict /findcolorrendering known{ + /findcolorrendering systemdict /findcolorrendering get def +}if +systemdict /setcolorrendering known{ + /setcolorrendering systemdict /setcolorrendering get def +}if +/test_cmyk_color_plate +{ + gsave + setcmykcolor currentgray 1 ne + grestore +}def +/inRip_spot_has_ink +{ + dup Adobe_AGM_Core/AGMCORE_name xddf + convert_spot_to_process not +}def +/map255_to_range +{ + 1 index sub + 3 -1 roll 255 div mul add +}def +/set_csa_crd +{ + /sep_colorspace_dict null AGMCORE_gput + begin + CSA map_csa setcolorspace_opt + set_crd + end +} +def +/setsepcolor +{ + /sep_colorspace_dict AGMCORE_gget begin + dup /sep_tint exch AGMCORE_gput + TintProc + end +} def +/setdevicencolor +{ + /devicen_colorspace_dict AGMCORE_gget begin + Names length copy + Names length 1 sub -1 0 + { + /devicen_tints AGMCORE_gget 3 1 roll xpt + } for + TintProc + end +} def +/sep_colorspace_proc +{ + Adobe_AGM_Core/AGMCORE_tmp xddf + /sep_colorspace_dict AGMCORE_gget begin + currentdict/Components known{ + Components aload pop + TintMethod/Lab eq{ + 2 {AGMCORE_tmp mul NComponents 1 roll} repeat + LMax sub AGMCORE_tmp mul LMax add NComponents 1 roll + }{ + TintMethod/Subtractive eq{ + NComponents{ + AGMCORE_tmp mul NComponents 1 roll + }repeat + }{ + NComponents{ + 1 sub AGMCORE_tmp mul 1 add NComponents 1 roll + } repeat + }ifelse + }ifelse + }{ + ColorLookup AGMCORE_tmp ColorLookup length 1 sub mul round cvi get + aload pop + }ifelse + end +} def +/sep_colorspace_gray_proc +{ + Adobe_AGM_Core/AGMCORE_tmp xddf + /sep_colorspace_dict AGMCORE_gget begin + GrayLookup AGMCORE_tmp GrayLookup length 1 sub mul round cvi get + end +} def +/sep_proc_name +{ + dup 0 get + dup /DeviceRGB eq exch /DeviceCMYK eq or level2 not and has_color not and{ + pop [/DeviceGray] + /sep_colorspace_gray_proc + }{ + /sep_colorspace_proc + }ifelse +} def +/setsepcolorspace +{ + current_spot_alias{ + dup begin + Name map_alias{ + exch pop + }if + end + }if + dup /sep_colorspace_dict exch AGMCORE_gput + begin + /MappedCSA CSA map_csa def + Adobe_AGM_Core/AGMCORE_sep_special Name dup () eq exch (All) eq or ddf + AGMCORE_avoid_L2_sep_space{ + [/Indexed MappedCSA sep_proc_name 255 exch + { 255 div } /exec cvx 3 -1 roll [ 4 1 roll load /exec cvx ] cvx + ] setcolorspace_opt + /TintProc { + 255 mul round cvi setcolor + }bdf + }{ + MappedCSA 0 get /DeviceCMYK eq + currentdict/Components known and + AGMCORE_sep_special not and{ + /TintProc [ + Components aload pop Name findcmykcustomcolor + /exch cvx /setcustomcolor cvx + ] cvx bdf + }{ + AGMCORE_host_sep Name (All) eq and{ + /TintProc { + 1 exch sub setseparationgray + }bdf + }{ + AGMCORE_in_rip_sep MappedCSA 0 get /DeviceCMYK eq and + AGMCORE_host_sep or + Name () eq and{ + /TintProc [ + MappedCSA sep_proc_name exch 0 get /DeviceCMYK eq{ + cvx /setcmykcolor cvx + }{ + cvx /setgray cvx + }ifelse + ] cvx bdf + }{ + AGMCORE_producing_seps MappedCSA 0 get dup /DeviceCMYK eq exch /DeviceGray eq or and AGMCORE_sep_special not and{ + /TintProc [ + /dup cvx + MappedCSA sep_proc_name cvx exch + 0 get /DeviceGray eq{ + 1 /exch cvx /sub cvx 0 0 0 4 -1 /roll cvx + }if + /Name cvx /findcmykcustomcolor cvx /exch cvx + AGMCORE_host_sep{ + AGMCORE_is_cmyk_sep + /Name cvx + /AGMCORE_IsSeparationAProcessColor load /exec cvx + /not cvx /and cvx + }{ + Name inRip_spot_has_ink not + }ifelse + [ + /pop cvx 1 + ] cvx /if cvx + /setcustomcolor cvx + ] cvx bdf + }{ + /TintProc /setcolor ldf + [/Separation Name MappedCSA sep_proc_name load ] setcolorspace_opt + }ifelse + }ifelse + }ifelse + }ifelse + }ifelse + set_crd + setsepcolor + end +} def +/additive_blend +{ + 3 dict begin + /numarrays xdf + /numcolors xdf + 0 1 numcolors 1 sub + { + /c1 xdf + 1 + 0 1 numarrays 1 sub + { + 1 exch add /index cvx + c1 /get cvx /mul cvx + }for + numarrays 1 add 1 /roll cvx + }for + numarrays [/pop cvx] cvx /repeat cvx + end +}def +/subtractive_blend +{ + 3 dict begin + /numarrays xdf + /numcolors xdf + 0 1 numcolors 1 sub + { + /c1 xdf + 1 1 + 0 1 numarrays 1 sub + { + 1 3 3 -1 roll add /index cvx + c1 /get cvx /sub cvx /mul cvx + }for + /sub cvx + numarrays 1 add 1 /roll cvx + }for + numarrays [/pop cvx] cvx /repeat cvx + end +}def +/exec_tint_transform +{ + /TintProc [ + /TintTransform cvx /setcolor cvx + ] cvx bdf + MappedCSA setcolorspace_opt +} bdf +/devn_makecustomcolor +{ + 2 dict begin + /names_index xdf + /Names xdf + 1 1 1 1 Names names_index get findcmykcustomcolor + /devicen_tints AGMCORE_gget names_index get setcustomcolor + Names length {pop} repeat + end +} bdf +/setdevicencolorspace +{ + dup /AliasedColorants known {false}{true}ifelse + current_spot_alias and { + 6 dict begin + /names_index 0 def + dup /names_len exch /Names get length def + /new_names names_len array def + /new_LookupTables names_len array def + /alias_cnt 0 def + dup /Names get + { + dup map_alias { + exch pop + dup /ColorLookup known { + dup begin + new_LookupTables names_index ColorLookup put + end + }{ + dup /Components known { + dup begin + new_LookupTables names_index Components put + end + }{ + dup begin + new_LookupTables names_index [null null null null] put + end + } ifelse + } ifelse + new_names names_index 3 -1 roll /Name get put + /alias_cnt alias_cnt 1 add def + }{ + /name xdf + new_names names_index name put + dup /LookupTables known { + dup begin + new_LookupTables names_index LookupTables names_index get put + end + }{ + dup begin + new_LookupTables names_index [null null null null] put + end + } ifelse + } ifelse + /names_index names_index 1 add def + } forall + alias_cnt 0 gt { + /AliasedColorants true def + 0 1 names_len 1 sub { + /names_index xdf + new_LookupTables names_index get 0 get null eq { + dup /Names get names_index get /name xdf + name (Cyan) eq name (Magenta) eq name (Yellow) eq name (Black) eq + or or or not { + /AliasedColorants false def + exit + } if + } if + } for + AliasedColorants { + dup begin + /Names new_names def + /AliasedColorants true def + /LookupTables new_LookupTables def + currentdict /TTTablesIdx known not { + /TTTablesIdx -1 def + } if + currentdict /NComponents known not { + /NComponents TintMethod /Subtractive eq {4}{3}ifelse def + } if + end + } if + }if + end + } if + dup /devicen_colorspace_dict exch AGMCORE_gput + begin + /MappedCSA CSA map_csa def + currentdict /AliasedColorants known { + AliasedColorants + }{ + false + } ifelse + /TintTransform load type /nulltype eq or { + /TintTransform [ + 0 1 Names length 1 sub + { + /TTTablesIdx TTTablesIdx 1 add def + dup LookupTables exch get dup 0 get null eq + { + 1 index + Names exch get + dup (Cyan) eq + { + pop exch + LookupTables length exch sub + /index cvx + 0 0 0 + } + { + dup (Magenta) eq + { + pop exch + LookupTables length exch sub + /index cvx + 0 /exch cvx 0 0 + } + { + (Yellow) eq + { + exch + LookupTables length exch sub + /index cvx + 0 0 3 -1 /roll cvx 0 + } + { + exch + LookupTables length exch sub + /index cvx + 0 0 0 4 -1 /roll cvx + } ifelse + } ifelse + } ifelse + 5 -1 /roll cvx /astore cvx + } + { + dup length 1 sub + LookupTables length 4 -1 roll sub 1 add + /index cvx /mul cvx /round cvx /cvi cvx /get cvx + } ifelse + Names length TTTablesIdx add 1 add 1 /roll cvx + } for + Names length [/pop cvx] cvx /repeat cvx + NComponents Names length + TintMethod /Subtractive eq + { + subtractive_blend + } + { + additive_blend + } ifelse + ] cvx bdf + } if + AGMCORE_host_sep { + Names convert_to_process { + exec_tint_transform + } + { + currentdict /AliasedColorants known { + AliasedColorants not + }{ + false + } ifelse + 5 dict begin + /AvoidAliasedColorants xdf + /painted? false def + /names_index 0 def + /names_len Names length def + Names { + AvoidAliasedColorants { + /currentspotalias current_spot_alias def + false set_spot_alias + } if + AGMCORE_is_cmyk_sep { + dup (Cyan) eq AGMCORE_cyan_plate and exch + dup (Magenta) eq AGMCORE_magenta_plate and exch + dup (Yellow) eq AGMCORE_yellow_plate and exch + (Black) eq AGMCORE_black_plate and or or or { + /devicen_colorspace_dict AGMCORE_gget /TintProc [ + Names names_index /devn_makecustomcolor cvx + ] cvx ddf + /painted? true def + } if + painted? {exit} if + }{ + 0 0 0 0 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq { + /devicen_colorspace_dict AGMCORE_gget /TintProc [ + Names names_index /devn_makecustomcolor cvx + ] cvx ddf + /painted? true def + exit + } if + } ifelse + AvoidAliasedColorants { + currentspotalias set_spot_alias + } if + /names_index names_index 1 add def + } forall + painted? { + /devicen_colorspace_dict AGMCORE_gget /names_index names_index put + }{ + /devicen_colorspace_dict AGMCORE_gget /TintProc [ + names_len [/pop cvx] cvx /repeat cvx 1 /setseparationgray cvx + 0 0 0 0 () /findcmykcustomcolor cvx 0 /setcustomcolor cvx + ] cvx ddf + } ifelse + end + } ifelse + } + { + AGMCORE_in_rip_sep { + Names convert_to_process not + }{ + level3 + } ifelse + { + [/DeviceN Names MappedCSA /TintTransform load] setcolorspace_opt + /TintProc level3 not AGMCORE_in_rip_sep and { + [ + Names /length cvx [/pop cvx] cvx /repeat cvx + ] cvx bdf + }{ + /setcolor ldf + } ifelse + }{ + exec_tint_transform + } ifelse + } ifelse + set_crd + /AliasedColorants false def + end +} def +/setindexedcolorspace +{ + dup /indexed_colorspace_dict exch AGMCORE_gput + begin + currentdict /CSD known { + CSD get_csd /Names known { + CSD get_csd begin + currentdict devncs + AGMCORE_host_sep{ + 4 dict begin + /devnCompCnt Names length def + /NewLookup HiVal 1 add string def + 0 1 HiVal { + /tableIndex xdf + Lookup dup type /stringtype eq { + devnCompCnt tableIndex map_index + }{ + exec + } ifelse + setdevicencolor + currentgray + tableIndex exch + HiVal mul cvi + NewLookup 3 1 roll put + } for + [/Indexed currentcolorspace HiVal NewLookup] setcolorspace_opt + end + }{ + level3 + { + [/Indexed [/DeviceN Names MappedCSA /TintTransform load] HiVal Lookup] setcolorspace_opt + }{ + [/Indexed MappedCSA HiVal + [ + Lookup dup type /stringtype eq + {/exch cvx CSD get_csd /Names get length dup /mul cvx exch /getinterval cvx {255 div} /forall cvx} + {/exec cvx}ifelse + /TintTransform load /exec cvx + ]cvx + ]setcolorspace_opt + }ifelse + } ifelse + end + }{ + } ifelse + set_crd + } + { + /MappedCSA CSA map_csa def + AGMCORE_host_sep level2 not and{ + 0 0 0 0 setcmykcolor + }{ + [/Indexed MappedCSA + level2 not has_color not and{ + dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or{ + pop [/DeviceGray] + }if + HiVal GrayLookup + }{ + HiVal + currentdict/RangeArray known{ + { + /indexed_colorspace_dict AGMCORE_gget begin + Lookup exch + dup HiVal gt{ + pop HiVal + }if + NComponents mul NComponents getinterval {} forall + NComponents 1 sub -1 0{ + RangeArray exch 2 mul 2 getinterval aload pop map255_to_range + NComponents 1 roll + }for + end + } bind + }{ + Lookup + }ifelse + }ifelse + ] setcolorspace_opt + set_crd + }ifelse + }ifelse + end +}def +/setindexedcolor +{ + AGMCORE_host_sep { + /indexed_colorspace_dict AGMCORE_gget dup /CSD known { + begin + CSD get_csd begin + map_indexed_devn + devn + end + end + }{ + AGMCORE_gget/Lookup get 4 3 -1 roll map_index + pop setcmykcolor + } ifelse + }{ + level3 not AGMCORE_in_rip_sep and /indexed_colorspace_dict AGMCORE_gget /CSD known and { + /indexed_colorspace_dict AGMCORE_gget /CSD get get_csd begin + map_indexed_devn + devn + end + } + { + setcolor + } ifelse + }ifelse +} def +/ignoreimagedata +{ + currentoverprint not{ + gsave + dup clonedict begin + 1 setgray + /Decode [0 1] def + /DataSource def + /MultipleDataSources false def + /BitsPerComponent 8 def + currentdict end + systemdict /image get exec + grestore + }if + consumeimagedata +}def +/add_csa +{ + Adobe_AGM_Core begin + /AGMCORE_CSA_cache xput + end +}def +/get_csa_by_name +{ + dup type dup /nametype eq exch /stringtype eq or{ + Adobe_AGM_Core begin + 1 dict begin + /name xdf + AGMCORE_CSA_cache + { + 0 get name eq { + exit + }{ + pop + } ifelse + }forall + end + end + }{ + pop + } ifelse +}def +/map_csa +{ + dup type /nametype eq{ + Adobe_AGM_Core/AGMCORE_CSA_cache get exch get + }if +}def +/add_csd +{ + Adobe_AGM_Core begin + /AGMCORE_CSD_cache xput + end +}def +/get_csd +{ + dup type /nametype eq{ + Adobe_AGM_Core/AGMCORE_CSD_cache get exch get + }if +}def +/pattern_buf_init +{ + /count get 0 0 put +} def +/pattern_buf_next +{ + dup /count get dup 0 get + dup 3 1 roll + 1 add 0 xpt + get +} def +/cachepattern_compress +{ + 5 dict begin + currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def + /patarray 20 dict def + /string_size 16000 def + /readbuffer string_size string def + currentglobal true setglobal + patarray 1 array dup 0 1 put /count xpt + setglobal + /LZWFilter + { + exch + dup length 0 eq { + pop + }{ + patarray dup length 1 sub 3 -1 roll put + } ifelse + {string_size}{0}ifelse string + } /LZWEncode filter def + { + ReadFilter readbuffer readstring + exch LZWFilter exch writestring + not {exit} if + } loop + LZWFilter closefile + patarray + end +}def +/cachepattern +{ + 2 dict begin + currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def + /patarray 20 dict def + currentglobal true setglobal + patarray 1 array dup 0 1 put /count xpt + setglobal + { + ReadFilter 16000 string readstring exch + patarray dup length 1 sub 3 -1 roll put + not {exit} if + } loop + patarray dup dup length 1 sub () put + end +}def +/add_pattern +{ + Adobe_AGM_Core begin + /AGMCORE_pattern_cache xput + end +}def +/get_pattern +{ + dup type /nametype eq{ + Adobe_AGM_Core/AGMCORE_pattern_cache get exch get + dup wrap_paintproc + }if +}def +/wrap_paintproc +{ + statusdict /currentfilenameextend known{ + begin + /OldPaintProc /PaintProc load def + /PaintProc + { + mark exch + dup /OldPaintProc get stopped + {closefile restore end} if + cleartomark + } def + end + } {pop} ifelse +} def +/make_pattern +{ + dup matrix currentmatrix matrix concatmatrix 0 0 3 2 roll itransform + exch 3 index /XStep get 1 index exch 2 copy div cvi mul sub sub + exch 3 index /YStep get 1 index exch 2 copy div cvi mul sub sub + matrix translate exch matrix concatmatrix + 1 index begin + BBox 0 get XStep div cvi XStep mul /xshift exch neg def + BBox 1 get YStep div cvi YStep mul /yshift exch neg def + BBox 0 get xshift add + BBox 1 get yshift add + BBox 2 get xshift add + BBox 3 get yshift add + 4 array astore + /BBox exch def + [ xshift yshift /translate load null /exec load ] dup + 3 /PaintProc load put cvx /PaintProc exch def + end + gsave 0 setgray + makepattern + grestore +}def +/set_pattern +{ + dup /PatternType get 1 eq{ + dup /PaintType get 1 eq{ + currentoverprint sop [/DeviceGray] setcolorspace 0 setgray + }if + }if + setpattern +}def +/setcolorspace_opt +{ + dup currentcolorspace eq{ + pop + }{ + setcolorspace + }ifelse +}def +/updatecolorrendering +{ + currentcolorrendering/Intent known{ + currentcolorrendering/Intent get + }{ + null + }ifelse + Intent ne{ + false + Intent + AGMCORE_CRD_cache { + exch pop + begin + dup Intent eq{ + currentdict setcolorrendering_opt + end + exch pop true exch + exit + }if + end + } forall + pop + not{ + systemdict /findcolorrendering known{ + Intent findcolorrendering pop + /ColorRendering findresource + dup length dict copy + setcolorrendering_opt + }if + }if + }if +} def +/add_crd +{ + AGMCORE_CRD_cache 3 1 roll put +}def +/set_crd +{ + AGMCORE_host_sep not level2 and{ + currentdict/CRD known{ + AGMCORE_CRD_cache CRD get dup null ne{ + setcolorrendering_opt + }{ + pop + }ifelse + }{ + currentdict/Intent known{ + updatecolorrendering + }if + }ifelse + currentcolorspace dup type /arraytype eq + {0 get}if + /DeviceRGB eq + { + currentdict/UCR known + {/UCR}{/AGMCORE_currentucr}ifelse + load setundercolorremoval + currentdict/BG known + {/BG}{/AGMCORE_currentbg}ifelse + load setblackgeneration + }if + }if +}def +/setcolorrendering_opt +{ + dup currentcolorrendering eq{ + pop + }{ + begin + /Intent Intent def + currentdict + end + setcolorrendering + }ifelse +}def +/cpaint_gcomp +{ + convert_to_process Adobe_AGM_Core/AGMCORE_ConvertToProcess xddf + Adobe_AGM_Core/AGMCORE_ConvertToProcess get not + { + (%end_cpaint_gcomp) flushinput + }if +}def +/cpaint_gsep +{ + Adobe_AGM_Core/AGMCORE_ConvertToProcess get + { + (%end_cpaint_gsep) flushinput + }if +}def +/cpaint_gend +{ + newpath +}def +/path_rez +{ + dup 0 ne{ + AGMCORE_deviceDPI exch div + dup 1 lt{ + pop 1 + }if + setflat + }{ + pop + }ifelse +}def +/set_spot_alias_ary +{ + /AGMCORE_SpotAliasAry where{ + pop pop + }{ + Adobe_AGM_Core/AGMCORE_SpotAliasAry xddf + true set_spot_alias + }ifelse +}def +/set_spot_alias +{ + /AGMCORE_SpotAliasAry where{ + /AGMCORE_current_spot_alias 3 -1 roll put + }{ + pop + }ifelse +}def +/current_spot_alias +{ + /AGMCORE_SpotAliasAry where{ + /AGMCORE_current_spot_alias get + }{ + false + }ifelse +}def +/map_alias +{ + /AGMCORE_SpotAliasAry where{ + begin + /AGMCORE_name xdf + false + AGMCORE_SpotAliasAry{ + dup/Name get AGMCORE_name eq{ + save exch + /Adobe_AGM_Core currentdict def + /CSD get get_csd + exch restore + exch pop true + exit + }{ + pop + }ifelse + }forall + end + }{ + pop false + }ifelse +}bdf +/spot_alias +{ + true set_spot_alias + /AGMCORE_&setcustomcolor AGMCORE_key_known not { + Adobe_AGM_Core/AGMCORE_&setcustomcolor /setcustomcolor load put + } if + /customcolor_tint 1 AGMCORE_gput + Adobe_AGM_Core begin + /setcustomcolor + { + dup /customcolor_tint exch AGMCORE_gput + current_spot_alias{ + 1 index 4 get map_alias{ + mark 3 1 roll + setsepcolorspace + counttomark 0 ne{ + setsepcolor + }if + pop + pop + }{ + AGMCORE_&setcustomcolor + }ifelse + }{ + AGMCORE_&setcustomcolor + }ifelse + }bdf + end +}def +/begin_feature +{ + Adobe_AGM_Core/AGMCORE_feature_dictCount countdictstack put + count Adobe_AGM_Core/AGMCORE_feature_opCount 3 -1 roll put + {Adobe_AGM_Core/AGMCORE_feature_ctm matrix currentmatrix put}if +}def +/end_feature +{ + 2 dict begin + /spd /setpagedevice load def + /setpagedevice { get_gstate spd set_gstate } def + stopped{$error/newerror false put}if + end + count Adobe_AGM_Core/AGMCORE_feature_opCount get sub dup 0 gt{{pop}repeat}{pop}ifelse + countdictstack Adobe_AGM_Core/AGMCORE_feature_dictCount get sub dup 0 gt{{end}repeat}{pop}ifelse + {Adobe_AGM_Core/AGMCORE_feature_ctm get setmatrix}if +}def +/set_negative +{ + Adobe_AGM_Core begin + /AGMCORE_inverting exch def + level2{ + currentpagedevice/NegativePrint known{ + currentpagedevice/NegativePrint get Adobe_AGM_Core/AGMCORE_inverting get ne{ + true begin_feature true{ + bdict /NegativePrint Adobe_AGM_Core/AGMCORE_inverting get edict setpagedevice + }end_feature + }if + /AGMCORE_inverting false def + }if + }if + AGMCORE_inverting{ + [{1 exch sub}/exec load dup currenttransfer exch]cvx bind settransfer + gsave newpath clippath 1 /setseparationgray where{pop setseparationgray}{setgray}ifelse + /AGMIRS_&fill where {pop AGMIRS_&fill}{fill} ifelse grestore + }if + end +}def +/lw_save_restore_override { + /md where { + pop + md begin + initializepage + /initializepage{}def + /pmSVsetup{} def + /endp{}def + /pse{}def + /psb{}def + /orig_showpage where + {pop} + {/orig_showpage /showpage load def} + ifelse + /showpage {orig_showpage gR} def + end + }if +}def +/pscript_showpage_override { + /NTPSOct95 where + { + begin + showpage + save + /showpage /restore load def + /restore {exch pop}def + end + }if +}def +/driver_media_override +{ + /md where { + pop + md /initializepage known { + md /initializepage {} put + } if + md /rC known { + md /rC {4{pop}repeat} put + } if + }if + /mysetup where { + /mysetup [1 0 0 1 0 0] put + }if + Adobe_AGM_Core /AGMCORE_Default_CTM matrix currentmatrix put + level2 + {Adobe_AGM_Core /AGMCORE_Default_PageSize currentpagedevice/PageSize get put}if +}def +/driver_check_media_override +{ + /PrepsDict where + {pop} + { + Adobe_AGM_Core /AGMCORE_Default_CTM get matrix currentmatrix ne + Adobe_AGM_Core /AGMCORE_Default_PageSize get type /arraytype eq + { + Adobe_AGM_Core /AGMCORE_Default_PageSize get 0 get currentpagedevice/PageSize get 0 get eq and + Adobe_AGM_Core /AGMCORE_Default_PageSize get 1 get currentpagedevice/PageSize get 1 get eq and + }if + { + Adobe_AGM_Core /AGMCORE_Default_CTM get setmatrix + }if + }ifelse +}def +AGMCORE_err_strings begin + /AGMCORE_bad_environ (Environment not satisfactory for this job. Ensure that the PPD is correct or that the PostScript level requested is supported by this printer. ) def + /AGMCORE_color_space_onhost_seps (This job contains colors that will not separate with on-host methods. ) def + /AGMCORE_invalid_color_space (This job contains an invalid color space. ) def +end +end +systemdict /setpacking known +{ + setpacking +} if +%%EndResource +%%BeginResource: procset Adobe_CoolType_Core 2.23 0 +%%Copyright: Copyright 1997-2003 Adobe Systems Incorporated. All Rights Reserved. +%%Version: 2.23 0 +10 dict begin +/Adobe_CoolType_Passthru currentdict def +/Adobe_CoolType_Core_Defined userdict /Adobe_CoolType_Core known def +Adobe_CoolType_Core_Defined + { /Adobe_CoolType_Core userdict /Adobe_CoolType_Core get def } +if +userdict /Adobe_CoolType_Core 60 dict dup begin put +/Adobe_CoolType_Version 2.23 def +/Level2? + systemdict /languagelevel known dup + { pop systemdict /languagelevel get 2 ge } + if def +Level2? not + { + /currentglobal false def + /setglobal /pop load def + /gcheck { pop false } bind def + /currentpacking false def + /setpacking /pop load def + /SharedFontDirectory 0 dict def + } +if +currentpacking +true setpacking +/@_SaveStackLevels + { + Adobe_CoolType_Data + begin + @opStackCountByLevel @opStackLevel + 2 copy known not + { 2 copy 3 dict dup /args 7 index 5 add array put put get } + { + get dup /args get dup length 3 index lt + { + dup length 5 add array exch + 1 index exch 0 exch putinterval + 1 index exch /args exch put + } + { pop } + ifelse + } + ifelse + begin + count 2 sub 1 index lt + { pop count 1 sub } + if + dup /argCount exch def + dup 0 gt + { + exch 1 index 2 add 1 roll + args exch 0 exch getinterval + astore pop + } + { pop } + ifelse + count 1 sub /restCount exch def + end + /@opStackLevel @opStackLevel 1 add def + countdictstack 1 sub + @dictStackCountByLevel exch @dictStackLevel exch put + /@dictStackLevel @dictStackLevel 1 add def + end + } bind def +/@_RestoreStackLevels + { + Adobe_CoolType_Data + begin + /@opStackLevel @opStackLevel 1 sub def + @opStackCountByLevel @opStackLevel get + begin + count restCount sub dup 0 gt + { { pop } repeat } + { pop } + ifelse + args 0 argCount getinterval {} forall + end + /@dictStackLevel @dictStackLevel 1 sub def + @dictStackCountByLevel @dictStackLevel get + end + countdictstack exch sub dup 0 gt + { { end } repeat } + { pop } + ifelse + } bind def +/@_PopStackLevels + { + Adobe_CoolType_Data + begin + /@opStackLevel @opStackLevel 1 sub def + /@dictStackLevel @dictStackLevel 1 sub def + end + } bind def +/@Raise + { + exch cvx exch errordict exch get exec + stop + } bind def +/@ReRaise + { + cvx $error /errorname get errordict exch get exec + stop + } bind def +/@Stopped + { + 0 @#Stopped + } bind def +/@#Stopped + { + @_SaveStackLevels + stopped + { @_RestoreStackLevels true } + { @_PopStackLevels false } + ifelse + } bind def +/@Arg + { + Adobe_CoolType_Data + begin + @opStackCountByLevel @opStackLevel 1 sub get /args get exch get + end + } bind def +currentglobal true setglobal +/CTHasResourceForAllBug + Level2? + { + 1 dict dup begin + mark + { + (*) { pop stop } 128 string /Category + resourceforall + } + stopped + cleartomark + currentdict eq dup + { end } + if + not + } + { false } + ifelse + def +/CTHasResourceStatusBug + Level2? + { + mark + { /steveamerige /Category resourcestatus } + stopped + { cleartomark true } + { cleartomark currentglobal not } + ifelse + } + { false } + ifelse + def +setglobal +/CTResourceStatus + { + mark 3 1 roll + /Category findresource + begin + ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec + { cleartomark false } + { { 3 2 roll pop true } { cleartomark false } ifelse } + ifelse + end + } bind def +/CTWorkAroundBugs + { + Level2? + { + /cid_PreLoad /ProcSet resourcestatus + { + pop pop + currentglobal + mark + { + (*) + { + dup /CMap CTHasResourceStatusBug + { CTResourceStatus } + { resourcestatus } + ifelse + { + pop dup 0 eq exch 1 eq or + { + dup /CMap findresource gcheck setglobal + /CMap undefineresource + } + { + pop CTHasResourceForAllBug + { exit } + { stop } + ifelse + } + ifelse + } + { pop } + ifelse + } + 128 string /CMap resourceforall + } + stopped + { cleartomark } + stopped pop + setglobal + } + if + } + if + } bind def +/doc_setup + { + Adobe_CoolType_Core + begin + CTWorkAroundBugs + /mov /moveto load def + /nfnt /newencodedfont load def + /mfnt /makefont load def + /sfnt /setfont load def + /ufnt /undefinefont load def + /chp /charpath load def + /awsh /awidthshow load def + /wsh /widthshow load def + /ash /ashow load def + /sh /show load def + end + userdict /Adobe_CoolType_Data 10 dict dup + begin + /AddWidths? false def + /CC 0 def + /charcode 2 string def + /@opStackCountByLevel 32 dict def + /@opStackLevel 0 def + /@dictStackCountByLevel 32 dict def + /@dictStackLevel 0 def + /InVMFontsByCMap 10 dict def + /InVMDeepCopiedFonts 10 dict def + end put + } bind def +/doc_trailer + { + currentdict Adobe_CoolType_Core eq + { end } + if + } bind def +/page_setup + { + Adobe_CoolType_Core begin + } bind def +/page_trailer + { + end + } bind def +/unload + { + systemdict /languagelevel known + { + systemdict/languagelevel get 2 ge + { + userdict/Adobe_CoolType_Core 2 copy known + { undef } + { pop pop } + ifelse + } + if + } + if + } bind def +/ndf + { + 1 index where + { pop pop pop } + { dup xcheck { bind } if def } + ifelse + } def +/findfont systemdict + begin + userdict + begin + /globaldict where { /globaldict get begin } if + dup where pop exch get + /globaldict where { pop end } if + end + end +Adobe_CoolType_Core_Defined + { /systemfindfont exch def } + { + /findfont 1 index def + /systemfindfont exch def + } +ifelse +/undefinefont + { pop } ndf +/copyfont + { + currentglobal 3 1 roll + 1 index gcheck setglobal + dup null eq { 0 } { dup length } ifelse + 2 index length add 1 add dict + begin + exch + { + 1 index /FID eq + { pop pop } + { def } + ifelse + } + forall + dup null eq + { pop } + { { def } forall } + ifelse + currentdict + end + exch setglobal + } bind def +/copyarray + { + currentglobal exch + dup gcheck setglobal + dup length array copy + exch setglobal + } bind def +/newencodedfont + { + currentglobal + { + SharedFontDirectory 3 index known + { SharedFontDirectory 3 index get /FontReferenced known } + { false } + ifelse + } + { + FontDirectory 3 index known + { FontDirectory 3 index get /FontReferenced known } + { + SharedFontDirectory 3 index known + { SharedFontDirectory 3 index get /FontReferenced known } + { false } + ifelse + } + ifelse + } + ifelse + dup + { + 3 index findfont /FontReferenced get + 2 index dup type /nametype eq + {findfont} + if ne + { pop false } + if + } + if + { + pop + 1 index findfont + /Encoding get exch + 0 1 255 + { 2 copy get 3 index 3 1 roll put } + for + pop pop pop + } + { + dup type /nametype eq + { findfont } + if + dup dup maxlength 2 add dict + begin + exch + { + 1 index /FID ne + {def} + {pop pop} + ifelse + } + forall + /FontReferenced exch def + /Encoding exch dup length array copy def + /FontName 1 index dup type /stringtype eq { cvn } if def dup + currentdict + end + definefont def + } + ifelse + } bind def +/SetSubstituteStrategy + { + $SubstituteFont + begin + dup type /dicttype ne + { 0 dict } + if + currentdict /$Strategies known + { + exch $Strategies exch + 2 copy known + { + get + 2 copy maxlength exch maxlength add dict + begin + { def } forall + { def } forall + currentdict + dup /$Init known + { dup /$Init get exec } + if + end + /$Strategy exch def + } + { pop pop pop } + ifelse + } + { pop pop } + ifelse + end + } bind def +/scff + { + $SubstituteFont + begin + dup type /stringtype eq + { dup length exch } + { null } + ifelse + /$sname exch def + /$slen exch def + /$inVMIndex + $sname null eq + { + 1 index $str cvs + dup length $slen sub $slen getinterval cvn + } + { $sname } + ifelse def + end + { findfont } + @Stopped + { + dup length 8 add string exch + 1 index 0 (BadFont:) putinterval + 1 index exch 8 exch dup length string cvs putinterval cvn + { findfont } + @Stopped + { pop /Courier findfont } + if + } + if + $SubstituteFont + begin + /$sname null def + /$slen 0 def + /$inVMIndex null def + end + } bind def +/isWidthsOnlyFont + { + dup /WidthsOnly known + { pop pop true } + { + dup /FDepVector known + { /FDepVector get { isWidthsOnlyFont dup { exit } if } forall } + { + dup /FDArray known + { /FDArray get { isWidthsOnlyFont dup { exit } if } forall } + { pop } + ifelse + } + ifelse + } + ifelse + } bind def +/?str1 256 string def +/?set + { + $SubstituteFont + begin + /$substituteFound false def + /$fontname 4 index def + /$doSmartSub false def + end + 3 index + currentglobal false setglobal exch + /CompatibleFonts /ProcSet resourcestatus + { + pop pop + /CompatibleFonts /ProcSet findresource + begin + dup /CompatibleFont currentexception + 1 index /CompatibleFont true setexception + 1 index /Font resourcestatus + { + pop pop + 3 2 roll setglobal + end + exch + dup findfont + /CompatibleFonts /ProcSet findresource + begin + 3 1 roll exch /CompatibleFont exch setexception + end + } + { + 3 2 roll setglobal + 1 index exch /CompatibleFont exch setexception + end + findfont + $SubstituteFont /$substituteFound true put + } + ifelse + } + { exch setglobal findfont } + ifelse + $SubstituteFont + begin + $substituteFound + { + false + (%%[Using embedded font ) print + 5 index ?str1 cvs print + ( to avoid the font substitution problem noted earlier.]%%\n) print + } + { + dup /FontName known + { + dup /FontName get $fontname eq + 1 index /DistillerFauxFont known not and + /currentdistillerparams where + { pop false 2 index isWidthsOnlyFont not and } + if + } + { false } + ifelse + } + ifelse + exch pop + /$doSmartSub true def + end + { + exch pop exch pop exch + 2 dict dup /Found 3 index put + exch findfont exch + } + { + exch exec + exch dup findfont + dup /FontType get 3 eq + { + exch ?str1 cvs + dup length 1 sub + -1 0 + { + exch dup 2 index get 42 eq + { + exch 0 exch getinterval cvn 4 1 roll 3 2 roll pop + exit + } + {exch pop} ifelse + }for + } + { + exch pop + } ifelse + 2 dict dup /Downloaded 6 5 roll put + } + ifelse + dup /FontName 4 index put copyfont definefont pop + } bind def +/?str2 256 string def +/?add + { + 1 index type /integertype eq + { exch true 4 2 } + { false 3 1 } + ifelse + roll + 1 index findfont + dup /Widths known + { + Adobe_CoolType_Data /AddWidths? true put + gsave dup 1000 scalefont setfont + } + if + /Downloaded known + { + exec + exch + { + exch ?str2 cvs exch + findfont /Downloaded get 1 dict begin /Downloaded 1 index def ?str1 cvs length + ?str1 1 index 1 add 3 index putinterval + exch length 1 add 1 index add + ?str1 2 index (*) putinterval + ?str1 0 2 index getinterval cvn findfont + ?str1 3 index (+) putinterval + 2 dict dup /FontName ?str1 0 6 index getinterval cvn put + dup /Downloaded Downloaded put end copyfont + dup /FontName get exch definefont pop pop pop + } + { + pop + } + ifelse + } + { + pop + exch + { + findfont + dup /Found get + dup length exch ?str1 cvs pop + ?str1 1 index (+) putinterval + ?str1 1 index 1 add 4 index ?str2 cvs putinterval + ?str1 exch 0 exch 5 4 roll ?str2 cvs length 1 add add getinterval cvn + 1 dict exch 1 index exch /FontName exch put copyfont + dup /FontName get exch definefont pop + } + { + pop + } + ifelse + } + ifelse + Adobe_CoolType_Data /AddWidths? get + { grestore Adobe_CoolType_Data /AddWidths? false put } + if + } bind def +/?sh + { + currentfont /Downloaded known { exch } if pop + } bind def +/?chp + { + currentfont /Downloaded known { pop } { false chp } ifelse + } bind def +/?mv + { + currentfont /Downloaded known { moveto pop pop } { pop pop moveto } ifelse + } bind def +setpacking +userdict /$SubstituteFont 25 dict put +1 dict + begin + /SubstituteFont + dup $error exch 2 copy known + { get } + { pop pop { pop /Courier } bind } + ifelse def + /currentdistillerparams where dup + { + pop pop + currentdistillerparams /CannotEmbedFontPolicy 2 copy known + { get /Error eq } + { pop pop false } + ifelse + } + if not + { + countdictstack array dictstack 0 get + begin + userdict + begin + $SubstituteFont + begin + /$str 128 string def + /$fontpat 128 string def + /$slen 0 def + /$sname null def + /$match false def + /$fontname null def + /$substituteFound false def + /$inVMIndex null def + /$doSmartSub true def + /$depth 0 def + /$fontname null def + /$italicangle 26.5 def + /$dstack null def + /$Strategies 10 dict dup + begin + /$Type3Underprint + { + currentglobal exch false setglobal + 11 dict + begin + /UseFont exch + $WMode 0 ne + { + dup length dict copy + dup /WMode $WMode put + /UseFont exch definefont + } + if def + /FontName $fontname dup type /stringtype eq { cvn } if def + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /Encoding 256 array dup 0 1 255 { /.notdef put dup } for pop def + /FontBBox [ 0 0 0 0 ] def + /CCInfo 7 dict dup + begin + /cc null def + /x 0 def + /y 0 def + end def + /BuildChar + { + exch + begin + CCInfo + begin + 1 string dup 0 3 index put exch pop + /cc exch def + UseFont 1000 scalefont setfont + cc stringwidth /y exch def /x exch def + x y setcharwidth + $SubstituteFont /$Strategy get /$Underprint get exec + 0 0 moveto cc show + x y moveto + end + end + } bind def + currentdict + end + exch setglobal + } bind def + /$GetaTint + 2 dict dup + begin + /$BuildFont + { + dup /WMode known + { dup /WMode get } + { 0 } + ifelse + /$WMode exch def + $fontname exch + dup /FontName known + { + dup /FontName get + dup type /stringtype eq { cvn } if + } + { /unnamedfont } + ifelse + exch + Adobe_CoolType_Data /InVMDeepCopiedFonts get + 1 index /FontName get known + { + pop + Adobe_CoolType_Data /InVMDeepCopiedFonts get + 1 index get + null copyfont + } + { $deepcopyfont } + ifelse + exch 1 index exch /FontBasedOn exch put + dup /FontName $fontname dup type /stringtype eq { cvn } if put + definefont + Adobe_CoolType_Data /InVMDeepCopiedFonts get + begin + dup /FontBasedOn get 1 index def + end + } bind def + /$Underprint + { + gsave + x abs y abs gt + { /y 1000 def } + { /x -1000 def 500 120 translate } + ifelse + Level2? + { + [ /Separation (All) /DeviceCMYK { 0 0 0 1 pop } ] + setcolorspace + } + { 0 setgray } + ifelse + 10 setlinewidth + x .8 mul + [ 7 3 ] + { + y mul 8 div 120 sub x 10 div exch moveto + 0 y 4 div neg rlineto + dup 0 rlineto + 0 y 4 div rlineto + closepath + gsave + Level2? + { .2 setcolor } + { .8 setgray } + ifelse + fill grestore + stroke + } + forall + pop + grestore + } bind def + end def + /$Oblique + 1 dict dup + begin + /$BuildFont + { + currentglobal exch dup gcheck setglobal + null copyfont + begin + /FontBasedOn + currentdict /FontName known + { + FontName + dup type /stringtype eq { cvn } if + } + { /unnamedfont } + ifelse + def + /FontName $fontname dup type /stringtype eq { cvn } if def + /currentdistillerparams where + { pop } + { + /FontInfo currentdict /FontInfo known + { FontInfo null copyfont } + { 2 dict } + ifelse + dup + begin + /ItalicAngle $italicangle def + /FontMatrix FontMatrix + [ 1 0 ItalicAngle dup sin exch cos div 1 0 0 ] + matrix concatmatrix readonly + end + 4 2 roll def + def + } + ifelse + FontName currentdict + end + definefont + exch setglobal + } bind def + end def + /$None + 1 dict dup + begin + /$BuildFont {} bind def + end def + end def + /$Oblique SetSubstituteStrategy + /$findfontByEnum + { + dup type /stringtype eq { cvn } if + dup /$fontname exch def + $sname null eq + { $str cvs dup length $slen sub $slen getinterval } + { pop $sname } + ifelse + $fontpat dup 0 (fonts/*) putinterval exch 7 exch putinterval + /$match false def + $SubstituteFont /$dstack countdictstack array dictstack put + mark + { + $fontpat 0 $slen 7 add getinterval + { /$match exch def exit } + $str filenameforall + } + stopped + { + cleardictstack + currentdict + true + $SubstituteFont /$dstack get + { + exch + { + 1 index eq + { pop false } + { true } + ifelse + } + { begin false } + ifelse + } + forall + pop + } + if + cleartomark + /$slen 0 def + $match false ne + { $match (fonts/) anchorsearch pop pop cvn } + { /Courier } + ifelse + } bind def + /$ROS 1 dict dup + begin + /Adobe 4 dict dup + begin + /Japan1 [ /Ryumin-Light /HeiseiMin-W3 + /GothicBBB-Medium /HeiseiKakuGo-W5 + /HeiseiMaruGo-W4 /Jun101-Light ] def + /Korea1 [ /HYSMyeongJo-Medium /HYGoThic-Medium ] def + /GB1 [ /STSong-Light /STHeiti-Regular ] def + /CNS1 [ /MKai-Medium /MHei-Medium ] def + end def + end def + /$cmapname null def + /$deepcopyfont + { + dup /FontType get 0 eq + { + 1 dict dup /FontName /copied put copyfont + begin + /FDepVector FDepVector copyarray + 0 1 2 index length 1 sub + { + 2 copy get $deepcopyfont + dup /FontName /copied put + /copied exch definefont + 3 copy put pop pop + } + for + def + currentdict + end + } + { $Strategies /$Type3Underprint get exec } + ifelse + } bind def + /$buildfontname + { + dup /CIDFont findresource /CIDSystemInfo get + begin + Registry length Ordering length Supplement 8 string cvs + 3 copy length 2 add add add string + dup 5 1 roll dup 0 Registry putinterval + dup 4 index (-) putinterval + dup 4 index 1 add Ordering putinterval + 4 2 roll add 1 add 2 copy (-) putinterval + end + 1 add 2 copy 0 exch getinterval $cmapname $fontpat cvs exch + anchorsearch + { pop pop 3 2 roll putinterval cvn /$cmapname exch def } + { pop pop pop pop pop } + ifelse + length + $str 1 index (-) putinterval 1 add + $str 1 index $cmapname $fontpat cvs putinterval + $cmapname length add + $str exch 0 exch getinterval cvn + } bind def + /$findfontByROS + { + /$fontname exch def + $ROS Registry 2 copy known + { + get Ordering 2 copy known + { get } + { pop pop [] } + ifelse + } + { pop pop [] } + ifelse + false exch + { + dup /CIDFont resourcestatus + { + pop pop + save + 1 index /CIDFont findresource + dup /WidthsOnly known + { dup /WidthsOnly get } + { false } + ifelse + exch pop + exch restore + { pop } + { exch pop true exit } + ifelse + } + { pop } + ifelse + } + forall + { $str cvs $buildfontname } + { + false (*) + { + save exch + dup /CIDFont findresource + dup /WidthsOnly known + { dup /WidthsOnly get not } + { true } + ifelse + exch /CIDSystemInfo get + dup /Registry get Registry eq + exch /Ordering get Ordering eq and and + { exch restore exch pop true exit } + { pop restore } + ifelse + } + $str /CIDFont resourceforall + { $buildfontname } + { $fontname $findfontByEnum } + ifelse + } + ifelse + } bind def + end + end + currentdict /$error known currentdict /languagelevel known and dup + { pop $error /SubstituteFont known } + if + dup + { $error } + { Adobe_CoolType_Core } + ifelse + begin + { + /SubstituteFont + /CMap /Category resourcestatus + { + pop pop + { + $SubstituteFont + begin + /$substituteFound true def + dup length $slen gt + $sname null ne or + $slen 0 gt and + { + $sname null eq + { dup $str cvs dup length $slen sub $slen getinterval cvn } + { $sname } + ifelse + Adobe_CoolType_Data /InVMFontsByCMap get + 1 index 2 copy known + { + get + false exch + { + pop + currentglobal + { + GlobalFontDirectory 1 index known + { exch pop true exit } + { pop } + ifelse + } + { + FontDirectory 1 index known + { exch pop true exit } + { + GlobalFontDirectory 1 index known + { exch pop true exit } + { pop } + ifelse + } + ifelse + } + ifelse + } + forall + } + { pop pop false } + ifelse + { + exch pop exch pop + } + { + dup /CMap resourcestatus + { + pop pop + dup /$cmapname exch def + /CMap findresource /CIDSystemInfo get { def } forall + $findfontByROS + } + { + 128 string cvs + dup (-) search + { + 3 1 roll search + { + 3 1 roll pop + { dup cvi } + stopped + { pop pop pop pop pop $findfontByEnum } + { + 4 2 roll pop pop + exch length + exch + 2 index length + 2 index + sub + exch 1 sub -1 0 + { + $str cvs dup length + 4 index + 0 + 4 index + 4 3 roll add + getinterval + exch 1 index exch 3 index exch + putinterval + dup /CMap resourcestatus + { + pop pop + 4 1 roll pop pop pop + dup /$cmapname exch def + /CMap findresource /CIDSystemInfo get { def } forall + $findfontByROS + true exit + } + { pop } + ifelse + } + for + dup type /booleantype eq + { pop } + { pop pop pop $findfontByEnum } + ifelse + } + ifelse + } + { pop pop pop $findfontByEnum } + ifelse + } + { pop pop $findfontByEnum } + ifelse + } + ifelse + } + ifelse + } + { //SubstituteFont exec } + ifelse + /$slen 0 def + end + } + } + { + { + $SubstituteFont + begin + /$substituteFound true def + dup length $slen gt + $sname null ne or + $slen 0 gt and + { $findfontByEnum } + { //SubstituteFont exec } + ifelse + end + } + } + ifelse + bind readonly def + Adobe_CoolType_Core /scfindfont /systemfindfont load put + } + { + /scfindfont + { + $SubstituteFont + begin + dup systemfindfont + dup /FontName known + { dup /FontName get dup 3 index ne } + { /noname true } + ifelse + dup + { + /$origfontnamefound 2 index def + /$origfontname 4 index def /$substituteFound true def + } + if + exch pop + { + $slen 0 gt + $sname null ne + 3 index length $slen gt or and + { + pop dup $findfontByEnum findfont + dup maxlength 1 add dict + begin + { 1 index /FID eq { pop pop } { def } ifelse } + forall + currentdict + end + definefont + dup /FontName known { dup /FontName get } { null } ifelse + $origfontnamefound ne + { + $origfontname $str cvs print + ( substitution revised, using ) print + dup /FontName known + { dup /FontName get } { (unspecified font) } + ifelse + $str cvs print (.\n) print + } + if + } + { exch pop } + ifelse + } + { exch pop } + ifelse + end + } bind def + } + ifelse + end + end + Adobe_CoolType_Core_Defined not + { + Adobe_CoolType_Core /findfont + { + $SubstituteFont + begin + $depth 0 eq + { + /$fontname 1 index dup type /stringtype ne { $str cvs } if def + /$substituteFound false def + } + if + /$depth $depth 1 add def + end + scfindfont + $SubstituteFont + begin + /$depth $depth 1 sub def + $substituteFound $depth 0 eq and + { + $inVMIndex null ne + { dup $inVMIndex $AddInVMFont } + if + $doSmartSub + { + currentdict /$Strategy known + { $Strategy /$BuildFont get exec } + if + } + if + } + if + end + } bind put + } + if + } + if + end +/$AddInVMFont + { + exch /FontName 2 copy known + { + get + 1 dict dup begin exch 1 index gcheck def end exch + Adobe_CoolType_Data /InVMFontsByCMap get exch + $DictAdd + } + { pop pop pop } + ifelse + } bind def +/$DictAdd + { + 2 copy known not + { 2 copy 4 index length dict put } + if + Level2? not + { + 2 copy get dup maxlength exch length 4 index length add lt + 2 copy get dup length 4 index length add exch maxlength 1 index lt + { + 2 mul dict + begin + 2 copy get { forall } def + 2 copy currentdict put + end + } + { pop } + ifelse + } + if + get + begin + { def } + forall + end + } bind def +end +end +%%EndResource +%%BeginResource: procset Adobe_CoolType_Utility_MAKEOCF 1.19 0 +%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. +%%Version: 1.19 0 +systemdict /languagelevel known dup + { currentglobal false setglobal } + { false } +ifelse +exch +userdict /Adobe_CoolType_Utility 2 copy known + { 2 copy get dup maxlength 25 add dict copy } + { 25 dict } +ifelse put +Adobe_CoolType_Utility + begin + /ct_Level2? exch def + /ct_Clone? 1183615869 internaldict dup + /CCRun known not + exch /eCCRun known not + ct_Level2? and or def +ct_Level2? + { globaldict begin currentglobal true setglobal } +if + /ct_AddStdCIDMap + ct_Level2? + { { + ((Hex) 57 StartData + 0615 1e27 2c39 1c60 d8a8 cc31 fe2b f6e0 + 7aa3 e541 e21c 60d8 a8c9 c3d0 6d9e 1c60 + d8a8 c9c2 02d7 9a1c 60d8 a849 1c60 d8a8 + cc36 74f4 1144 b13b 77) 0 () /SubFileDecode filter cvx exec + } } + { { + eexec + } } + ifelse bind def +userdict /cid_extensions known +dup { cid_extensions /cid_UpdateDB known and } if + { + cid_extensions + begin + /cid_GetCIDSystemInfo + { + 1 index type /stringtype eq + { exch cvn exch } + if + cid_extensions + begin + dup load 2 index known + { + 2 copy + cid_GetStatusInfo + dup null ne + { + 1 index load + 3 index get + dup null eq + { pop pop cid_UpdateDB } + { + exch + 1 index /Created get eq + { exch pop exch pop } + { pop cid_UpdateDB } + ifelse + } + ifelse + } + { pop cid_UpdateDB } + ifelse + } + { cid_UpdateDB } + ifelse + end + } bind def + end + } +if +ct_Level2? + { end setglobal } +if + /ct_UseNativeCapability? systemdict /composefont known def + /ct_MakeOCF 35 dict def + /ct_Vars 25 dict def + /ct_GlyphDirProcs 6 dict def + /ct_BuildCharDict 15 dict dup + begin + /charcode 2 string def + /dst_string 1500 string def + /nullstring () def + /usewidths? true def + end def + ct_Level2? { setglobal } { pop } ifelse + ct_GlyphDirProcs + begin + /GetGlyphDirectory + { + systemdict /languagelevel known + { pop /CIDFont findresource /GlyphDirectory get } + { + 1 index /CIDFont findresource /GlyphDirectory + get dup type /dicttype eq + { + dup dup maxlength exch length sub 2 index lt + { + dup length 2 index add dict copy 2 index + /CIDFont findresource/GlyphDirectory 2 index put + } + if + } + if + exch pop exch pop + } + ifelse + + + } def + /+ + { + systemdict /languagelevel known + { + currentglobal false setglobal + 3 dict begin + /vm exch def + } + { 1 dict begin } + ifelse + /$ exch def + systemdict /languagelevel known + { + vm setglobal + /gvm currentglobal def + $ gcheck setglobal + } + if + ? { $ begin } if + } def + /? { $ type /dicttype eq } def + /| { + userdict /Adobe_CoolType_Data known + { + Adobe_CoolType_Data /AddWidths? known + { + currentdict Adobe_CoolType_Data + begin + begin + AddWidths? + { + Adobe_CoolType_Data /CC 3 index put + ? { def } { $ 3 1 roll put } ifelse + CC charcode exch 1 index 0 2 index 256 idiv put + 1 index exch 1 exch 256 mod put + stringwidth 2 array astore + currentfont /Widths get exch CC exch put + } + { ? { def } { $ 3 1 roll put } ifelse } + ifelse + end + end + } + { ? { def } { $ 3 1 roll put } ifelse } ifelse + } + { ? { def } { $ 3 1 roll put } ifelse } + ifelse + } def + /! + { + ? { end } if + systemdict /languagelevel known + { gvm setglobal } + if + end + } def + /: { string currentfile exch readstring pop } executeonly def + end + ct_MakeOCF + begin + /ct_cHexEncoding + [/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/c10/c11/c12 + /c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/c23/c24/c25 + /c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/c36/c37/c38 + /c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/c49/c4A/c4B + /c4C/c4D/c4E/c4F/c50/c51/c52/c53/c54/c55/c56/c57/c58/c59/c5A/c5B/c5C/c5D/c5E + /c5F/c60/c61/c62/c63/c64/c65/c66/c67/c68/c69/c6A/c6B/c6C/c6D/c6E/c6F/c70/c71 + /c72/c73/c74/c75/c76/c77/c78/c79/c7A/c7B/c7C/c7D/c7E/c7F/c80/c81/c82/c83/c84 + /c85/c86/c87/c88/c89/c8A/c8B/c8C/c8D/c8E/c8F/c90/c91/c92/c93/c94/c95/c96/c97 + /c98/c99/c9A/c9B/c9C/c9D/c9E/c9F/cA0/cA1/cA2/cA3/cA4/cA5/cA6/cA7/cA8/cA9/cAA + /cAB/cAC/cAD/cAE/cAF/cB0/cB1/cB2/cB3/cB4/cB5/cB6/cB7/cB8/cB9/cBA/cBB/cBC/cBD + /cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/cCE/cCF/cD0 + /cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/cE1/cE2/cE3 + /cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/cF4/cF5/cF6 + /cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def + /ct_CID_STR_SIZE 8000 def + /ct_mkocfStr100 100 string def + /ct_defaultFontMtx [.001 0 0 .001 0 0] def + /ct_1000Mtx [1000 0 0 1000 0 0] def + /ct_raise {exch cvx exch errordict exch get exec stop} bind def + /ct_reraise + { cvx $error /errorname get (Error: ) print dup ( ) cvs print + errordict exch get exec stop + } bind def + /ct_cvnsi + { + 1 index add 1 sub 1 exch 0 4 1 roll + { + 2 index exch get + exch 8 bitshift + add + } + for + exch pop + } bind def + /ct_GetInterval + { + Adobe_CoolType_Utility /ct_BuildCharDict get + begin + /dst_index 0 def + dup dst_string length gt + { dup string /dst_string exch def } + if + 1 index ct_CID_STR_SIZE idiv + /arrayIndex exch def + 2 index arrayIndex get + 2 index + arrayIndex ct_CID_STR_SIZE mul + sub + { + dup 3 index add 2 index length le + { + 2 index getinterval + dst_string dst_index 2 index putinterval + length dst_index add /dst_index exch def + exit + } + { + 1 index length 1 index sub + dup 4 1 roll + getinterval + dst_string dst_index 2 index putinterval + pop dup dst_index add /dst_index exch def + sub + /arrayIndex arrayIndex 1 add def + 2 index dup length arrayIndex gt + { arrayIndex get } + { + pop + exit + } + ifelse + 0 + } + ifelse + } + loop + pop pop pop + dst_string 0 dst_index getinterval + end + } bind def + ct_Level2? + { + /ct_resourcestatus + currentglobal mark true setglobal + { /unknowninstancename /Category resourcestatus } + stopped + { cleartomark setglobal true } + { cleartomark currentglobal not exch setglobal } + ifelse + { + { + mark 3 1 roll /Category findresource + begin + ct_Vars /vm currentglobal put + ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec + { cleartomark false } + { { 3 2 roll pop true } { cleartomark false } ifelse } + ifelse + ct_Vars /vm get setglobal + end + } + } + { { resourcestatus } } + ifelse bind def + /CIDFont /Category ct_resourcestatus + { pop pop } + { + currentglobal true setglobal + /Generic /Category findresource + dup length dict copy + dup /InstanceType /dicttype put + /CIDFont exch /Category defineresource pop + setglobal + } + ifelse + ct_UseNativeCapability? + { + /CIDInit /ProcSet findresource begin + 12 dict begin + begincmap + /CIDSystemInfo 3 dict dup begin + /Registry (Adobe) def + /Ordering (Identity) def + /Supplement 0 def + end def + /CMapName /Identity-H def + /CMapVersion 1.000 def + /CMapType 1 def + 1 begincodespacerange + <0000> + endcodespacerange + 1 begincidrange + <0000> 0 + endcidrange + endcmap + CMapName currentdict /CMap defineresource pop + end + end + } + if + } + { + /ct_Category 2 dict begin + /CIDFont 10 dict def + /ProcSet 2 dict def + currentdict + end + def + /defineresource + { + ct_Category 1 index 2 copy known + { + get + dup dup maxlength exch length eq + { + dup length 10 add dict copy + ct_Category 2 index 2 index put + } + if + 3 index 3 index put + pop exch pop + } + { pop pop /defineresource /undefined ct_raise } + ifelse + } bind def + /findresource + { + ct_Category 1 index 2 copy known + { + get + 2 index 2 copy known + { get 3 1 roll pop pop} + { pop pop /findresource /undefinedresource ct_raise } + ifelse + } + { pop pop /findresource /undefined ct_raise } + ifelse + } bind def + /resourcestatus + { + ct_Category 1 index 2 copy known + { + get + 2 index known + exch pop exch pop + { + 0 -1 true + } + { + false + } + ifelse + } + { pop pop /findresource /undefined ct_raise } + ifelse + } bind def + /ct_resourcestatus /resourcestatus load def + } + ifelse + /ct_CIDInit 2 dict + begin + /ct_cidfont_stream_init + { + { + dup (Binary) eq + { + pop + null + currentfile + ct_Level2? + { + { cid_BYTE_COUNT () /SubFileDecode filter } + stopped + { pop pop pop } + if + } + if + /readstring load + exit + } + if + dup (Hex) eq + { + pop + currentfile + ct_Level2? + { + { null exch /ASCIIHexDecode filter /readstring } + stopped + { pop exch pop (>) exch /readhexstring } + if + } + { (>) exch /readhexstring } + ifelse + load + exit + } + if + /StartData /typecheck ct_raise + } + loop + cid_BYTE_COUNT ct_CID_STR_SIZE le + { + 2 copy cid_BYTE_COUNT string exch exec + pop + 1 array dup + 3 -1 roll + 0 exch put + } + { + cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi + dup array exch 2 sub 0 exch 1 exch + { + 2 copy + 5 index + ct_CID_STR_SIZE + string + 6 index exec + pop + put + pop + } + for + 2 index + cid_BYTE_COUNT ct_CID_STR_SIZE mod string + 3 index exec + pop + 1 index exch + 1 index length 1 sub + exch put + } + ifelse + cid_CIDFONT exch /GlyphData exch put + 2 index null eq + { + pop pop pop + } + { + pop /readstring load + 1 string exch + { + 3 copy exec + pop + dup length 0 eq + { + pop pop pop pop pop + true exit + } + if + 4 index + eq + { + pop pop pop pop + false exit + } + if + } + loop + pop + } + ifelse + } bind def + /StartData + { + mark + { + currentdict + dup /FDArray get 0 get /FontMatrix get + 0 get 0.001 eq + { + dup /CDevProc known not + { + /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known + { get } + { + pop pop + { pop pop pop pop pop 0 -1000 7 index 2 div 880 } + } + ifelse + def + } + if + } + { + /CDevProc + { + pop pop pop pop pop + 0 + 1 cid_temp /cid_CIDFONT get + /FDArray get 0 get + /FontMatrix get 0 get div + 7 index 2 div + 1 index 0.88 mul + } def + } + ifelse + /cid_temp 15 dict def + cid_temp + begin + /cid_CIDFONT exch def + 3 copy pop + dup /cid_BYTE_COUNT exch def 0 gt + { + ct_cidfont_stream_init + FDArray + { + /Private get + dup /SubrMapOffset known + { + begin + /Subrs SubrCount array def + Subrs + SubrMapOffset + SubrCount + SDBytes + ct_Level2? + { + currentdict dup /SubrMapOffset undef + dup /SubrCount undef + /SDBytes undef + } + if + end + /cid_SD_BYTES exch def + /cid_SUBR_COUNT exch def + /cid_SUBR_MAP_OFFSET exch def + /cid_SUBRS exch def + cid_SUBR_COUNT 0 gt + { + GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval + 0 cid_SD_BYTES ct_cvnsi + 0 1 cid_SUBR_COUNT 1 sub + { + exch 1 index + 1 add + cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add + GlyphData exch cid_SD_BYTES ct_GetInterval + 0 cid_SD_BYTES ct_cvnsi + cid_SUBRS 4 2 roll + GlyphData exch + 4 index + 1 index + sub + ct_GetInterval + dup length string copy put + } + for + pop + } + if + } + { pop } + ifelse + } + forall + } + if + cleartomark pop pop + end + CIDFontName currentdict /CIDFont defineresource pop + end end + } + stopped + { cleartomark /StartData ct_reraise } + if + } bind def + currentdict + end def + /ct_saveCIDInit + { + /CIDInit /ProcSet ct_resourcestatus + { true } + { /CIDInitC /ProcSet ct_resourcestatus } + ifelse + { + pop pop + /CIDInit /ProcSet findresource + ct_UseNativeCapability? + { pop null } + { /CIDInit ct_CIDInit /ProcSet defineresource pop } + ifelse + } + { /CIDInit ct_CIDInit /ProcSet defineresource pop null } + ifelse + ct_Vars exch /ct_oldCIDInit exch put + } bind def + /ct_restoreCIDInit + { + ct_Vars /ct_oldCIDInit get dup null ne + { /CIDInit exch /ProcSet defineresource pop } + { pop } + ifelse + } bind def + /ct_BuildCharSetUp + { + 1 index + begin + CIDFont + begin + Adobe_CoolType_Utility /ct_BuildCharDict get + begin + /ct_dfCharCode exch def + /ct_dfDict exch def + CIDFirstByte ct_dfCharCode add + dup CIDCount ge + { pop 0 } + if + /cid exch def + { + GlyphDirectory cid 2 copy known + { get } + { pop pop nullstring } + ifelse + dup length FDBytes sub 0 gt + { + dup + FDBytes 0 ne + { 0 FDBytes ct_cvnsi } + { pop 0 } + ifelse + /fdIndex exch def + dup length FDBytes sub FDBytes exch getinterval + /charstring exch def + exit + } + { + pop + cid 0 eq + { /charstring nullstring def exit } + if + /cid 0 def + } + ifelse + } + loop + } def + /ct_SetCacheDevice + { + 0 0 moveto + dup stringwidth + 3 -1 roll + true charpath + pathbbox + 0 -1000 + 7 index 2 div 880 + setcachedevice2 + 0 0 moveto + } def + /ct_CloneSetCacheProc + { + 1 eq + { + stringwidth + pop -2 div -880 + 0 -1000 setcharwidth + moveto + } + { + usewidths? + { + currentfont /Widths get cid + 2 copy known + { get exch pop aload pop } + { pop pop stringwidth } + ifelse + } + { stringwidth } + ifelse + setcharwidth + 0 0 moveto + } + ifelse + } def + /ct_Type3ShowCharString + { + ct_FDDict fdIndex 2 copy known + { get } + { + currentglobal 3 1 roll + 1 index gcheck setglobal + ct_Type1FontTemplate dup maxlength dict copy + begin + FDArray fdIndex get + dup /FontMatrix 2 copy known + { get } + { pop pop ct_defaultFontMtx } + ifelse + /FontMatrix exch dup length array copy def + /Private get + /Private exch def + /Widths rootfont /Widths get def + /CharStrings 1 dict dup /.notdef + dup length string copy put def + currentdict + end + /ct_Type1Font exch definefont + dup 5 1 roll put + setglobal + } + ifelse + dup /CharStrings get 1 index /Encoding get + ct_dfCharCode get charstring put + rootfont /WMode 2 copy known + { get } + { pop pop 0 } + ifelse + exch + 1000 scalefont setfont + ct_str1 0 ct_dfCharCode put + ct_str1 exch ct_dfSetCacheProc + ct_SyntheticBold + { + currentpoint + ct_str1 show + newpath + moveto + ct_str1 true charpath + ct_StrokeWidth setlinewidth + stroke + } + { ct_str1 show } + ifelse + } def + /ct_Type4ShowCharString + { + ct_dfDict ct_dfCharCode charstring + FDArray fdIndex get + dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not + { ct_1000Mtx matrix concatmatrix concat } + { pop } + ifelse + /Private get + Adobe_CoolType_Utility /ct_Level2? get not + { + ct_dfDict /Private + 3 -1 roll + { put } + 1183615869 internaldict /superexec get exec + } + if + 1183615869 internaldict + Adobe_CoolType_Utility /ct_Level2? get + { 1 index } + { 3 index /Private get mark 6 1 roll } + ifelse + dup /RunInt known + { /RunInt get } + { pop /CCRun } + ifelse + get exec + Adobe_CoolType_Utility /ct_Level2? get not + { cleartomark } + if + } bind def + /ct_BuildCharIncremental + { + { + Adobe_CoolType_Utility /ct_MakeOCF get begin + ct_BuildCharSetUp + ct_ShowCharString + } + stopped + { stop } + if + end + end + end + end + } bind def + /BaseFontNameStr (BF00) def + /ct_Type1FontTemplate 14 dict + begin + /FontType 1 def + /FontMatrix [0.001 0 0 0.001 0 0] def + /FontBBox [-250 -250 1250 1250] def + /Encoding ct_cHexEncoding def + /PaintType 0 def + currentdict + end def + /BaseFontTemplate 11 dict + begin + /FontMatrix [0.001 0 0 0.001 0 0] def + /FontBBox [-250 -250 1250 1250] def + /Encoding ct_cHexEncoding def + /BuildChar /ct_BuildCharIncremental load def + ct_Clone? + { + /FontType 3 def + /ct_ShowCharString /ct_Type3ShowCharString load def + /ct_dfSetCacheProc /ct_CloneSetCacheProc load def + /ct_SyntheticBold false def + /ct_StrokeWidth 1 def + } + { + /FontType 4 def + /Private 1 dict dup /lenIV 4 put def + /CharStrings 1 dict dup /.notdef put def + /PaintType 0 def + /ct_ShowCharString /ct_Type4ShowCharString load def + } + ifelse + /ct_str1 1 string def + currentdict + end def + /BaseFontDictSize BaseFontTemplate length 5 add def + /ct_matrixeq + { + true 0 1 5 + { + dup 4 index exch get exch 3 index exch get eq and + dup not + { exit } + if + } + for + exch pop exch pop + } bind def + /ct_makeocf + { + 15 dict + begin + exch /WMode exch def + exch /FontName exch def + /FontType 0 def + /FMapType 2 def + dup /FontMatrix known + { dup /FontMatrix get /FontMatrix exch def } + { /FontMatrix matrix def } + ifelse + /bfCount 1 index /CIDCount get 256 idiv 1 add + dup 256 gt { pop 256} if def + /Encoding + 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for + bfCount 1 255 { 2 copy bfCount put pop } for + def + /FDepVector bfCount dup 256 lt { 1 add } if array def + BaseFontTemplate BaseFontDictSize dict copy + begin + /CIDFont exch def + CIDFont /FontBBox known + { CIDFont /FontBBox get /FontBBox exch def } + if + CIDFont /CDevProc known + { CIDFont /CDevProc get /CDevProc exch def } + if + currentdict + end + BaseFontNameStr 3 (0) putinterval + 0 1 bfCount dup 256 eq { 1 sub } if + { + FDepVector exch + 2 index BaseFontDictSize dict copy + begin + dup /CIDFirstByte exch 256 mul def + FontType 3 eq + { /ct_FDDict 2 dict def } + if + currentdict + end + 1 index 16 + BaseFontNameStr 2 2 getinterval cvrs pop + BaseFontNameStr exch definefont + put + } + for + ct_Clone? + { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def } + if + FontName + currentdict + end + definefont + ct_Clone? + { + gsave + dup 1000 scalefont setfont + ct_BuildCharDict + begin + /usewidths? false def + currentfont /Widths get + begin + exch /CIDFont get /GlyphDirectory get + { + pop + dup charcode exch 1 index 0 2 index 256 idiv put + 1 index exch 1 exch 256 mod put + stringwidth 2 array astore def + } + forall + end + /usewidths? true def + end + grestore + } + { exch pop } + ifelse + } bind def + /ct_ComposeFont + { + ct_UseNativeCapability? + { + 2 index /CMap ct_resourcestatus + { pop pop exch pop } + { + /CIDInit /ProcSet findresource + begin + 12 dict + begin + begincmap + /CMapName 3 index def + /CMapVersion 1.000 def + /CMapType 1 def + exch /WMode exch def + /CIDSystemInfo 3 dict dup + begin + /Registry (Adobe) def + /Ordering + CMapName ct_mkocfStr100 cvs + (Adobe-) search + { + pop pop + (-) search + { + dup length string copy + exch pop exch pop + } + { pop (Identity)} + ifelse + } + { pop (Identity) } + ifelse + def + /Supplement 0 def + end def + 1 begincodespacerange + <0000> + endcodespacerange + 1 begincidrange + <0000> 0 + endcidrange + endcmap + CMapName currentdict /CMap defineresource pop + end + end + } + ifelse + composefont + } + { + 3 2 roll pop + 0 get /CIDFont findresource + ct_makeocf + } + ifelse + } bind def + /ct_MakeIdentity + { + ct_UseNativeCapability? + { + 1 index /CMap ct_resourcestatus + { pop pop } + { + /CIDInit /ProcSet findresource begin + 12 dict begin + begincmap + /CMapName 2 index def + /CMapVersion 1.000 def + /CMapType 1 def + /CIDSystemInfo 3 dict dup + begin + /Registry (Adobe) def + /Ordering + CMapName ct_mkocfStr100 cvs + (Adobe-) search + { + pop pop + (-) search + { dup length string copy exch pop exch pop } + { pop (Identity) } + ifelse + } + { pop (Identity) } + ifelse + def + /Supplement 0 def + end def + 1 begincodespacerange + <0000> + endcodespacerange + 1 begincidrange + <0000> 0 + endcidrange + endcmap + CMapName currentdict /CMap defineresource pop + end + end + } + ifelse + composefont + } + { + exch pop + 0 get /CIDFont findresource + ct_makeocf + } + ifelse + } bind def + currentdict readonly pop + end + end +%%EndResource +%%BeginResource: procset Adobe_CoolType_Utility_T42 1.0 0 +%%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. +%%Version: 1.0 0 +userdict /ct_T42Dict 15 dict put +ct_T42Dict begin +/Is2015? +{ + version + cvi + 2015 + ge +} bind def +/AllocGlyphStorage +{ + Is2015? + { + pop + } + { + {string} forall + } ifelse +} bind def +/Type42DictBegin +{ + 25 dict begin + /FontName exch def + /CharStrings 256 dict + begin + /.notdef 0 def + currentdict + end def + /Encoding exch def + /PaintType 0 def + /FontType 42 def + /FontMatrix [1 0 0 1 0 0] def + 4 array astore cvx /FontBBox exch def + /sfnts +} bind def +/Type42DictEnd +{ + currentdict dup /FontName get exch definefont end + ct_T42Dict exch + dup /FontName get exch put +} bind def +/RD {string currentfile exch readstring pop} executeonly def +/PrepFor2015 +{ + Is2015? + { + /GlyphDirectory + 16 + dict def + sfnts 0 get + dup + 2 index + (glyx) + putinterval + 2 index + (locx) + putinterval + pop + pop + } + { + pop + pop + } ifelse +} bind def +/AddT42Char +{ + Is2015? + { + /GlyphDirectory get + begin + def + end + pop + pop + } + { + /sfnts get + 4 index + get + 3 index + 2 index + putinterval + pop + pop + pop + pop + } ifelse +} bind def +end +%%EndResource +Adobe_CoolType_Core begin /$Oblique SetSubstituteStrategy end +%%BeginResource: procset Adobe_AGM_Image 1.0 0 +%%Version: 1.0 0 +%%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. +systemdict /setpacking known +{ + currentpacking + true setpacking +} if +userdict /Adobe_AGM_Image 75 dict dup begin put +/Adobe_AGM_Image_Id /Adobe_AGM_Image_1.0_0 def +/nd{ + null def +}bind def +/AGMIMG_&image nd +/AGMIMG_&colorimage nd +/AGMIMG_&imagemask nd +/AGMIMG_mbuf () def +/AGMIMG_ybuf () def +/AGMIMG_kbuf () def +/AGMIMG_c 0 def +/AGMIMG_m 0 def +/AGMIMG_y 0 def +/AGMIMG_k 0 def +/AGMIMG_tmp nd +/AGMIMG_imagestring0 nd +/AGMIMG_imagestring1 nd +/AGMIMG_imagestring2 nd +/AGMIMG_imagestring3 nd +/AGMIMG_imagestring4 nd +/AGMIMG_imagestring5 nd +/AGMIMG_cnt nd +/AGMIMG_fsave nd +/AGMIMG_colorAry nd +/AGMIMG_override nd +/AGMIMG_name nd +/AGMIMG_maskSource nd +/invert_image_samples nd +/knockout_image_samples nd +/img nd +/sepimg nd +/devnimg nd +/idximg nd +/doc_setup +{ + Adobe_AGM_Core begin + Adobe_AGM_Image begin + /AGMIMG_&image systemdict/image get def + /AGMIMG_&imagemask systemdict/imagemask get def + /colorimage where{ + pop + /AGMIMG_&colorimage /colorimage ldf + }if + end + end +}def +/page_setup +{ + Adobe_AGM_Image begin + /AGMIMG_ccimage_exists {/customcolorimage where + { + pop + /Adobe_AGM_OnHost_Seps where + { + pop false + }{ + /Adobe_AGM_InRip_Seps where + { + pop false + }{ + true + }ifelse + }ifelse + }{ + false + }ifelse + }bdf + level2{ + /invert_image_samples + { + Adobe_AGM_Image/AGMIMG_tmp Decode length ddf + /Decode [ Decode 1 get Decode 0 get] def + }def + /knockout_image_samples + { + Operator/imagemask ne{ + /Decode [1 1] def + }if + }def + }{ + /invert_image_samples + { + {1 exch sub} currenttransfer addprocs settransfer + }def + /knockout_image_samples + { + { pop 1 } currenttransfer addprocs settransfer + }def + }ifelse + /img /imageormask ldf + /sepimg /sep_imageormask ldf + /devnimg /devn_imageormask ldf + /idximg /indexed_imageormask ldf + /_ctype 7 def + currentdict{ + dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and{ + bind + }if + def + }forall +}def +/page_trailer +{ + end +}def +/doc_trailer +{ +}def +/imageormask_sys +{ + begin + save mark + level2{ + currentdict + Operator /imagemask eq{ + AGMIMG_&imagemask + }{ + use_mask { + level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation}ifelse + }{ + AGMIMG_&image + }ifelse + }ifelse + }{ + Width Height + Operator /imagemask eq{ + Decode 0 get 1 eq Decode 1 get 0 eq and + ImageMatrix /DataSource load + AGMIMG_&imagemask + }{ + BitsPerComponent ImageMatrix /DataSource load + AGMIMG_&image + }ifelse + }ifelse + cleartomark restore + end +}def +/overprint_plate +{ + currentoverprint { + 0 get dup type /nametype eq { + dup /DeviceGray eq{ + pop AGMCORE_black_plate not + }{ + /DeviceCMYK eq{ + AGMCORE_is_cmyk_sep not + }if + }ifelse + }{ + false exch + { + AGMOHS_sepink eq or + } forall + not + } ifelse + }{ + pop false + }ifelse +}def +/process_mask_L3 +{ + dup begin + /ImageType 1 def + end + 4 dict begin + /DataDict exch def + /ImageType 3 def + /InterleaveType 3 def + /MaskDict 9 dict begin + /ImageType 1 def + /Width DataDict dup /MaskWidth known {/MaskWidth}{/Width} ifelse get def + /Height DataDict dup /MaskHeight known {/MaskHeight}{/Height} ifelse get def + /ImageMatrix [Width 0 0 Height neg 0 Height] def + /NComponents 1 def + /BitsPerComponent 1 def + /Decode [0 1] def + /DataSource AGMIMG_maskSource def + currentdict end def + currentdict end +}def +/use_mask +{ + dup type /dicttype eq + { + dup /Mask known { + dup /Mask get { + level3 + {true} + { + dup /MaskWidth known {dup /MaskWidth get 1 index /Width get eq}{true}ifelse exch + dup /MaskHeight known {dup /MaskHeight get 1 index /Height get eq}{true}ifelse + 3 -1 roll and + } ifelse + } + {false} ifelse + } + {false} ifelse + } + {false} ifelse +}def +/make_line_source +{ + begin + MultipleDataSources { + [ + Decode length 2 div cvi {Width string} repeat + ] + }{ + Width Decode length 2 div mul cvi string + }ifelse + end +}def +/datasource_to_str +{ + exch dup type + dup /filetype eq { + pop exch readstring + }{ + /arraytype eq { + exec exch copy + }{ + pop + }ifelse + }ifelse + pop +}def +/masked_image_simulation +{ + 3 dict begin + dup make_line_source /line_source xdf + /mask_source AGMIMG_maskSource /LZWDecode filter def + dup /Width get 8 div ceiling cvi string /mask_str xdf + begin + gsave + 0 1 translate 1 -1 Height div scale + 1 1 Height { + pop + gsave + MultipleDataSources { + 0 1 DataSource length 1 sub { + dup DataSource exch get + exch line_source exch get + datasource_to_str + } for + }{ + DataSource line_source datasource_to_str + } ifelse + << + /PatternType 1 + /PaintProc [ + /pop cvx + << + /ImageType 1 + /Width Width + /Height 1 + /ImageMatrix Width 1.0 sub 1 matrix scale 0.5 0 matrix translate matrix concatmatrix + /MultipleDataSources MultipleDataSources + /DataSource line_source + /BitsPerComponent BitsPerComponent + /Decode Decode + >> + /image cvx + ] cvx + /BBox [0 0 Width 1] + /XStep Width + /YStep 1 + /PaintType 1 + /TilingType 2 + >> + matrix makepattern set_pattern + << + /ImageType 1 + /Width Width + /Height 1 + /ImageMatrix Width 1 matrix scale + /MultipleDataSources false + /DataSource mask_source mask_str readstring pop + /BitsPerComponent 1 + /Decode [0 1] + >> + imagemask + grestore + 0 1 translate + } for + grestore + end + end +}def +/imageormask +{ + begin + SkipImageProc { + currentdict consumeimagedata + } + { + save mark + level2 AGMCORE_host_sep not and{ + currentdict + Operator /imagemask eq DeviceN_PS2 not and { + imagemask + }{ + AGMCORE_in_rip_sep currentoverprint and currentcolorspace 0 get /DeviceGray eq and{ + [/Separation /Black /DeviceGray {}] setcolorspace + /Decode [ Decode 1 get Decode 0 get ] def + }if + use_mask { + level3 {process_mask_L3 image}{masked_image_simulation}ifelse + }{ + DeviceN_NoneName DeviceN_PS2 Indexed_DeviceN level3 not and or or AGMCORE_in_rip_sep and + { + Names convert_to_process not { + 2 dict begin + /imageDict xdf + /names_index 0 def + gsave + imageDict write_image_file { + Names { + dup (None) ne { + [/Separation 3 -1 roll /DeviceGray {1 exch sub}] setcolorspace + Operator imageDict read_image_file + names_index 0 eq {true setoverprint} if + /names_index names_index 1 add def + }{ + pop + } ifelse + } forall + close_image_file + } if + grestore + end + }{ + Operator /imagemask eq { + imagemask + }{ + image + } ifelse + } ifelse + }{ + Operator /imagemask eq { + imagemask + }{ + image + } ifelse + } ifelse + }ifelse + }ifelse + }{ + Width Height + Operator /imagemask eq{ + Decode 0 get 1 eq Decode 1 get 0 eq and + ImageMatrix /DataSource load + /Adobe_AGM_OnHost_Seps where { + pop imagemask + }{ + currentgray 1 ne{ + currentdict imageormask_sys + }{ + currentoverprint not{ + 1 AGMCORE_&setgray + currentdict imageormask_sys + }{ + currentdict ignoreimagedata + }ifelse + }ifelse + }ifelse + }{ + BitsPerComponent ImageMatrix + MultipleDataSources{ + 0 1 NComponents 1 sub{ + DataSource exch get + }for + }{ + /DataSource load + }ifelse + Operator /colorimage eq{ + AGMCORE_host_sep{ + MultipleDataSources level2 or NComponents 4 eq and{ + AGMCORE_is_cmyk_sep{ + MultipleDataSources{ + /DataSource [ + DataSource 0 get /exec cvx + DataSource 1 get /exec cvx + DataSource 2 get /exec cvx + DataSource 3 get /exec cvx + /AGMCORE_get_ink_data cvx + ] cvx def + }{ + /DataSource + Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul + /DataSource load + filter_cmyk 0 () /SubFileDecode filter def + }ifelse + /Decode [ Decode 0 get Decode 1 get ] def + /MultipleDataSources false def + /NComponents 1 def + /Operator /image def + invert_image_samples + 1 AGMCORE_&setgray + currentdict imageormask_sys + }{ + currentoverprint not Operator/imagemask eq and{ + 1 AGMCORE_&setgray + currentdict imageormask_sys + }{ + currentdict ignoreimagedata + }ifelse + }ifelse + }{ + MultipleDataSources NComponents AGMIMG_&colorimage + }ifelse + }{ + true NComponents colorimage + }ifelse + }{ + Operator /image eq{ + AGMCORE_host_sep{ + /DoImage true def + HostSepColorImage{ + invert_image_samples + }{ + AGMCORE_black_plate not Operator/imagemask ne and{ + /DoImage false def + currentdict ignoreimagedata + }if + }ifelse + 1 AGMCORE_&setgray + DoImage + {currentdict imageormask_sys} if + }{ + use_mask { + level3 {process_mask_L3 image}{masked_image_simulation}ifelse + }{ + image + }ifelse + }ifelse + }{ + Operator/knockout eq{ + pop pop pop pop pop + currentcolorspace overprint_plate not{ + knockout_unitsq + }if + }if + }ifelse + }ifelse + }ifelse + }ifelse + cleartomark restore + }ifelse + end +}def +/sep_imageormask +{ + /sep_colorspace_dict AGMCORE_gget begin + /MappedCSA CSA map_csa def + begin + SkipImageProc { + currentdict consumeimagedata + } + { + save mark + AGMCORE_avoid_L2_sep_space{ + /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def + }if + AGMIMG_ccimage_exists + MappedCSA 0 get /DeviceCMYK eq and + currentdict/Components known and + Name () ne and + Name (All) ne and + Operator /image eq and + AGMCORE_producing_seps not and + level2 not and + { + Width Height BitsPerComponent ImageMatrix + [ + /DataSource load /exec cvx + { + 0 1 2 index length 1 sub{ + 1 index exch + 2 copy get 255 xor put + }for + } /exec cvx + ] cvx bind + MappedCSA 0 get /DeviceCMYK eq{ + Components aload pop + }{ + 0 0 0 Components aload pop 1 exch sub + }ifelse + Name findcmykcustomcolor + customcolorimage + }{ + AGMCORE_producing_seps not{ + level2{ + AGMCORE_avoid_L2_sep_space not currentcolorspace 0 get /Separation ne and{ + [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt + /sep_tint AGMCORE_gget setcolor + }if + currentdict imageormask + }{ + currentdict + Operator /imagemask eq{ + imageormask + }{ + sep_imageormask_lev1 + }ifelse + }ifelse + }{ + AGMCORE_host_sep{ + Operator/knockout eq{ + currentdict/ImageMatrix get concat + knockout_unitsq + }{ + currentgray 1 ne{ + AGMCORE_is_cmyk_sep Name (All) ne and{ + level2{ + [ /Separation Name [/DeviceGray] + { + sep_colorspace_proc AGMCORE_get_ink_data + 1 exch sub + } bind + ] AGMCORE_&setcolorspace + /sep_tint AGMCORE_gget AGMCORE_&setcolor + currentdict imageormask_sys + }{ + currentdict + Operator /imagemask eq{ + imageormask_sys + }{ + sep_image_lev1_sep + }ifelse + }ifelse + }{ + Operator/imagemask ne{ + invert_image_samples + }if + currentdict imageormask_sys + }ifelse + }{ + currentoverprint not Name (All) eq or Operator/imagemask eq and{ + currentdict imageormask_sys + }{ + currentoverprint not + { + gsave + knockout_unitsq + grestore + }if + currentdict consumeimagedata + }ifelse + }ifelse + }ifelse + }{ + currentcolorspace 0 get /Separation ne{ + [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt + /sep_tint AGMCORE_gget setcolor + }if + currentoverprint + MappedCSA 0 get /DeviceCMYK eq and + Name inRip_spot_has_ink not and + Name (All) ne and { + imageormask_l2_overprint + }{ + currentdict imageormask + }ifelse + }ifelse + }ifelse + }ifelse + cleartomark restore + }ifelse + end + end +}def +/decode_image_sample +{ + 4 1 roll exch dup 5 1 roll + sub 2 4 -1 roll exp 1 sub div mul add +} bdf +/colorSpaceElemCnt +{ + currentcolorspace 0 get dup /DeviceCMYK eq { + pop 4 + } + { + /DeviceRGB eq { + pop 3 + }{ + 1 + } ifelse + } ifelse +} bdf +/devn_sep_datasource +{ + 1 dict begin + /dataSource xdf + [ + 0 1 dataSource length 1 sub { + dup currentdict /dataSource get /exch cvx /get cvx /exec cvx + /exch cvx names_index /ne cvx [ /pop cvx ] cvx /if cvx + } for + ] cvx bind + end +} bdf +/devn_alt_datasource +{ + 11 dict begin + /srcDataStrs xdf + /dstDataStr xdf + /convProc xdf + /origcolorSpaceElemCnt xdf + /origMultipleDataSources xdf + /origBitsPerComponent xdf + /origDecode xdf + /origDataSource xdf + /dsCnt origMultipleDataSources {origDataSource length}{1}ifelse def + /samplesNeedDecoding + 0 0 1 origDecode length 1 sub { + origDecode exch get add + } for + origDecode length 2 div div + dup 1 eq { + /decodeDivisor 2 origBitsPerComponent exp 1 sub def + } if + 2 origBitsPerComponent exp 1 sub ne + def + [ + 0 1 dsCnt 1 sub [ + currentdict /origMultipleDataSources get { + dup currentdict /origDataSource get exch get dup type + }{ + currentdict /origDataSource get dup type + } ifelse + dup /filetype eq { + pop currentdict /srcDataStrs get 3 -1 /roll cvx /get cvx /readstring cvx /pop cvx + }{ + /stringtype ne { + /exec cvx + } if + currentdict /srcDataStrs get /exch cvx 3 -1 /roll cvx /xpt cvx + } ifelse + ] cvx /for cvx + currentdict /srcDataStrs get 0 /get cvx /length cvx 0 /ne cvx [ + 0 1 Width 1 sub [ + Adobe_AGM_Utils /AGMUTIL_ndx /xddf cvx + currentdict /origMultipleDataSources get { + 0 1 dsCnt 1 sub [ + Adobe_AGM_Utils /AGMUTIL_ndx1 /xddf cvx + currentdict /srcDataStrs get /AGMUTIL_ndx1 /load cvx /get cvx /AGMUTIL_ndx /load cvx /get cvx + samplesNeedDecoding { + currentdict /decodeDivisor known { + currentdict /decodeDivisor get /div cvx + }{ + currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvxs + BitsPerComponent /decode_image_sample load /exec cvx + } ifelse + } if + ] cvx /for cvx + }{ + Adobe_AGM_Utils /AGMUTIL_ndx1 0 /ddf cvx + currentdict /srcDataStrs get 0 /get cvx /AGMUTIL_ndx /load cvx + currentdict /origDecode get length 2 idiv dup 3 1 /roll cvx /mul cvx /exch cvx /getinterval cvx + [ + samplesNeedDecoding { + currentdict /decodeDivisor known { + currentdict /decodeDivisor get /div cvx + }{ + currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvx + BitsPerComponent /decode_image_sample load /exec cvx + Adobe_AGM_Utils /AGMUTIL_ndx1 /AGMUTIL_ndx1 /load cvx 1 /add cvx /ddf cvx + } ifelse + } if + ] cvx /forall cvx + } ifelse + currentdict /convProc get /exec cvx + currentdict /origcolorSpaceElemCnt get 1 sub -1 0 [ + currentdict /dstDataStr get 3 1 /roll cvx /AGMUTIL_ndx /load cvx currentdict /origcolorSpaceElemCnt get /mul cvx /add cvx /exch cvx + currentdict /convProc get /filter_indexed_devn load ne { + 255 /mul cvx /cvi cvx + } if + /put cvx + ] cvx /for cvx + ] cvx /for cvx + currentdict /dstDataStr get + ] cvx /if cvx + ] cvx bind + end +} bdf +/devn_imageormask +{ + /devicen_colorspace_dict AGMCORE_gget begin + /MappedCSA CSA map_csa def + 2 dict begin + dup dup + /dstDataStr exch /Width get colorSpaceElemCnt mul string def + /srcDataStrs [ 3 -1 roll begin + currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse + { + Width Decode length 2 div mul cvi string + } repeat + end ] def + begin + SkipImageProc { + currentdict consumeimagedata + } + { + save mark + AGMCORE_producing_seps not { + level3 not { + Operator /imagemask ne { + /DataSource [ + DataSource Decode BitsPerComponent currentdict /MultipleDataSources known {MultipleDataSources}{false} ifelse + colorSpaceElemCnt /devicen_colorspace_dict AGMCORE_gget /TintTransform get + dstDataStr srcDataStrs devn_alt_datasource /exec cvx + ] cvx 0 () /SubFileDecode filter def + /MultipleDataSources false def + /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def + } if + }if + currentdict imageormask + }{ + AGMCORE_host_sep{ + Names convert_to_process { + CSA map_csa 0 get /DeviceCMYK eq { + /DataSource + Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul + [ + DataSource Decode BitsPerComponent currentdict /MultipleDataSources known {MultipleDataSources}{false} ifelse + 4 /devicen_colorspace_dict AGMCORE_gget /TintTransform get + dstDataStr srcDataStrs devn_alt_datasource /exec cvx + ] cvx + filter_cmyk 0 () /SubFileDecode filter def + /MultipleDataSources false def + /Decode [1 0] def + /DeviceGray setcolorspace + currentdict imageormask_sys + }{ + AGMCORE_report_unsupported_color_space + AGMCORE_black_plate { + /DataSource [ + DataSource Decode BitsPerComponent currentdict /MultipleDataSources known {MultipleDataSources}{false} ifelse + CSA map_csa 0 get /DeviceRGB eq{3}{1}ifelse /devicen_colorspace_dict AGMCORE_gget /TintTransform get + dstDataStr srcDataStrs devn_alt_datasource /exec cvx + ] cvx 0 () /SubFileDecode filter def + /MultipleDataSources false def + /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def + currentdict imageormask_sys + } + { + gsave + knockout_unitsq + grestore + currentdict consumeimagedata + } ifelse + } ifelse + } + { + /devicen_colorspace_dict AGMCORE_gget /names_index known { + Operator/imagemask ne{ + MultipleDataSources { + /DataSource [ DataSource devn_sep_datasource /exec cvx ] cvx def + /MultipleDataSources false def + }{ + /DataSource /DataSource load dstDataStr srcDataStrs 0 get filter_devn def + } ifelse + invert_image_samples + } if + currentdict imageormask_sys + }{ + currentoverprint not Operator/imagemask eq and{ + currentdict imageormask_sys + }{ + currentoverprint not + { + gsave + knockout_unitsq + grestore + }if + currentdict consumeimagedata + }ifelse + }ifelse + }ifelse + }{ + currentdict imageormask + }ifelse + }ifelse + cleartomark restore + }ifelse + end + end + end +}def +/imageormask_l2_overprint +{ + currentdict + currentcmykcolor add add add 0 eq{ + currentdict consumeimagedata + }{ + level3{ + currentcmykcolor + /AGMIMG_k xdf + /AGMIMG_y xdf + /AGMIMG_m xdf + /AGMIMG_c xdf + Operator/imagemask eq{ + [/DeviceN [ + AGMIMG_c 0 ne {/Cyan} if + AGMIMG_m 0 ne {/Magenta} if + AGMIMG_y 0 ne {/Yellow} if + AGMIMG_k 0 ne {/Black} if + ] /DeviceCMYK {}] setcolorspace + AGMIMG_c 0 ne {AGMIMG_c} if + AGMIMG_m 0 ne {AGMIMG_m} if + AGMIMG_y 0 ne {AGMIMG_y} if + AGMIMG_k 0 ne {AGMIMG_k} if + setcolor + }{ + /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def + [/Indexed + [ + /DeviceN [ + AGMIMG_c 0 ne {/Cyan} if + AGMIMG_m 0 ne {/Magenta} if + AGMIMG_y 0 ne {/Yellow} if + AGMIMG_k 0 ne {/Black} if + ] + /DeviceCMYK { + AGMIMG_k 0 eq {0} if + AGMIMG_y 0 eq {0 exch} if + AGMIMG_m 0 eq {0 3 1 roll} if + AGMIMG_c 0 eq {0 4 1 roll} if + } + ] + 255 + { + 255 div + mark exch + dup dup dup + AGMIMG_k 0 ne{ + /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 1 roll pop pop pop + counttomark 1 roll + }{ + pop + }ifelse + AGMIMG_y 0 ne{ + /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 2 roll pop pop pop + counttomark 1 roll + }{ + pop + }ifelse + AGMIMG_m 0 ne{ + /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 3 roll pop pop pop + counttomark 1 roll + }{ + pop + }ifelse + AGMIMG_c 0 ne{ + /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec pop pop pop + counttomark 1 roll + }{ + pop + }ifelse + counttomark 1 add -1 roll pop + } + ] setcolorspace + }ifelse + imageormask_sys + }{ + write_image_file{ + currentcmykcolor + 0 ne{ + [/Separation /Black /DeviceGray {}] setcolorspace + gsave + /Black + [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 1 roll pop pop pop 1 exch sub} /exec cvx] + cvx modify_halftone_xfer + Operator currentdict read_image_file + grestore + }if + 0 ne{ + [/Separation /Yellow /DeviceGray {}] setcolorspace + gsave + /Yellow + [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 2 roll pop pop pop 1 exch sub} /exec cvx] + cvx modify_halftone_xfer + Operator currentdict read_image_file + grestore + }if + 0 ne{ + [/Separation /Magenta /DeviceGray {}] setcolorspace + gsave + /Magenta + [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 3 roll pop pop pop 1 exch sub} /exec cvx] + cvx modify_halftone_xfer + Operator currentdict read_image_file + grestore + }if + 0 ne{ + [/Separation /Cyan /DeviceGray {}] setcolorspace + gsave + /Cyan + [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {pop pop pop 1 exch sub} /exec cvx] + cvx modify_halftone_xfer + Operator currentdict read_image_file + grestore + } if + close_image_file + }{ + imageormask + }ifelse + }ifelse + }ifelse +} def +/indexed_imageormask +{ + begin + save mark + currentdict + AGMCORE_host_sep{ + Operator/knockout eq{ + /indexed_colorspace_dict AGMCORE_gget dup /CSA known { + /CSA get map_csa + }{ + /CSD get get_csd /Names get + } ifelse + overprint_plate not{ + knockout_unitsq + }if + }{ + Indexed_DeviceN { + /devicen_colorspace_dict AGMCORE_gget /names_index known { + indexed_image_lev2_sep + }{ + currentoverprint not{ + knockout_unitsq + }if + currentdict consumeimagedata + } ifelse + }{ + AGMCORE_is_cmyk_sep{ + Operator /imagemask eq{ + imageormask_sys + }{ + level2{ + indexed_image_lev2_sep + }{ + indexed_image_lev1_sep + }ifelse + }ifelse + }{ + currentoverprint not{ + knockout_unitsq + }if + currentdict consumeimagedata + }ifelse + }ifelse + }ifelse + }{ + level2{ + Indexed_DeviceN { + /indexed_colorspace_dict AGMCORE_gget begin + CSD get_csd begin + }{ + /indexed_colorspace_dict AGMCORE_gget begin + CSA map_csa 0 get /DeviceCMYK eq ps_level 3 ge and ps_version 3015.007 lt and { + [/Indexed [/DeviceN [/Cyan /Magenta /Yellow /Black] /DeviceCMYK {}] HiVal Lookup] + setcolorspace + } if + end + } ifelse + imageormask + Indexed_DeviceN { + end + end + } if + }{ + Operator /imagemask eq{ + imageormask + }{ + indexed_imageormask_lev1 + }ifelse + }ifelse + }ifelse + cleartomark restore + end +}def +/indexed_image_lev2_sep +{ + /indexed_colorspace_dict AGMCORE_gget begin + begin + Indexed_DeviceN not { + currentcolorspace + dup 1 /DeviceGray put + dup 3 + currentcolorspace 2 get 1 add string + 0 1 2 3 AGMCORE_get_ink_data 4 currentcolorspace 3 get length 1 sub + { + dup 4 idiv exch currentcolorspace 3 get exch get 255 exch sub 2 index 3 1 roll put + }for + put setcolorspace + } if + currentdict + Operator /imagemask eq{ + AGMIMG_&imagemask + }{ + use_mask { + level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation}ifelse + }{ + AGMIMG_&image + }ifelse + }ifelse + end end +}def + /OPIimage + { + dup type /dicttype ne{ + 10 dict begin + /DataSource xdf + /ImageMatrix xdf + /BitsPerComponent xdf + /Height xdf + /Width xdf + /ImageType 1 def + /Decode [0 1 def] + currentdict + end + }if + dup begin + /NComponents 1 cdndf + /MultipleDataSources false cdndf + /SkipImageProc {false} cdndf + /HostSepColorImage false cdndf + /Decode [ + 0 + currentcolorspace 0 get /Indexed eq{ + 2 BitsPerComponent exp 1 sub + }{ + 1 + }ifelse + ] cdndf + /Operator /image cdndf + end + /sep_colorspace_dict AGMCORE_gget null eq{ + imageormask + }{ + gsave + dup begin invert_image_samples end + sep_imageormask + grestore + }ifelse + }def +/cachemask_level2 +{ + 3 dict begin + /LZWEncode filter /WriteFilter xdf + /readBuffer 256 string def + /ReadFilter + currentfile + 0 (%EndMask) /SubFileDecode filter + /ASCII85Decode filter + /RunLengthDecode filter + def + { + ReadFilter readBuffer readstring exch + WriteFilter exch writestring + not {exit} if + }loop + WriteFilter closefile + end +}def +/cachemask_level3 +{ + currentfile + << + /Filter [ /SubFileDecode /ASCII85Decode /RunLengthDecode ] + /DecodeParms [ << /EODCount 0 /EODString (%EndMask) >> null null ] + /Intent 1 + >> + /ReusableStreamDecode filter +}def +/spot_alias +{ + /mapto_sep_imageormask + { + dup type /dicttype ne{ + 12 dict begin + /ImageType 1 def + /DataSource xdf + /ImageMatrix xdf + /BitsPerComponent xdf + /Height xdf + /Width xdf + /MultipleDataSources false def + }{ + begin + }ifelse + /Decode [/customcolor_tint AGMCORE_gget 0] def + /Operator /image def + /HostSepColorImage false def + /SkipImageProc {false} def + currentdict + end + sep_imageormask + }bdf + /customcolorimage + { + Adobe_AGM_Image/AGMIMG_colorAry xddf + /customcolor_tint AGMCORE_gget + bdict + /Name AGMIMG_colorAry 4 get + /CSA [ /DeviceCMYK ] + /TintMethod /Subtractive + /TintProc null + /MappedCSA null + /NComponents 4 + /Components [ AGMIMG_colorAry aload pop pop ] + edict + setsepcolorspace + mapto_sep_imageormask + }ndf + Adobe_AGM_Image/AGMIMG_&customcolorimage /customcolorimage load put + /customcolorimage + { + Adobe_AGM_Image/AGMIMG_override false put + dup 4 get map_alias{ + /customcolor_tint AGMCORE_gget exch setsepcolorspace + pop + mapto_sep_imageormask + }{ + AGMIMG_&customcolorimage + }ifelse + }bdf +}def +/snap_to_device +{ + 6 dict begin + matrix currentmatrix + dup 0 get 0 eq 1 index 3 get 0 eq and + 1 index 1 get 0 eq 2 index 2 get 0 eq and or exch pop + { + 1 1 dtransform 0 gt exch 0 gt /AGMIMG_xSign? exch def /AGMIMG_ySign? exch def + 0 0 transform + AGMIMG_ySign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch + AGMIMG_xSign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch + itransform /AGMIMG_llY exch def /AGMIMG_llX exch def + 1 1 transform + AGMIMG_ySign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch + AGMIMG_xSign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch + itransform /AGMIMG_urY exch def /AGMIMG_urX exch def + [AGMIMG_urX AGMIMG_llX sub 0 0 AGMIMG_urY AGMIMG_llY sub AGMIMG_llX AGMIMG_llY] concat + }{ + }ifelse + end +} def +level2 not{ + /colorbuf + { + 0 1 2 index length 1 sub{ + dup 2 index exch get + 255 exch sub + 2 index + 3 1 roll + put + }for + }def + /tint_image_to_color + { + begin + Width Height BitsPerComponent ImageMatrix + /DataSource load + end + Adobe_AGM_Image begin + /AGMIMG_mbuf 0 string def + /AGMIMG_ybuf 0 string def + /AGMIMG_kbuf 0 string def + { + colorbuf dup length AGMIMG_mbuf length ne + { + dup length dup dup + /AGMIMG_mbuf exch string def + /AGMIMG_ybuf exch string def + /AGMIMG_kbuf exch string def + } if + dup AGMIMG_mbuf copy AGMIMG_ybuf copy AGMIMG_kbuf copy pop + } + addprocs + {AGMIMG_mbuf}{AGMIMG_ybuf}{AGMIMG_kbuf} true 4 colorimage + end + } def + /sep_imageormask_lev1 + { + begin + MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ + { + 255 mul round cvi GrayLookup exch get + } currenttransfer addprocs settransfer + currentdict imageormask + }{ + /sep_colorspace_dict AGMCORE_gget/Components known{ + MappedCSA 0 get /DeviceCMYK eq{ + Components aload pop + }{ + 0 0 0 Components aload pop 1 exch sub + }ifelse + Adobe_AGM_Image/AGMIMG_k xddf + Adobe_AGM_Image/AGMIMG_y xddf + Adobe_AGM_Image/AGMIMG_m xddf + Adobe_AGM_Image/AGMIMG_c xddf + AGMIMG_y 0.0 eq AGMIMG_m 0.0 eq and AGMIMG_c 0.0 eq and{ + {AGMIMG_k mul 1 exch sub} currenttransfer addprocs settransfer + currentdict imageormask + }{ + currentcolortransfer + {AGMIMG_k mul 1 exch sub} exch addprocs 4 1 roll + {AGMIMG_y mul 1 exch sub} exch addprocs 4 1 roll + {AGMIMG_m mul 1 exch sub} exch addprocs 4 1 roll + {AGMIMG_c mul 1 exch sub} exch addprocs 4 1 roll + setcolortransfer + currentdict tint_image_to_color + }ifelse + }{ + MappedCSA 0 get /DeviceGray eq { + {255 mul round cvi ColorLookup exch get 0 get} currenttransfer addprocs settransfer + currentdict imageormask + }{ + MappedCSA 0 get /DeviceCMYK eq { + currentcolortransfer + {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} exch addprocs 4 1 roll + setcolortransfer + currentdict tint_image_to_color + }{ + currentcolortransfer + {pop 1} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 2 get} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 1 get} exch addprocs 4 1 roll + {255 mul round cvi ColorLookup exch get 0 get} exch addprocs 4 1 roll + setcolortransfer + currentdict tint_image_to_color + }ifelse + }ifelse + }ifelse + }ifelse + end + }def + /sep_image_lev1_sep + { + begin + /sep_colorspace_dict AGMCORE_gget/Components known{ + Components aload pop + Adobe_AGM_Image/AGMIMG_k xddf + Adobe_AGM_Image/AGMIMG_y xddf + Adobe_AGM_Image/AGMIMG_m xddf + Adobe_AGM_Image/AGMIMG_c xddf + {AGMIMG_c mul 1 exch sub} + {AGMIMG_m mul 1 exch sub} + {AGMIMG_y mul 1 exch sub} + {AGMIMG_k mul 1 exch sub} + }{ + {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} + {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} + {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} + {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} + }ifelse + AGMCORE_get_ink_data currenttransfer addprocs settransfer + currentdict imageormask_sys + end + }def + /indexed_imageormask_lev1 + { + /indexed_colorspace_dict AGMCORE_gget begin + begin + currentdict + MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ + {HiVal mul round cvi GrayLookup exch get HiVal div} currenttransfer addprocs settransfer + imageormask + }{ + MappedCSA 0 get /DeviceGray eq { + {HiVal mul round cvi Lookup exch get HiVal div} currenttransfer addprocs settransfer + imageormask + }{ + MappedCSA 0 get /DeviceCMYK eq { + currentcolortransfer + {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll + {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll + {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll + {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll + setcolortransfer + tint_image_to_color + }{ + currentcolortransfer + {pop 1} exch addprocs 4 1 roll + {3 mul HiVal mul round cvi 2 add Lookup exch get HiVal div} exch addprocs 4 1 roll + {3 mul HiVal mul round cvi 1 add Lookup exch get HiVal div} exch addprocs 4 1 roll + {3 mul HiVal mul round cvi Lookup exch get HiVal div} exch addprocs 4 1 roll + setcolortransfer + tint_image_to_color + }ifelse + }ifelse + }ifelse + end end + }def + /indexed_image_lev1_sep + { + /indexed_colorspace_dict AGMCORE_gget begin + begin + {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} + {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} + {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} + {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} + AGMCORE_get_ink_data currenttransfer addprocs settransfer + currentdict imageormask_sys + end end + }def +}if +end +systemdict /setpacking known +{ + setpacking +} if +%%EndResource +currentdict Adobe_AGM_Utils eq {end} if +%%EndProlog +%%BeginSetup +Adobe_AGM_Utils begin +2 2010 Adobe_AGM_Core/doc_setup get exec +Adobe_CoolType_Core/doc_setup get exec +Adobe_AGM_Image/doc_setup get exec +currentdict Adobe_AGM_Utils eq {end} if +%%EndSetup +%%Page: reHaRegel.png 1 +%%EndPageComments +%%BeginPageSetup +/currentdistillerparams where +{pop currentdistillerparams /CoreDistVersion get 5000 lt} {true} ifelse +{ userdict /AI11_PDFMark5 /cleartomark load put +userdict /AI11_ReadMetadata_PDFMark5 {flushfile cleartomark } bind put} +{ userdict /AI11_PDFMark5 /pdfmark load put +userdict /AI11_ReadMetadata_PDFMark5 {/PUT pdfmark} bind put } ifelse +[/NamespacePush AI11_PDFMark5 +[/_objdef {ai_metadata_stream_123} /type /stream /OBJ AI11_PDFMark5 +[{ai_metadata_stream_123} +currentfile 0 (% &&end XMP packet marker&&) +/SubFileDecode filter AI11_ReadMetadata_PDFMark5 + + + + + + + + + + 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+s+:9&s+:9&s+:9&s+:9&s+:9&s+:9/s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9& +s+:9&s+:9&s+:9&s,6o/s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9& +s+:9/s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s+:9&s,6o/s+:9& +s+:9&s+:9Hs*t~> + +grestore % PSGState +newpath % image +grestore % PSGState +%ADOBeginClientInjection: EndPageContent "AI11EPS" +userdict /annotatepage 2 copy known {get exec}{pop pop} ifelse +%ADOEndClientInjection: EndPageContent "AI11EPS" +% page clip +grestore +grestore % PSGState +Adobe_AGM_Core/AGMCORE_save get restore +%%PageTrailer +[/EMC AI11_PDFMark5 +[/NamespacePop AI11_PDFMark5 +Adobe_AGM_Image/page_trailer get exec +Adobe_CoolType_Core/page_trailer get exec +Adobe_AGM_Core/page_trailer get exec +currentdict Adobe_AGM_Utils eq {end} if +%%Trailer +Adobe_AGM_Image/doc_trailer get exec +Adobe_CoolType_Core/doc_trailer get exec +Adobe_AGM_Core/doc_trailer get exec +%%EOF +%AI9_PrintingDataEnd + +userdict /AI9_read_buffer 256 string put +userdict begin +/ai9_skip_data +{ + mark + { + currentfile AI9_read_buffer { readline } stopped + { + } + { + not + { + exit + } if + (%AI9_PrivateDataEnd) eq + { + exit + } if + } ifelse + } loop + cleartomark +} def +end +userdict /ai9_skip_data get exec +%AI9_PrivateDataBegin +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: Adobe Illustrator(R) 11.0 +%%AI8_CreatorVersion: 11.0.0 +%%For: (----- -----) () +%%Title: (reHa.eps) +%%CreationDate: 5/11/2006 9:36 AM +%AI9_DataStream +%Gb"-6l&I%2FY?,Q+MauZ%YE2Tmir[EPN7>pKrCKp@6t:?[[2!jl=CB +%bPSd;5CECnrUS"\n*Y\qqJ5lgp&4p^q"F+P5MXS'?[qlu3+r(jqo/*MgW/@O&)Y,#FPf:soO7\%Sc!CJi@O0ms-Cu\p?p,5T>,^M +%'qG=!e^(s`mm#5Zr>5+g2ijRp_-OrY9>%$,s5WHak,7sm_a+7FqnN$K\*nhDqX+7Om@2/"*^BQ>&-'E&]='.=4JX"q;?-:NgM\1k +%L4]gqVJWB]*V2'HjMTRkri>IVGBRNK^4,t_)t!UYc_'(,J+qFhU!W7Wq>&d;^]*9R +%#Bu;[qQn/b:V;hL,:ah,!^pqChj<_jdjH53f3GJUc$6 +%aSt/uU]-UlKP1;Vl1(>$G5oOrIe3BihnFI9#)B(-H`;aHU(m2D>]P8kl1Ij@a0m!sm/PE1r5VU?QOA&g2?)r'r&Kf4F'8.a]#NWM 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