commit eb31e0dbc152c6295c52f9762420572a25550bf0 Author: Sven Riwoldt Date: Sat Jun 29 08:05:31 2024 +0200 Init diff --git a/Calc01.pdf b/Calc01.pdf new file mode 100644 index 0000000..3626ac8 Binary files /dev/null and b/Calc01.pdf differ diff --git a/Calc01.tex b/Calc01.tex new file mode 100644 index 0000000..08fb314 --- /dev/null +++ b/Calc01.tex @@ -0,0 +1,44 @@ +\documentclass[]{scrbook} +\usepackage{color} +\usepackage{marginnote} +\usepackage[fleqn]{amsmath} +\usepackage{amssymb} +\newcommand\mpar[1]{\marginpar {\flushleft\sffamily\small #1}} +\setlength{\marginparwidth}{35mm} + +\usepackage{slashed} +\usepackage{pgfplots} +\usepackage{tikz} + +\usepackage{graphicx} + + +\usepackage[T1]{fontenc} +%\newcommand{\changefont}[3]{ +% \fontfamily{#1} \fontseries{#2} \fontshape{#3} \selectfont} + +\setlength\parindent{0pt} +%\changefont{pag}{m}{n} + +%\usepackage[sc]{mathpazo} % Palatino Font +\usepackage{cmbright} +%\usepackage{charter} + +% %%% Überschriften %%%% +%\setkomafont{disposition}{\normalcolor\sffamily\bfseries} % standard +\setkomafont{disposition}{\normalcolor\bfseries} % alle überschriften fett und serifenlos +%\setkomafont{disposition}{\normalcolor} + + + +\everymath{\displaystyle} +\begin{document} + +%\input{Eingangstest} + + + +\input{Quiz1.tex} + + +\end{document} diff --git a/Eingangstest.tex b/Eingangstest.tex new file mode 100644 index 0000000..c75b299 --- /dev/null +++ b/Eingangstest.tex @@ -0,0 +1,221 @@ + \begin{description} + \item[1. Aufgabe ] Was ist die Ableitung von $x^4-2 x^3+3 x^2-5 x+11$ ? + \mpar{\textcolor{red}{\textbf{Potenzregel:} $f(x)=x^n$\\$f'(x)=nx^{x-1}$}} + \begin{itemize} + \item $x^3-2 x^2+3 x+6$ + \item $4 x^3-6 x^2-6 x-5$ + \item $\frac{x^5}{5}-\frac{x^4}{2}+x^3-\frac{5 x^2}{2}+11 x+C$, wobei $C$ eine Konstante ist. + \item Keiner von ihnen. + \item $4 x^3-6 x^2+6 x-5$ + \item $x^3-2 x^2+3 x-5$ + \item $\frac{x^5}{5}-\frac{x^4}{2}+x^3-\frac{5 x^2}{2}+11 x$ + \item $4 x^4-6 x^3+6 x^2-5 x+11$ + \end{itemize} + + \textbf{Lösung:} + + $4x^3-6x^2+6x-5$ + + \begin{figure}[ht] + \centering + \includegraphics[width=0.75\linewidth]{Grafiken/A1} + \label{fig:a1} + \end{figure} + + \newpage + + \item[2. Aufgabe] Welche der folgenden Gleichungen gibt die Gleichung eines Kreises mit dem Radius $2$ und dem Mittelpunkt im Punkt $(-1,2)$ an? + \mpar{\textcolor{red}{\textbf{Kreisgleichung:} $(x-x_m)^2+(y-y_m)^2=r^2$}} + \begin{itemize} + \item $(x+1)^2-(y-2)^2=2$ + \item $(x-1)^2+(y+2)^2=4$ + \item $x^2+\frac{y^2}{2}=4$ + \item $x^2+y^2=4$ + \item $(x+1)^2+(y-2)^2=4$ + \item $(x+1)^2+(y-2)^2=2$ + \item $(x-1)^2+(y+2)^2=2$ + \end{itemize} + + \textbf{Lösung:} + + Einsetzen in Kreisgleichung + $(x-(-1))^2+(y-2)^2=4$ somit $(x+1)^2+(y-2)^2=4$ + + \begin{figure}[ht] + \centering + \includegraphics[width=0.75\linewidth]{Grafiken/A2} + \caption{} + \label{fig:a2} + \end{figure} + + \newpage + + \item[3. Aufgabe] Vereinfachen Sie $\left(\frac{-125}{8}\right)^{2/3}$ + \begin{itemize} + \item $\frac{15625}{64}$ + \item $-\frac{2}{5}$ + \item $\frac{2}{5}$ + \item $-\frac{5}{2}$ + \item $\frac{3}{5}$ + \item $\frac{4}{25}$ + \item \underline{\underline{$\frac{25}{4}$}} + \end{itemize} + + \textbf{Lösung:} Ohne TR + + $\left(\frac{-125}{8}\right)^{2/3}=\frac{\sqrt[3]{(-125)^2}}{\sqrt[3]{8^2}}=\frac{\sqrt[3]{15625}}{\sqrt[3]{64}}=\frac{\sqrt[3]{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5}}{\sqrt[3]{2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2}}=\frac{\slashed{5}\cdot \slashed{5}\cdot \slashed{5}\cdot \slashed{5}\cdot 5\cdot 5}{\slashed{2}\cdot \slashed{2}\cdot \slashed{2}\cdot \slashed{2}\cdot 2\cdot 2}=\frac{5\cdot 5}{2 \cdot 2}=\frac{25}{4}$ + + \newpage + + \item[4. Aufgabe]Lösen Sie $e^{2-3 x}=125$ für $x$. + + \begin{itemize} + \item $\frac{2}{3}+\ln 25$ + \item $\frac{2}{3}-\ln 125$ + \item $\frac{2}{3}+\ln 125$ + \item $\frac{3}{2}+\ln 125$ + \item $\frac{2}{3}-\ln 5$ + \item $\frac{3}{2}-\ln 5$ + \item $\frac{3}{2}+\ln 25$ + \item $\frac{3}{2}-\ln 125$ + \end{itemize} + + \textbf{Lösung:} + + \mpar{\textcolor{red}{$\ln e=1$}} + + \mpar{\textcolor{red}{$\log_b (x^z) = z \cdot \log_b(x)$}} + + \begin{tabular}{rll} + & $e^{2-3 x}=125$ & $\vert{} \ln()$ \\ + $\Leftrightarrow$ & $\ln e^{2-3x}=\ln 125$ & $\vert{}$ siehe Regel \\ + $\Leftrightarrow$ & $\left(2-3x\right) \cdot \ln e = \ln 125$ & $\vert{}$ siehe Regel \\ + $\Leftrightarrow$ & $2-3x=\ln 125$ & $\vert{} -2$\\ + $\Leftrightarrow$ & $-3x=\ln 125-2$ &$\vert{} \div(-3)$\\ + $\Leftrightarrow$ & $x=\ln 125-2$ &\\ + $\Leftrightarrow$ & $x=\frac{2}{3} -\frac{\ln 125}{3}$ &\\ + + \end{tabular} + + + \newpage + + \item[5. Aufgabe]Bewerten Sie $\int_1^3 \frac{d x}{x^2}$. + + \begin{itemize} + \item $-\frac{1}{2}$ + \item $-\frac{2}{3}$ + \item $-\frac{1}{3}$ + \item $-\frac{8}{9}$ + \item $\frac{1}{3}$ + \item $-\frac{26}{27}$ + \item $\frac{2}{3}$ + \item $\frac{1}{2}$ + \end{itemize} + + \textbf{Lösung:} + + \mpar{\textcolor{red}{$\int_a^b f(x) d x=[F(x)]_a^b=F(b)-F(a)$}} + + \mpar{$\frac{1}{x^{2}}dx=-\frac{1}{x}$} + + $\int_1^3 \frac{d x}{x^2}=\int_1^3 \frac{1}{x^2}dx=\left[ -\frac{1}{x}\right]_1^3=-\frac{1}{3}-\left(-\frac{1}{1}\right)=1-\frac{1}{3}=\frac{2}{3}$ + + + \begin{figure}[ht] + \centering + \includegraphics[width=0.65\linewidth]{Grafiken/A5} + \label{fig:a5} + \end{figure} + + + \newpage + + \item[6. Aufgabe]Es sei $f(x)=x+\sin 2 x$. Finden Sie die Ableitung $f^{\prime}(0)$. + \mpar{Summenregel: $f(x)=g(x)+k(x) \quad \rightarrow \quad f^{\prime}(x)=g^{\prime}(x)+k^{\prime}(x)$} + \mpar{Kettenregel: $\left[u\left(v\left(x\right)\right)\right]^{\prime}=u^{\prime}\left(v\left(x\right)\right)\cdot v^{\prime}\left(x\right)$} + \begin{itemize} + \item $3$ + \item $2$ + \item $6$ + \item $-1$ + \item $-3$ + \item $0$ + \item $-2$ + \item $1$ + \end{itemize} + + \textbf{Lösung:} + + $f(x)=x+\sin 2 x \Rightarrow f'(x)=1+2\cdot \cos(2x)$ + + $f(0)^\prime=1+2\cdot \cos(2\cdot 0)= 1+2\cdot 1=3$ + + + Nebenrechnung wegen Verkettung: + $\left(\sin(2x)\right)^\prime$ + \begin{itemize} + \item $u=2x$; $u^\prime = 2$ + \item $\left(\sin(u)\right)^\prime = \cos(u)$ + \item somit: $\left(\sin(2x)\right)^\prime = 2\cdot \cos(2x)$ + \end{itemize} + + \begin{figure}[ht] + \centering + \includegraphics[width=0.65\linewidth]{Grafiken/A6} + \label{fig:a6} + \end{figure} + + \newpage + + \item[7. Aufgabe]Bewerten Sie $\cos \frac{2 \pi}{3}-\arctan 1$. Seien Sie vorsichtig und prüfen Sie alle Optionen. + + \begin{itemize} + \item $\frac{\sqrt{3}-1}{2}$ + \item $\frac{1-\pi}{2}$ + \item $-\frac{\sqrt{3}+1}{2}$ + \item $-\frac{\sqrt{3}+2}{4}$ + \item $\frac{\pi+2}{4}$ + \item $-\frac{\pi+2}{4}$ + \item $\frac{1-\sqrt{3}}{2}$ + \item $\frac{\pi-2}{4}$ + \end{itemize} + + + \textbf{Lösung: } + + + $\cos \frac{2 \pi}{3}=-\frac{1}{2}$ + + $\arctan 1 = \frac{\pi}{4}$ + + $-\frac{1}{2}-\frac{\pi}{4}=-\frac{2}{4}-\frac{\pi}{4}=\frac{-2-\pi}{4}=-\frac{\pi+2}{4}$ + + \newpage + + \item[8. Aufgabe]Bewerten Sie $\lim _{x \rightarrow 1} \frac{2 x^2+x-3}{x^2-x}$ + + \begin{itemize} + \item $\frac{4 x+1}{2 x-1}$ + \item $\frac{5}{2}$ + \item $0$ + \item $-3$ + \item $2$ + \item $5$ + \item $\frac{7}{2}$ + \item $\frac{0}{0}$ + \end{itemize} + + $\lim _{x \rightarrow 1} \frac{2 \cdot1^2+1-3}{1^2-1}=\frac{0}{0}$ + + daher L'Hospital: + + $\lim _{x \rightarrow 1} \frac{2 x^2+x-3}{x^2-x}=\lim _{x \rightarrow 1} \frac{4 x+1}{2x-1}=\frac{5}{1}=5$ + + \begin{figure}[ht] + \centering + \includegraphics[width=0.7\linewidth]{Grafiken/A8} + \label{fig:a8} + \end{figure} + + \end{description} \ No newline at end of file diff --git a/Grafiken/A1-eps-converted-to.pdf b/Grafiken/A1-eps-converted-to.pdf new file mode 100644 index 0000000..3387308 Binary files /dev/null and b/Grafiken/A1-eps-converted-to.pdf differ diff --git a/Grafiken/A1.eps b/Grafiken/A1.eps new file mode 100644 index 0000000..5713467 --- /dev/null +++ b/Grafiken/A1.eps @@ -0,0 +1,4300 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%BoundingBox: 20 198 575 593 +%%Creator: FreeHEP Graphics2D Driver +%%Producer: com.maplesoft.mathdoc.view.plot.paint.PlotPSGraphics2D Revision: 12753 +%%For: +%%Title: +%%CreationDate: Freitag, 17. 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vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} % UR +{calcval widx dx add neg widy 2 div dy add neg rmoveto} % CR +{calcval widx dx add neg 0 rmoveto} % BR +{calcval widx dx add neg dy neg rmoveto} % LR +{calcval widx 2 div dx add neg widy dy add neg rmoveto} % UC +{calcval widx 2 div dx add neg widy 2 div dy add neg rmoveto} % CC +{calcval widx 2 div dx add neg 0 rmoveto} % BC +{calcval widx 2 div dx add neg dy neg rmoveto} % LC +] def + +/vg&str {m q 1 -1 scale dup stringsize 4 copy align 11 -1 roll get exec + q inflate relative frame exch exec Q recshow Q} def + +end /procDict exch def +%%EndProlog + +%%BeginSetup +save +procDict begin +printColorMap begin +595 791 setpagesize +20 20 20 20 setmargins +0 0 setorigin +700 496 setsize +fittopage +portrait +imagescale +cliptobounds +setbasematrix +/Helvetica 10 sf +defaultGraphicsState +%%EndSetup + +0 0 0 RG +[ 1.00000 0 0 1.00000 0 0 ] defaultmatrix matrix concatmatrix setmatrix +cliprestore +1.00000 1.00000 1.00000 RG +newpath +0 0 m +700.000 0 l +700.000 496.000 l +0 496.000 l 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concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 348.000 m +345.000 348.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 377.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -377.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 297.000 m +345.000 297.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 326.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -326.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 245.000 m +345.000 245.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 275.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -275.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 194.000 m +345.000 194.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 223.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -223.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 143.000 m +345.000 143.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 172.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -172.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 91.0000 m +345.000 91.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 121.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -121.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +348.000 40.0000 m +345.000 40.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -30.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 69.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -69.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 30.0000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +Q +2 J +0 j +Q +Q +cliprestore +1 0 700 496 rc +[ 1.00000 0 0 1.00000 1.00000 0 ] concat +[ 1.00000 0 0 1.00000 -1.00000 0 ] concat +cliprestore +q +1 477 691 15 rc +[ 1.00000 0 0 1.00000 1.00000 477.000 ] concat +q +[ 1.00000 0 0 1.00000 0 0 ] concat +q +0 0 692 14 rc +Q +cliprestore +newpath +0 0 m +0 15.0000 l +691.000 15.0000 l +691.000 0 l +h +W +Q +[ 1.00000 0 0 1.00000 1.00000 477.000 ] defaultmatrix matrix concatmatrix setmatrix +[ 1.00000 0 0 1.00000 -1.00000 -477.000 ] concat +cliprestore +Q +1.00000 w +2 J +0 j +end end restore showpage + +%%Trailer +%%EOF diff --git a/Grafiken/A10.png b/Grafiken/A10.png new file mode 100644 index 0000000..9831bb2 Binary files /dev/null and b/Grafiken/A10.png differ diff --git a/Grafiken/A11.png b/Grafiken/A11.png new file mode 100644 index 0000000..e378cd6 Binary files /dev/null and b/Grafiken/A11.png differ diff --git a/Grafiken/A12.png b/Grafiken/A12.png new file mode 100644 index 0000000..3f2b57e Binary files /dev/null and b/Grafiken/A12.png differ diff --git a/Grafiken/A2-eps-converted-to.pdf b/Grafiken/A2-eps-converted-to.pdf new file mode 100644 index 0000000..004607e Binary files /dev/null and b/Grafiken/A2-eps-converted-to.pdf differ diff --git a/Grafiken/A2.eps b/Grafiken/A2.eps new file mode 100644 index 0000000..c0d7cbf --- /dev/null +++ b/Grafiken/A2.eps @@ -0,0 +1,2814 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%BoundingBox: 20 113 575 678 +%%Creator: FreeHEP Graphics2D Driver +%%Producer: com.maplesoft.mathdoc.view.plot.paint.PlotPSGraphics2D Revision: 12753 +%%For: +%%Title: +%%CreationDate: Freitag, 17. Mai 2024, 18:39:26 Mitteleuropäische Sommerzeit +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +100 dict dup begin + +% +% File: org/freehep/graphicsio.ps/PSProlog.txt +% Author: Charles Loomis +% + +% Redefinitions which save some space in the output file. These are also +% the same as the PDF operators. +/q {gsave} def +/Q {grestore} def + +/n {newpath} def +/m {moveto} def +/l {lineto} def +/c {curveto} def +/h {closepath} def + +/re {4 -2 roll moveto + dup 0 exch rlineto exch 0 rlineto + neg 0 exch rlineto closepath} def + +/f {fill} def +/f* {eofill} def +/F {gsave vg&FC fill grestore} def +/F* {gsave vg&FC eofill grestore} def + +/s {closepath stroke} def +/S {stroke} def + +/b {closepath gsave vg&FC fill grestore + gsave stroke grestore newpath} def +/B {gsave vg&FC fill grestore gsave stroke grestore newpath} def +/b* {closepath gsave vg&FC eofill grestore + gsave stroke grestore newpath} def +/B* {gsave vg&FC eofill grestore gsave stroke grestore newpath} def + +/g {1 array astore /vg&fcolor exch def} def +/G {setgray} def +/k {4 array astore /vg&fcolor exch def} def +/K {setcmykcolor} def +/rg {3 array astore /vg&fcolor exch def} def +/RG {setrgbcolor} def + +% Initialize the fill color. +0 0 0 rg + +/vg&FC {mark vg&fcolor aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/vg&DFC {/vg&fcolor exch def} def + +/vg&C {mark exch aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/w {setlinewidth} def +/j {setlinejoin} def +/J {setlinecap} def +/M {setmiterlimit} def +/d {setdash} def +/i {setflat} def + +/W {clip} def +/W* {eoclip} def + +% Setup the default graphics state. +% (black; 1 pt. linewidth; miter join; butt-ends; solid) +/defaultGraphicsState {0 g 1 w 0 j 0 J [] 0 d} def + +% Emulation of the rectangle operators for PostScript implementations +% which do not implement all Level 2 features. This is an INCOMPLETE +% emulation; only the "x y width height rect..." form is emulated. +/*rf {gsave newpath re fill grestore} def +/*rs {gsave newpath re stroke grestore} def +/*rc {newpath re clip} def +/rf /rectfill where {pop /rectfill}{/*rf} ifelse load def +/rs /rectstroke where {pop /rectstroke}{/*rs} ifelse load def +/rc /rectclip where {pop /rectclip}{/*rc} ifelse load def + +% Emulation of the selectfont operator. This includes a 20% increase in +% the fontsize which is necessary to get sizes similar to the Java fonts. +/*sf {exch findfont exch + dup type /arraytype eq {makefont}{scalefont} ifelse setfont} bind def +/sf /selectfont where {pop {1.2 mul selectfont}}{{1.2 mul *sf}} ifelse def + +% Special version of stroke which allows the dash pattern to continue +% across path segments. (This may be needed for PostScript although +% modern printers seem to do this correctly.) +/vg&stroke { + currentdash pop length 0 eq + {stroke} + { + currentdash /vg&doffset exch def pop + flattenpath + {m vg&resetdash} + {2 copy + currentpoint + 3 -1 roll sub dup mul + 3 1 roll sub dup mul + add sqrt + 3 1 roll l + currentdash 3 -1 roll add setdash} + {} + {h vg&resetdash} + pathforall + stroke + vg&resetdash + } ifelse +} def +/vg&resetdash {currentdash pop vg&doffset setdash} def + +% Initialize variables for safety. +/delta 0 def +/xv 0 def /yv 0 def /width 0 def /height 0 def + +% Initialize to portrait INTERNATIONAL (Letter-height, A4-width) page. +/pw 595 def /ph 791 def /po true def /ftp false def + +% Initialize margins to 20 points. +/ml 20 def /mr 20 def /mt 20 def /mb 20 def + +% Temporary matrices. +/smatrix 0 def /nmatrix 0 def + +% set page size (usage: setpagesize) +/setpagesize {/ph exch def /pw exch def} def + +% set page orientation (usage: portrait or landscape) +/portrait {/po true def} def +/landscape {/po false def} def + +% force natural size for image (usage: naturalsize) +/naturalsize {/ftp false def} def + +% resize image to fill page (usage: fittopage) +/fittopage {/ftp true def} def + +% set margins of the page (usage: setmargins) +/setmargins {/mr exch def /mt exch def /mb exch def /ml exch def} def + +% set the graphic's size (usage: setsize) +/setsize {/gh exch def /gw exch def} def + +% set the graphic's origin (usage: setorigin) +/setorigin {/gy exch def /gx exch def} def + +% calculate image center +/imagecenter {pw ml sub mr sub 2 div ml add + ph mt sub mb sub 2 div mb add} def + +% calculate the necessary scaling +/imagescale {po {gw}{gh} ifelse pw ml sub mr sub div + po {gh}{gw} ifelse ph mt sub mb sub div + 2 copy lt {exch} if pop + ftp not {1 2 copy lt {exch} if pop} if + 1 exch div /sfactor exch def + /gw gw sfactor mul def /gh gh sfactor mul def} def + +% calculate image origin +/imageorigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div po {add}{sub} ifelse} def + +% calculate the clipping origin +/cliporigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub floor + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div sub floor} def + +% Set the clipping region to the bounding box. +/cliptobounds {cliporigin po {gw}{gh} ifelse 1 add + po {gh}{gw} ifelse 1 add rc} def + +% set the base transformation matrix (usage: setbasematrix) +/setbasematrix {imageorigin translate + po {0}{90} ifelse rotate + sfactor sfactor neg scale + /defaultmatrix matrix currentmatrix def} def + +% The lower-right bias in drawing 1 pt. wide lines. +/bias {q 0.5 0.5 translate} def +/unbias {Q} def + +% Draw a line. (x0 y0 x1 y1 line) +/L {bias n m l S unbias} def + +% Polyline primitive. +/polyline {n m 1 exch 1 exch + {pop currentfile token pop currentfile token pop l} for + } def + +% Draw a polyline (n x0 y0 OPL x1 y1 x2 y2 ... ... xn yn) +/OPL {bias polyline S unbias} def + +% Draw a closed polyline (n x0 y0 CPL x1 y1 x2 y2 ... ... xn yn) +/CPL {bias polyline s unbias} def + +% Draw a filled polyline (n x0 y0 FPL x1 y1 x2 y2 ... ... xn yn) +/FPL {polyline h f*} def + +% Draw an oval. (x y w h OVL) +/OVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width currentlinewidth sub 2 div + height currentlinewidth sub 2 div neg + scale n 0 0 1 5 -2 roll arc + smatrix setmatrix S} def + +% Draw a filled oval. (x y w h FOVL) +/FOVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width 2 div + height 2 div neg + scale n 0 0 m 0 0 1 5 -2 roll arc + h smatrix setmatrix f} def + +% Draw a rounded rectangle. (x y w h arcwidth archeight RREC) +/RREC {matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + s} def + +% Draw a filled rounded rectangle. (x y w h arcwidth archeight FRREC) +/FRREC{matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + h f} def + +% Draw a string. (string x y STR) +/STR {q m 1 -1 scale recshow Q} def + +% Define basic plot symbols. +/xys {/siz exch def /yv exch def /xv exch def} def +/hline {xys n xv siz 2. div sub yv m siz 0 rlineto S} def +/vline {xys n xv yv siz 2. div sub m 0 siz rlineto S} def +/plus {xys n xv yv siz 2. div sub m 0 siz rlineto + xv siz 2. div sub yv m siz 0 rlineto S} def +/dot {n 2. div 0 360 arc s} def +/fdot {n 2. div 0 360 arc h f} def +/box {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rs} def +/fbox {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rf} def +/tridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto s} def +/ftridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto h f} def + +% Symbols defined in terms of the others. +/star {3 copy cross plus} def +/cross {xys q xv yv translate 45 rotate 0 0 siz plus Q} def +/diamond {xys q xv yv translate 45 rotate 0 0 siz box Q} def +/fdiamond {xys q xv yv translate 45 rotate 0 0 siz fbox Q} def +/triup {xys q xv yv translate 180 rotate 0 0 siz tridn Q} def +/ftriup {xys q xv yv translate 180 rotate 0 0 siz ftridn Q} def + +% Define the composite fonts used to print Unicode strings. +% Undefine particular values in an encoding array. +/vg&undef { {exch dup 3 -1 roll /.notdef put} forall } def +/vg&redef { {3 -1 roll dup 4 2 roll put} forall } def + +% usage: key encoding basefontname vg&newbasefont font +/vg&newbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + currentdict + end +definefont +} def + +% usage: key encoding basefontname vg&newskewedbasefont font +/vg&newskewedbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + exch FontMatrix exch matrix concatmatrix /FontMatrix exch def + currentdict + end +definefont +} def + +% usage: basekey suffix vg&nconcat name +/vg&nconcat { + 2 {dup length string cvs exch} repeat + dup length 3 -1 roll dup length 3 -1 roll add string + dup 0 4 -1 roll dup length 5 1 roll putinterval + dup 4 -2 roll exch putinterval cvn +} def + +%usage: fontname vg&skewmatrix matrix +/vg&skewmatrix { +findfont dup /FontInfo known + { + /FontInfo get dup /ItalicAngle known + { + [ 1 0 4 -1 roll /ItalicAngle get neg dup sin exch cos div 1 0 0 ] + } + {pop matrix} ifelse + } + {pop matrix} ifelse +} def + +% usage: newfontname basefontname vg&newcompositefont -- +/vg&newcompositefont { +/vg&fstyle exch def +/vg&bfont exch def +/vg&fname exch def +<< +/FontStyleBits vg&fstyle +/FontType 0 +/FontMatrix matrix +/FontName vg&fname +/FMapType 2 +/Encoding [ 0 1 255 {pop 6} for ] + dup 16#00 0 put % Latin + dup 16#03 1 put % Greek + dup 16#20 2 put % Punctuation + dup 16#21 3 put % Arrows + dup 16#22 4 put % MathOps + dup 16#27 5 put % Dingbats + +/FDepVector [ +vg&bfont /-UC-Latin vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} % UR +{calcval widx dx add neg widy 2 div dy add neg rmoveto} % CR +{calcval widx dx add neg 0 rmoveto} % BR +{calcval widx dx add neg dy neg rmoveto} % LR +{calcval widx 2 div dx add neg widy dy add neg rmoveto} % UC +{calcval widx 2 div dx add neg widy 2 div dy add neg rmoveto} % CC +{calcval widx 2 div dx add neg 0 rmoveto} % BC +{calcval widx 2 div dx add neg dy neg rmoveto} % LC +] def + +/vg&str {m q 1 -1 scale dup stringsize 4 copy align 11 -1 roll get exec + q inflate relative frame exch exec Q recshow Q} def + +end /procDict exch def +%%EndProlog + +%%BeginSetup +save +procDict begin +printColorMap begin +595 791 setpagesize +20 20 20 20 setmargins +0 0 setorigin +568 578 setsize +fittopage +portrait +imagescale +cliptobounds +setbasematrix +/Helvetica 10 sf +defaultGraphicsState +%%EndSetup + +0 0 0 RG +[ 1.00000 0 0 1.00000 0 0 ] defaultmatrix matrix concatmatrix setmatrix +cliprestore +1.00000 1.00000 1.00000 RG +newpath +0 0 m +568.000 0 l +568.000 578.000 l +0 578.000 l 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385.302 409.618 385.433 c +h +f +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +418.000 259.000 m +413.000 259.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 411.000 264.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -411.000 -264.000 ] concat +newpath +413.960 266.343 m +413.357 268.000 l +408.279 268.000 l +408.279 267.765 l +409.773 266.402 410.824 265.289 411.434 264.426 c +412.043 263.563 412.348 262.773 412.348 262.058 c +412.348 261.512 412.181 261.064 411.846 260.712 c +411.512 260.361 411.112 260.186 410.647 260.186 c +410.223 260.186 409.844 260.309 409.507 260.557 c +409.171 260.804 408.922 261.167 408.761 261.646 c +408.526 261.646 l +408.632 260.863 408.904 260.262 409.342 259.843 c +409.780 259.424 410.327 259.214 410.983 259.214 c +411.681 259.214 412.264 259.439 412.732 259.887 c +413.199 260.336 413.433 260.865 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setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +418.000 446.000 m +415.000 446.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 450.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -450.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +418.000 321.000 m +415.000 321.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 325.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -325.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +418.000 196.000 m +415.000 196.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 201.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -201.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +418.000 71.0000 m +415.000 71.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 76.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -76.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +Q +2 J +0 j +Q +Q +cliprestore +1 0 568 578 rc +[ 1.00000 0 0 1.00000 1.00000 0 ] concat +[ 1.00000 0 0 1.00000 -1.00000 0 ] concat +cliprestore +1.00000 w +2 J +0 j +end end restore showpage + +%%Trailer +%%EOF diff --git a/Grafiken/A5-eps-converted-to.pdf b/Grafiken/A5-eps-converted-to.pdf new file mode 100644 index 0000000..7d85284 Binary files /dev/null and b/Grafiken/A5-eps-converted-to.pdf differ diff --git a/Grafiken/A5.eps b/Grafiken/A5.eps new file mode 100644 index 0000000..c65e834 --- /dev/null +++ b/Grafiken/A5.eps @@ -0,0 +1,3090 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%BoundingBox: 20 118 575 673 +%%Creator: FreeHEP Graphics2D Driver +%%Producer: com.maplesoft.mathdoc.view.plot.paint.PlotPSGraphics2D Revision: 12753 +%%For: +%%Title: +%%CreationDate: Montag, 20. Mai 2024, 11:52:39 Mitteleuropäische Sommerzeit +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +100 dict dup begin + +% +% File: org/freehep/graphicsio.ps/PSProlog.txt +% Author: Charles Loomis +% + +% Redefinitions which save some space in the output file. These are also +% the same as the PDF operators. +/q {gsave} def +/Q {grestore} def + +/n {newpath} def +/m {moveto} def +/l {lineto} def +/c {curveto} def +/h {closepath} def + +/re {4 -2 roll moveto + dup 0 exch rlineto exch 0 rlineto + neg 0 exch rlineto closepath} def + +/f {fill} def +/f* {eofill} def +/F {gsave vg&FC fill grestore} def +/F* {gsave vg&FC eofill grestore} def + +/s {closepath stroke} def +/S {stroke} def + +/b {closepath gsave vg&FC fill grestore + gsave stroke grestore newpath} def +/B {gsave vg&FC fill grestore gsave stroke grestore newpath} def +/b* {closepath gsave vg&FC eofill grestore + gsave stroke grestore newpath} def +/B* {gsave vg&FC eofill grestore gsave stroke grestore newpath} def + +/g {1 array astore /vg&fcolor exch def} def +/G {setgray} def +/k {4 array astore /vg&fcolor exch def} def +/K {setcmykcolor} def +/rg {3 array astore /vg&fcolor exch def} def +/RG {setrgbcolor} def + +% Initialize the fill color. +0 0 0 rg + +/vg&FC {mark vg&fcolor aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/vg&DFC {/vg&fcolor exch def} def + +/vg&C {mark exch aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/w {setlinewidth} def +/j {setlinejoin} def +/J {setlinecap} def +/M {setmiterlimit} def +/d {setdash} def +/i {setflat} def + +/W {clip} def +/W* {eoclip} def + +% Setup the default graphics state. +% (black; 1 pt. linewidth; miter join; butt-ends; solid) +/defaultGraphicsState {0 g 1 w 0 j 0 J [] 0 d} def + +% Emulation of the rectangle operators for PostScript implementations +% which do not implement all Level 2 features. This is an INCOMPLETE +% emulation; only the "x y width height rect..." form is emulated. +/*rf {gsave newpath re fill grestore} def +/*rs {gsave newpath re stroke grestore} def +/*rc {newpath re clip} def +/rf /rectfill where {pop /rectfill}{/*rf} ifelse load def +/rs /rectstroke where {pop /rectstroke}{/*rs} ifelse load def +/rc /rectclip where {pop /rectclip}{/*rc} ifelse load def + +% Emulation of the selectfont operator. This includes a 20% increase in +% the fontsize which is necessary to get sizes similar to the Java fonts. +/*sf {exch findfont exch + dup type /arraytype eq {makefont}{scalefont} ifelse setfont} bind def +/sf /selectfont where {pop {1.2 mul selectfont}}{{1.2 mul *sf}} ifelse def + +% Special version of stroke which allows the dash pattern to continue +% across path segments. (This may be needed for PostScript although +% modern printers seem to do this correctly.) +/vg&stroke { + currentdash pop length 0 eq + {stroke} + { + currentdash /vg&doffset exch def pop + flattenpath + {m vg&resetdash} + {2 copy + currentpoint + 3 -1 roll sub dup mul + 3 1 roll sub dup mul + add sqrt + 3 1 roll l + currentdash 3 -1 roll add setdash} + {} + {h vg&resetdash} + pathforall + stroke + vg&resetdash + } ifelse +} def +/vg&resetdash {currentdash pop vg&doffset setdash} def + +% Initialize variables for safety. +/delta 0 def +/xv 0 def /yv 0 def /width 0 def /height 0 def + +% Initialize to portrait INTERNATIONAL (Letter-height, A4-width) page. +/pw 595 def /ph 791 def /po true def /ftp false def + +% Initialize margins to 20 points. +/ml 20 def /mr 20 def /mt 20 def /mb 20 def + +% Temporary matrices. +/smatrix 0 def /nmatrix 0 def + +% set page size (usage: setpagesize) +/setpagesize {/ph exch def /pw exch def} def + +% set page orientation (usage: portrait or landscape) +/portrait {/po true def} def +/landscape {/po false def} def + +% force natural size for image (usage: naturalsize) +/naturalsize {/ftp false def} def + +% resize image to fill page (usage: fittopage) +/fittopage {/ftp true def} def + +% set margins of the page (usage: setmargins) +/setmargins {/mr exch def /mt exch def /mb exch def /ml exch def} def + +% set the graphic's size (usage: setsize) +/setsize {/gh exch def /gw exch def} def + +% set the graphic's origin (usage: setorigin) +/setorigin {/gy exch def /gx exch def} def + +% calculate image center +/imagecenter {pw ml sub mr sub 2 div ml add + ph mt sub mb sub 2 div mb add} def + +% calculate the necessary scaling +/imagescale {po {gw}{gh} ifelse pw ml sub mr sub div + po {gh}{gw} ifelse ph mt sub mb sub div + 2 copy lt {exch} if pop + ftp not {1 2 copy lt {exch} if pop} if + 1 exch div /sfactor exch def + /gw gw sfactor mul def /gh gh sfactor mul def} def + +% calculate image origin +/imageorigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div po {add}{sub} ifelse} def + +% calculate the clipping origin +/cliporigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub floor + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div sub floor} def + +% Set the clipping region to the bounding box. +/cliptobounds {cliporigin po {gw}{gh} ifelse 1 add + po {gh}{gw} ifelse 1 add rc} def + +% set the base transformation matrix (usage: setbasematrix) +/setbasematrix {imageorigin translate + po {0}{90} ifelse rotate + sfactor sfactor neg scale + /defaultmatrix matrix currentmatrix def} def + +% The lower-right bias in drawing 1 pt. wide lines. +/bias {q 0.5 0.5 translate} def +/unbias {Q} def + +% Draw a line. (x0 y0 x1 y1 line) +/L {bias n m l S unbias} def + +% Polyline primitive. +/polyline {n m 1 exch 1 exch + {pop currentfile token pop currentfile token pop l} for + } def + +% Draw a polyline (n x0 y0 OPL x1 y1 x2 y2 ... ... xn yn) +/OPL {bias polyline S unbias} def + +% Draw a closed polyline (n x0 y0 CPL x1 y1 x2 y2 ... ... xn yn) +/CPL {bias polyline s unbias} def + +% Draw a filled polyline (n x0 y0 FPL x1 y1 x2 y2 ... ... xn yn) +/FPL {polyline h f*} def + +% Draw an oval. (x y w h OVL) +/OVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width currentlinewidth sub 2 div + height currentlinewidth sub 2 div neg + scale n 0 0 1 5 -2 roll arc + smatrix setmatrix S} def + +% Draw a filled oval. (x y w h FOVL) +/FOVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width 2 div + height 2 div neg + scale n 0 0 m 0 0 1 5 -2 roll arc + h smatrix setmatrix f} def + +% Draw a rounded rectangle. (x y w h arcwidth archeight RREC) +/RREC {matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + s} def + +% Draw a filled rounded rectangle. (x y w h arcwidth archeight FRREC) +/FRREC{matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + h f} def + +% Draw a string. (string x y STR) +/STR {q m 1 -1 scale recshow Q} def + +% Define basic plot symbols. +/xys {/siz exch def /yv exch def /xv exch def} def +/hline {xys n xv siz 2. div sub yv m siz 0 rlineto S} def +/vline {xys n xv yv siz 2. div sub m 0 siz rlineto S} def +/plus {xys n xv yv siz 2. div sub m 0 siz rlineto + xv siz 2. div sub yv m siz 0 rlineto S} def +/dot {n 2. div 0 360 arc s} def +/fdot {n 2. div 0 360 arc h f} def +/box {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rs} def +/fbox {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rf} def +/tridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto s} def +/ftridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto h f} def + +% Symbols defined in terms of the others. +/star {3 copy cross plus} def +/cross {xys q xv yv translate 45 rotate 0 0 siz plus Q} def +/diamond {xys q xv yv translate 45 rotate 0 0 siz box Q} def +/fdiamond {xys q xv yv translate 45 rotate 0 0 siz fbox Q} def +/triup {xys q xv yv translate 180 rotate 0 0 siz tridn Q} def +/ftriup {xys q xv yv translate 180 rotate 0 0 siz ftridn Q} def + +% Define the composite fonts used to print Unicode strings. +% Undefine particular values in an encoding array. +/vg&undef { {exch dup 3 -1 roll /.notdef put} forall } def +/vg&redef { {3 -1 roll dup 4 2 roll put} forall } def + +% usage: key encoding basefontname vg&newbasefont font +/vg&newbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + currentdict + end +definefont +} def + +% usage: key encoding basefontname vg&newskewedbasefont font +/vg&newskewedbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + exch FontMatrix exch matrix concatmatrix /FontMatrix exch def + currentdict + end +definefont +} def + +% usage: basekey suffix vg&nconcat name +/vg&nconcat { + 2 {dup length string cvs exch} repeat + dup length 3 -1 roll dup length 3 -1 roll add string + dup 0 4 -1 roll dup length 5 1 roll putinterval + dup 4 -2 roll exch putinterval cvn +} def + +%usage: fontname vg&skewmatrix matrix +/vg&skewmatrix { +findfont dup /FontInfo known + { + /FontInfo get dup /ItalicAngle known + { + [ 1 0 4 -1 roll /ItalicAngle get neg dup sin exch cos div 1 0 0 ] + } + {pop matrix} ifelse + } + {pop matrix} ifelse +} def + +% usage: newfontname basefontname vg&newcompositefont -- +/vg&newcompositefont { +/vg&fstyle exch def +/vg&bfont exch def +/vg&fname exch def +<< +/FontStyleBits vg&fstyle +/FontType 0 +/FontMatrix matrix +/FontName vg&fname +/FMapType 2 +/Encoding [ 0 1 255 {pop 6} for ] + dup 16#00 0 put % Latin + dup 16#03 1 put % Greek + dup 16#20 2 put % Punctuation + dup 16#21 3 put % Arrows + dup 16#22 4 put % MathOps + dup 16#27 5 put % Dingbats + +/FDepVector [ +vg&bfont /-UC-Latin vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} 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+1.00000 w +2 J +0 j +newpath +41.0000 70.0000 m +36.0000 70.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 35.0000 75.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -35.0000 -75.0000 ] concat +newpath +33.6601 72.0302 m +33.9056 71.4505 34.2155 71.0030 34.5900 70.6877 c +34.9646 70.3724 35.4311 70.2148 35.9897 70.2148 c +36.6795 70.2148 37.2085 70.4391 37.5766 70.8877 c +37.8559 71.2220 37.9956 71.5795 37.9956 71.9604 c +37.9956 72.5867 37.6020 73.2342 36.8149 73.9028 c +37.3439 74.1101 37.7438 74.4064 38.0146 74.7915 c +38.2854 75.1766 38.4209 75.6293 38.4209 76.1499 c +38.4209 76.8946 38.1839 77.5400 37.7099 78.0859 c +37.0921 78.7968 36.1971 79.1523 35.0249 79.1523 c +34.4451 79.1523 34.0505 79.0804 33.8410 78.9365 c +33.6315 78.7926 33.5268 78.6381 33.5268 78.4731 c +33.5268 78.3504 33.5765 78.2425 33.6760 78.1494 c +33.7754 78.0563 33.8950 78.0097 34.0346 78.0097 c +34.1404 78.0097 34.2483 78.0266 34.3584 78.0605 c +34.4303 78.0817 34.5932 78.1589 34.8471 78.2922 c +35.1010 78.4255 35.2766 78.5048 35.3740 78.5302 c +35.5306 78.5768 35.6977 78.6001 35.8754 78.6001 c +36.3071 78.6001 36.6827 78.4329 37.0022 78.0986 c +37.3217 77.7643 37.4814 77.3686 37.4814 76.9116 c +37.4814 76.5773 37.4073 76.2514 37.2592 75.9340 c +37.1492 75.6971 37.0286 75.5172 36.8974 75.3945 c +36.7154 75.2252 36.4658 75.0718 36.1484 74.9343 c +35.8310 74.7967 35.5073 74.7280 35.1772 74.7280 c +34.9741 74.7280 l +34.9741 74.5376 l +35.3084 74.4952 35.6438 74.3746 35.9802 74.1757 c +36.3166 73.9768 36.5610 73.7377 36.7133 73.4585 c +36.8657 73.1792 36.9418 72.8724 36.9418 72.5380 c +36.9418 72.1022 36.8054 71.7499 36.5324 71.4812 c +36.2595 71.2124 35.9199 71.0781 35.5136 71.0781 c +34.8577 71.0781 34.3097 71.4293 33.8696 72.1318 c +h +f +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 409.000 m +39.0000 409.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 413.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -413.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 333.000 m +39.0000 333.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 338.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -338.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 258.000 m +39.0000 258.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 262.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -262.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 183.000 m +39.0000 183.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 187.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -187.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 107.000 m +39.0000 107.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 112.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -112.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +41.0000 32.0000 m +39.0000 32.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 36.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -36.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +Q +2 J +0 j +Q +Q +cliprestore +1 0 500 500 rc +[ 1.00000 0 0 1.00000 1.00000 0 ] concat +[ 1.00000 0 0 1.00000 -1.00000 0 ] concat +cliprestore +1.00000 w +2 J +0 j +end end restore showpage + +%%Trailer +%%EOF diff --git a/Grafiken/A6-eps-converted-to.pdf b/Grafiken/A6-eps-converted-to.pdf new file mode 100644 index 0000000..d2361b1 Binary files /dev/null and b/Grafiken/A6-eps-converted-to.pdf differ diff --git a/Grafiken/A6.eps b/Grafiken/A6.eps new file mode 100644 index 0000000..71dae60 --- /dev/null +++ b/Grafiken/A6.eps @@ -0,0 +1,3146 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%BoundingBox: 20 118 575 673 +%%Creator: FreeHEP Graphics2D Driver +%%Producer: com.maplesoft.mathdoc.view.plot.paint.PlotPSGraphics2D Revision: 12753 +%%For: +%%Title: +%%CreationDate: Montag, 20. Mai 2024, 08:37:04 Mitteleuropäische Sommerzeit +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +100 dict dup begin + +% +% File: org/freehep/graphicsio.ps/PSProlog.txt +% Author: Charles Loomis +% + +% Redefinitions which save some space in the output file. These are also +% the same as the PDF operators. +/q {gsave} def +/Q {grestore} def + +/n {newpath} def +/m {moveto} def +/l {lineto} def +/c {curveto} def +/h {closepath} def + +/re {4 -2 roll moveto + dup 0 exch rlineto exch 0 rlineto + neg 0 exch rlineto closepath} def + +/f {fill} def +/f* {eofill} def +/F {gsave vg&FC fill grestore} def +/F* {gsave vg&FC eofill grestore} def + +/s {closepath stroke} def +/S {stroke} def + +/b {closepath gsave vg&FC fill grestore + gsave stroke grestore newpath} def +/B {gsave vg&FC fill grestore gsave stroke grestore newpath} def +/b* {closepath gsave vg&FC eofill grestore + gsave stroke grestore newpath} def +/B* {gsave vg&FC eofill grestore gsave stroke grestore newpath} def + +/g {1 array astore /vg&fcolor exch def} def +/G {setgray} def +/k {4 array astore /vg&fcolor exch def} def +/K {setcmykcolor} def +/rg {3 array astore /vg&fcolor exch def} def +/RG {setrgbcolor} def + +% Initialize the fill color. +0 0 0 rg + +/vg&FC {mark vg&fcolor aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/vg&DFC {/vg&fcolor exch def} def + +/vg&C {mark exch aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/w {setlinewidth} def +/j {setlinejoin} def +/J {setlinecap} def +/M {setmiterlimit} def +/d {setdash} def +/i {setflat} def + +/W {clip} def +/W* {eoclip} def + +% Setup the default graphics state. +% (black; 1 pt. linewidth; miter join; butt-ends; solid) +/defaultGraphicsState {0 g 1 w 0 j 0 J [] 0 d} def + +% Emulation of the rectangle operators for PostScript implementations +% which do not implement all Level 2 features. This is an INCOMPLETE +% emulation; only the "x y width height rect..." form is emulated. +/*rf {gsave newpath re fill grestore} def +/*rs {gsave newpath re stroke grestore} def +/*rc {newpath re clip} def +/rf /rectfill where {pop /rectfill}{/*rf} ifelse load def +/rs /rectstroke where {pop /rectstroke}{/*rs} ifelse load def +/rc /rectclip where {pop /rectclip}{/*rc} ifelse load def + +% Emulation of the selectfont operator. This includes a 20% increase in +% the fontsize which is necessary to get sizes similar to the Java fonts. +/*sf {exch findfont exch + dup type /arraytype eq {makefont}{scalefont} ifelse setfont} bind def +/sf /selectfont where {pop {1.2 mul selectfont}}{{1.2 mul *sf}} ifelse def + +% Special version of stroke which allows the dash pattern to continue +% across path segments. (This may be needed for PostScript although +% modern printers seem to do this correctly.) +/vg&stroke { + currentdash pop length 0 eq + {stroke} + { + currentdash /vg&doffset exch def pop + flattenpath + {m vg&resetdash} + {2 copy + currentpoint + 3 -1 roll sub dup mul + 3 1 roll sub dup mul + add sqrt + 3 1 roll l + currentdash 3 -1 roll add setdash} + {} + {h vg&resetdash} + pathforall + stroke + vg&resetdash + } ifelse +} def +/vg&resetdash {currentdash pop vg&doffset setdash} def + +% Initialize variables for safety. +/delta 0 def +/xv 0 def /yv 0 def /width 0 def /height 0 def + +% Initialize to portrait INTERNATIONAL (Letter-height, A4-width) page. +/pw 595 def /ph 791 def /po true def /ftp false def + +% Initialize margins to 20 points. +/ml 20 def /mr 20 def /mt 20 def /mb 20 def + +% Temporary matrices. +/smatrix 0 def /nmatrix 0 def + +% set page size (usage: setpagesize) +/setpagesize {/ph exch def /pw exch def} def + +% set page orientation (usage: portrait or landscape) +/portrait {/po true def} def +/landscape {/po false def} def + +% force natural size for image (usage: naturalsize) +/naturalsize {/ftp false def} def + +% resize image to fill page (usage: fittopage) +/fittopage {/ftp true def} def + +% set margins of the page (usage: setmargins) +/setmargins {/mr exch def /mt exch def /mb exch def /ml exch def} def + +% set the graphic's size (usage: setsize) +/setsize {/gh exch def /gw exch def} def + +% set the graphic's origin (usage: setorigin) +/setorigin {/gy exch def /gx exch def} def + +% calculate image center +/imagecenter {pw ml sub mr sub 2 div ml add + ph mt sub mb sub 2 div mb add} def + +% calculate the necessary scaling +/imagescale {po {gw}{gh} ifelse pw ml sub mr sub div + po {gh}{gw} ifelse ph mt sub mb sub div + 2 copy lt {exch} if pop + ftp not {1 2 copy lt {exch} if pop} if + 1 exch div /sfactor exch def + /gw gw sfactor mul def /gh gh sfactor mul def} def + +% calculate image origin +/imageorigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div po {add}{sub} ifelse} def + +% calculate the clipping origin +/cliporigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub floor + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div sub floor} def + +% Set the clipping region to the bounding box. +/cliptobounds {cliporigin po {gw}{gh} ifelse 1 add + po {gh}{gw} ifelse 1 add rc} def + +% set the base transformation matrix (usage: setbasematrix) +/setbasematrix {imageorigin translate + po {0}{90} ifelse rotate + sfactor sfactor neg scale + /defaultmatrix matrix currentmatrix def} def + +% The lower-right bias in drawing 1 pt. wide lines. +/bias {q 0.5 0.5 translate} def +/unbias {Q} def + +% Draw a line. (x0 y0 x1 y1 line) +/L {bias n m l S unbias} def + +% Polyline primitive. +/polyline {n m 1 exch 1 exch + {pop currentfile token pop currentfile token pop l} for + } def + +% Draw a polyline (n x0 y0 OPL x1 y1 x2 y2 ... ... xn yn) +/OPL {bias polyline S unbias} def + +% Draw a closed polyline (n x0 y0 CPL x1 y1 x2 y2 ... ... xn yn) +/CPL {bias polyline s unbias} def + +% Draw a filled polyline (n x0 y0 FPL x1 y1 x2 y2 ... ... xn yn) +/FPL {polyline h f*} def + +% Draw an oval. (x y w h OVL) +/OVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width currentlinewidth sub 2 div + height currentlinewidth sub 2 div neg + scale n 0 0 1 5 -2 roll arc + smatrix setmatrix S} def + +% Draw a filled oval. (x y w h FOVL) +/FOVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width 2 div + height 2 div neg + scale n 0 0 m 0 0 1 5 -2 roll arc + h smatrix setmatrix f} def + +% Draw a rounded rectangle. (x y w h arcwidth archeight RREC) +/RREC {matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + s} def + +% Draw a filled rounded rectangle. (x y w h arcwidth archeight FRREC) +/FRREC{matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + h f} def + +% Draw a string. (string x y STR) +/STR {q m 1 -1 scale recshow Q} def + +% Define basic plot symbols. +/xys {/siz exch def /yv exch def /xv exch def} def +/hline {xys n xv siz 2. div sub yv m siz 0 rlineto S} def +/vline {xys n xv yv siz 2. div sub m 0 siz rlineto S} def +/plus {xys n xv yv siz 2. div sub m 0 siz rlineto + xv siz 2. div sub yv m siz 0 rlineto S} def +/dot {n 2. div 0 360 arc s} def +/fdot {n 2. div 0 360 arc h f} def +/box {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rs} def +/fbox {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rf} def +/tridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto s} def +/ftridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto h f} def + +% Symbols defined in terms of the others. +/star {3 copy cross plus} def +/cross {xys q xv yv translate 45 rotate 0 0 siz plus Q} def +/diamond {xys q xv yv translate 45 rotate 0 0 siz box Q} def +/fdiamond {xys q xv yv translate 45 rotate 0 0 siz fbox Q} def +/triup {xys q xv yv translate 180 rotate 0 0 siz tridn Q} def +/ftriup {xys q xv yv translate 180 rotate 0 0 siz ftridn Q} def + +% Define the composite fonts used to print Unicode strings. +% Undefine particular values in an encoding array. +/vg&undef { {exch dup 3 -1 roll /.notdef put} forall } def +/vg&redef { {3 -1 roll dup 4 2 roll put} forall } def + +% usage: key encoding basefontname vg&newbasefont font +/vg&newbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + currentdict + end +definefont +} def + +% usage: key encoding basefontname vg&newskewedbasefont font +/vg&newskewedbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + exch FontMatrix exch matrix concatmatrix /FontMatrix exch def + currentdict + end +definefont +} def + +% usage: basekey suffix vg&nconcat name +/vg&nconcat { + 2 {dup length string cvs exch} repeat + dup length 3 -1 roll dup length 3 -1 roll add string + dup 0 4 -1 roll dup length 5 1 roll putinterval + dup 4 -2 roll exch putinterval cvn +} def + +%usage: fontname vg&skewmatrix matrix +/vg&skewmatrix { +findfont dup /FontInfo known + { + /FontInfo get dup /ItalicAngle known + { + [ 1 0 4 -1 roll /ItalicAngle get neg dup sin exch cos div 1 0 0 ] + } + {pop matrix} ifelse + } + {pop matrix} ifelse +} def + +% usage: newfontname basefontname vg&newcompositefont -- +/vg&newcompositefont { +/vg&fstyle exch def +/vg&bfont exch def +/vg&fname exch def +<< +/FontStyleBits vg&fstyle +/FontType 0 +/FontMatrix matrix +/FontName vg&fname +/FMapType 2 +/Encoding [ 0 1 255 {pop 6} for ] + dup 16#00 0 put % Latin + dup 16#03 1 put % Greek + dup 16#20 2 put % Punctuation + dup 16#21 3 put % Arrows + dup 16#22 4 put % MathOps + dup 16#27 5 put % Dingbats + +/FDepVector [ +vg&bfont /-UC-Latin vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} 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+0 j +newpath +169.000 201.000 m +164.000 201.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 163.000 206.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -163.000 -206.000 ] concat +newpath +166.960 209.343 m +166.357 211.000 l +161.279 211.000 l +161.279 210.765 l +162.773 209.402 163.824 208.289 164.434 207.426 c +165.043 206.563 165.348 205.773 165.348 205.058 c +165.348 204.512 165.181 204.064 164.846 203.712 c +164.512 203.361 164.112 203.186 163.647 203.186 c +163.223 203.186 162.844 203.309 162.507 203.557 c +162.171 203.804 161.922 204.167 161.761 204.646 c +161.526 204.646 l +161.632 203.863 161.904 203.262 162.342 202.843 c +162.780 202.424 163.327 202.214 163.983 202.214 c +164.681 202.214 165.264 202.439 165.732 202.887 c +166.199 203.336 166.433 203.865 166.433 204.474 c +166.433 204.910 166.332 205.346 166.128 205.782 c +165.815 206.467 165.307 207.193 164.605 207.959 c +163.551 209.110 162.893 209.804 162.631 210.041 c +164.878 210.041 l +165.335 210.041 165.656 210.024 165.840 209.990 c +166.024 209.956 166.190 209.888 166.338 209.784 c +166.486 209.680 166.615 209.533 166.725 209.343 c +h +f +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 135.000 m +164.000 135.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 163.000 140.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -163.000 -140.000 ] concat +newpath +161.660 137.030 m +161.905 136.450 162.215 136.003 162.590 135.687 c +162.964 135.372 163.431 135.214 163.989 135.214 c +164.679 135.214 165.208 135.439 165.576 135.887 c +165.856 136.222 165.995 136.579 165.995 136.960 c +165.995 137.586 165.602 138.234 164.814 138.902 c +165.343 139.110 165.743 139.406 166.014 139.791 c +166.285 140.176 166.420 140.629 166.420 141.149 c +166.420 141.894 166.183 142.540 165.710 143.085 c +165.092 143.796 164.197 144.152 163.024 144.152 c +162.445 144.152 162.050 144.080 161.841 143.936 c +161.631 143.792 161.526 143.638 161.526 143.473 c +161.526 143.350 161.576 143.242 161.676 143.149 c +161.775 143.056 161.895 143.009 162.034 143.009 c +162.140 143.009 162.248 143.026 162.358 143.060 c +162.430 143.081 162.593 143.158 162.847 143.292 c +163.101 143.425 163.276 143.504 163.374 143.530 c +163.530 143.576 163.697 143.600 163.875 143.600 c +164.307 143.600 164.682 143.432 165.002 143.098 c +165.321 142.764 165.481 142.368 165.481 141.911 c +165.481 141.577 165.407 141.251 165.259 140.934 c +165.149 140.697 165.028 140.517 164.897 140.394 c +164.715 140.225 164.465 140.071 164.148 139.934 c +163.831 139.796 163.507 139.728 163.177 139.728 c +162.974 139.728 l +162.974 139.537 l +163.308 139.495 163.643 139.374 163.980 139.175 c +164.316 138.976 164.561 138.737 164.713 138.458 c +164.865 138.179 164.941 137.872 164.941 137.538 c +164.941 137.102 164.805 136.749 164.532 136.481 c +164.259 136.212 163.919 136.078 163.513 136.078 c +162.857 136.078 162.309 136.429 161.869 137.131 c +h +f +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 69.0000 m +164.000 69.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 163.000 74.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -163.000 -74.0000 ] concat +newpath +167.049 74.8261 m +167.049 75.7275 l +165.894 75.7275 l +165.894 78.0000 l +164.846 78.0000 l +164.846 75.7275 l +161.203 75.7275 l +161.203 74.9150 l +165.195 69.2148 l +165.894 69.2148 l +165.894 74.8261 l +h +164.846 74.8261 m +164.846 70.5542 l +161.825 74.8261 l +h +f +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 433.000 m +167.000 433.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 437.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -437.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 366.000 m +167.000 366.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 371.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -371.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 300.000 m +167.000 300.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 305.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -305.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 234.000 m +167.000 234.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 239.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -239.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 168.000 m +167.000 168.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 172.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -172.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 102.000 m +167.000 102.000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 106.000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -106.000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +q +0 w +1.00000 w +2 J +0 j +newpath +169.000 36.0000 m +167.000 36.0000 l +S +[ 1.00000 0 0 1.00000 -6.00000 -5.00000 ] concat +[ 1.00000 0 0 1.00000 6.00000 40.0000 ] concat +[ 1.00000 0 0 1.00000 0 0 ] concat +[ 1.00000 0 0 1.00000 -6.00000 -40.0000 ] concat +[ 1.00000 0 0 1.00000 6.00000 5.00000 ] defaultmatrix matrix concatmatrix setmatrix +0 w +0 J +1 j +Q +Q +2 J +0 j +Q +Q +cliprestore +1 0 500 500 rc +[ 1.00000 0 0 1.00000 1.00000 0 ] concat +[ 1.00000 0 0 1.00000 -1.00000 0 ] concat +cliprestore +1.00000 w +2 J +0 j +end end restore showpage + +%%Trailer +%%EOF diff --git a/Grafiken/A8-eps-converted-to.pdf b/Grafiken/A8-eps-converted-to.pdf new file mode 100644 index 0000000..efb188d Binary files /dev/null and b/Grafiken/A8-eps-converted-to.pdf differ diff --git a/Grafiken/A8.eps b/Grafiken/A8.eps new file mode 100644 index 0000000..7af7839 --- /dev/null +++ b/Grafiken/A8.eps @@ -0,0 +1,3284 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%BoundingBox: 20 118 575 673 +%%Creator: FreeHEP Graphics2D Driver +%%Producer: com.maplesoft.mathdoc.view.plot.paint.PlotPSGraphics2D Revision: 12753 +%%For: +%%Title: +%%CreationDate: Samstag, 25. Mai 2024, 12:01:13 Mitteleuropäische Sommerzeit +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +100 dict dup begin + +% +% File: org/freehep/graphicsio.ps/PSProlog.txt +% Author: Charles Loomis +% + +% Redefinitions which save some space in the output file. These are also +% the same as the PDF operators. +/q {gsave} def +/Q {grestore} def + +/n {newpath} def +/m {moveto} def +/l {lineto} def +/c {curveto} def +/h {closepath} def + +/re {4 -2 roll moveto + dup 0 exch rlineto exch 0 rlineto + neg 0 exch rlineto closepath} def + +/f {fill} def +/f* {eofill} def +/F {gsave vg&FC fill grestore} def +/F* {gsave vg&FC eofill grestore} def + +/s {closepath stroke} def +/S {stroke} def + +/b {closepath gsave vg&FC fill grestore + gsave stroke grestore newpath} def +/B {gsave vg&FC fill grestore gsave stroke grestore newpath} def +/b* {closepath gsave vg&FC eofill grestore + gsave stroke grestore newpath} def +/B* {gsave vg&FC eofill grestore gsave stroke grestore newpath} def + +/g {1 array astore /vg&fcolor exch def} def +/G {setgray} def +/k {4 array astore /vg&fcolor exch def} def +/K {setcmykcolor} def +/rg {3 array astore /vg&fcolor exch def} def +/RG {setrgbcolor} def + +% Initialize the fill color. +0 0 0 rg + +/vg&FC {mark vg&fcolor aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/vg&DFC {/vg&fcolor exch def} def + +/vg&C {mark exch aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/w {setlinewidth} def +/j {setlinejoin} def +/J {setlinecap} def +/M {setmiterlimit} def +/d {setdash} def +/i {setflat} def + +/W {clip} def +/W* {eoclip} def + +% Setup the default graphics state. +% (black; 1 pt. linewidth; miter join; butt-ends; solid) +/defaultGraphicsState {0 g 1 w 0 j 0 J [] 0 d} def + +% Emulation of the rectangle operators for PostScript implementations +% which do not implement all Level 2 features. This is an INCOMPLETE +% emulation; only the "x y width height rect..." form is emulated. +/*rf {gsave newpath re fill grestore} def +/*rs {gsave newpath re stroke grestore} def +/*rc {newpath re clip} def +/rf /rectfill where {pop /rectfill}{/*rf} ifelse load def +/rs /rectstroke where {pop /rectstroke}{/*rs} ifelse load def +/rc /rectclip where {pop /rectclip}{/*rc} ifelse load def + +% Emulation of the selectfont operator. This includes a 20% increase in +% the fontsize which is necessary to get sizes similar to the Java fonts. +/*sf {exch findfont exch + dup type /arraytype eq {makefont}{scalefont} ifelse setfont} bind def +/sf /selectfont where {pop {1.2 mul selectfont}}{{1.2 mul *sf}} ifelse def + +% Special version of stroke which allows the dash pattern to continue +% across path segments. (This may be needed for PostScript although +% modern printers seem to do this correctly.) +/vg&stroke { + currentdash pop length 0 eq + {stroke} + { + currentdash /vg&doffset exch def pop + flattenpath + {m vg&resetdash} + {2 copy + currentpoint + 3 -1 roll sub dup mul + 3 1 roll sub dup mul + add sqrt + 3 1 roll l + currentdash 3 -1 roll add setdash} + {} + {h vg&resetdash} + pathforall + stroke + vg&resetdash + } ifelse +} def +/vg&resetdash {currentdash pop vg&doffset setdash} def + +% Initialize variables for safety. +/delta 0 def +/xv 0 def /yv 0 def /width 0 def /height 0 def + +% Initialize to portrait INTERNATIONAL (Letter-height, A4-width) page. +/pw 595 def /ph 791 def /po true def /ftp false def + +% Initialize margins to 20 points. +/ml 20 def /mr 20 def /mt 20 def /mb 20 def + +% Temporary matrices. +/smatrix 0 def /nmatrix 0 def + +% set page size (usage: setpagesize) +/setpagesize {/ph exch def /pw exch def} def + +% set page orientation (usage: portrait or landscape) +/portrait {/po true def} def +/landscape {/po false def} def + +% force natural size for image (usage: naturalsize) +/naturalsize {/ftp false def} def + +% resize image to fill page (usage: fittopage) +/fittopage {/ftp true def} def + +% set margins of the page (usage: setmargins) +/setmargins {/mr exch def /mt exch def /mb exch def /ml exch def} def + +% set the graphic's size (usage: setsize) +/setsize {/gh exch def /gw exch def} def + +% set the graphic's origin (usage: setorigin) +/setorigin {/gy exch def /gx exch def} def + +% calculate image center +/imagecenter {pw ml sub mr sub 2 div ml add + ph mt sub mb sub 2 div mb add} def + +% calculate the necessary scaling +/imagescale {po {gw}{gh} ifelse pw ml sub mr sub div + po {gh}{gw} ifelse ph mt sub mb sub div + 2 copy lt {exch} if pop + ftp not {1 2 copy lt {exch} if pop} if + 1 exch div /sfactor exch def + /gw gw sfactor mul def /gh gh sfactor mul def} def + +% calculate image origin +/imageorigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div po {add}{sub} ifelse} def + +% calculate the clipping origin +/cliporigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub floor + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div sub floor} def + +% Set the clipping region to the bounding box. +/cliptobounds {cliporigin po {gw}{gh} ifelse 1 add + po {gh}{gw} ifelse 1 add rc} def + +% set the base transformation matrix (usage: setbasematrix) +/setbasematrix {imageorigin translate + po {0}{90} ifelse rotate + sfactor sfactor neg scale + /defaultmatrix matrix currentmatrix def} def + +% The lower-right bias in drawing 1 pt. wide lines. +/bias {q 0.5 0.5 translate} def +/unbias {Q} def + +% Draw a line. (x0 y0 x1 y1 line) +/L {bias n m l S unbias} def + +% Polyline primitive. +/polyline {n m 1 exch 1 exch + {pop currentfile token pop currentfile token pop l} for + } def + +% Draw a polyline (n x0 y0 OPL x1 y1 x2 y2 ... ... xn yn) +/OPL {bias polyline S unbias} def + +% Draw a closed polyline (n x0 y0 CPL x1 y1 x2 y2 ... ... xn yn) +/CPL {bias polyline s unbias} def + +% Draw a filled polyline (n x0 y0 FPL x1 y1 x2 y2 ... ... xn yn) +/FPL {polyline h f*} def + +% Draw an oval. (x y w h OVL) +/OVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width currentlinewidth sub 2 div + height currentlinewidth sub 2 div neg + scale n 0 0 1 5 -2 roll arc + smatrix setmatrix S} def + +% Draw a filled oval. (x y w h FOVL) +/FOVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width 2 div + height 2 div neg + scale n 0 0 m 0 0 1 5 -2 roll arc + h smatrix setmatrix f} def + +% Draw a rounded rectangle. (x y w h arcwidth archeight RREC) +/RREC {matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + s} def + +% Draw a filled rounded rectangle. (x y w h arcwidth archeight FRREC) +/FRREC{matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + h f} def + +% Draw a string. (string x y STR) +/STR {q m 1 -1 scale recshow Q} def + +% Define basic plot symbols. +/xys {/siz exch def /yv exch def /xv exch def} def +/hline {xys n xv siz 2. div sub yv m siz 0 rlineto S} def +/vline {xys n xv yv siz 2. div sub m 0 siz rlineto S} def +/plus {xys n xv yv siz 2. div sub m 0 siz rlineto + xv siz 2. div sub yv m siz 0 rlineto S} def +/dot {n 2. div 0 360 arc s} def +/fdot {n 2. div 0 360 arc h f} def +/box {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rs} def +/fbox {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rf} def +/tridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto s} def +/ftridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto h f} def + +% Symbols defined in terms of the others. +/star {3 copy cross plus} def +/cross {xys q xv yv translate 45 rotate 0 0 siz plus Q} def +/diamond {xys q xv yv translate 45 rotate 0 0 siz box Q} def +/fdiamond {xys q xv yv translate 45 rotate 0 0 siz fbox Q} def +/triup {xys q xv yv translate 180 rotate 0 0 siz tridn Q} def +/ftriup {xys q xv yv translate 180 rotate 0 0 siz ftridn Q} def + +% Define the composite fonts used to print Unicode strings. +% Undefine particular values in an encoding array. +/vg&undef { {exch dup 3 -1 roll /.notdef put} forall } def +/vg&redef { {3 -1 roll dup 4 2 roll put} forall } def + +% usage: key encoding basefontname vg&newbasefont font +/vg&newbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + currentdict + end +definefont +} def + +% usage: key encoding basefontname vg&newskewedbasefont font +/vg&newskewedbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + exch FontMatrix exch matrix concatmatrix /FontMatrix exch def + currentdict + end +definefont +} def + +% usage: basekey suffix vg&nconcat name +/vg&nconcat { + 2 {dup length string cvs exch} repeat + dup length 3 -1 roll dup length 3 -1 roll add string + dup 0 4 -1 roll dup length 5 1 roll putinterval + dup 4 -2 roll exch putinterval cvn +} def + +%usage: fontname vg&skewmatrix matrix +/vg&skewmatrix { +findfont dup /FontInfo known + { + /FontInfo get dup /ItalicAngle known + { + [ 1 0 4 -1 roll /ItalicAngle get neg dup sin exch cos div 1 0 0 ] + } + {pop matrix} ifelse + } + {pop matrix} ifelse +} def + +% usage: newfontname basefontname vg&newcompositefont -- +/vg&newcompositefont { +/vg&fstyle exch def +/vg&bfont exch def +/vg&fname exch def +<< +/FontStyleBits vg&fstyle +/FontType 0 +/FontMatrix matrix +/FontName vg&fname +/FMapType 2 +/Encoding [ 0 1 255 {pop 6} for ] + dup 16#00 0 put % Latin + dup 16#03 1 put % Greek + dup 16#20 2 put % Punctuation + dup 16#21 3 put % Arrows + dup 16#22 4 put % MathOps + dup 16#27 5 put % Dingbats + +/FDepVector [ +vg&bfont /-UC-Latin vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} 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Mai 2024, 09:32:05 Mitteleuropäische Sommerzeit +%%LanguageLevel: 3 +%%EndComments +%%BeginProlog +100 dict dup begin + +% +% File: org/freehep/graphicsio.ps/PSProlog.txt +% Author: Charles Loomis +% + +% Redefinitions which save some space in the output file. These are also +% the same as the PDF operators. +/q {gsave} def +/Q {grestore} def + +/n {newpath} def +/m {moveto} def +/l {lineto} def +/c {curveto} def +/h {closepath} def + +/re {4 -2 roll moveto + dup 0 exch rlineto exch 0 rlineto + neg 0 exch rlineto closepath} def + +/f {fill} def +/f* {eofill} def +/F {gsave vg&FC fill grestore} def +/F* {gsave vg&FC eofill grestore} def + +/s {closepath stroke} def +/S {stroke} def + +/b {closepath gsave vg&FC fill grestore + gsave stroke grestore newpath} def +/B {gsave vg&FC fill grestore gsave stroke grestore newpath} def +/b* {closepath gsave vg&FC eofill grestore + gsave stroke grestore newpath} def +/B* {gsave vg&FC eofill grestore gsave stroke grestore newpath} def + +/g {1 array astore /vg&fcolor exch def} def +/G {setgray} def +/k {4 array astore /vg&fcolor exch def} def +/K {setcmykcolor} def +/rg {3 array astore /vg&fcolor exch def} def +/RG {setrgbcolor} def + +% Initialize the fill color. +0 0 0 rg + +/vg&FC {mark vg&fcolor aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/vg&DFC {/vg&fcolor exch def} def + +/vg&C {mark exch aload pop + counttomark 1 eq {G} if + counttomark 3 eq {RG} if + counttomark 4 eq {K} if + cleartomark } def + +/w {setlinewidth} def +/j {setlinejoin} def +/J {setlinecap} def +/M {setmiterlimit} def +/d {setdash} def +/i {setflat} def + +/W {clip} def +/W* {eoclip} def + +% Setup the default graphics state. +% (black; 1 pt. linewidth; miter join; butt-ends; solid) +/defaultGraphicsState {0 g 1 w 0 j 0 J [] 0 d} def + +% Emulation of the rectangle operators for PostScript implementations +% which do not implement all Level 2 features. This is an INCOMPLETE +% emulation; only the "x y width height rect..." form is emulated. +/*rf {gsave newpath re fill grestore} def +/*rs {gsave newpath re stroke grestore} def +/*rc {newpath re clip} def +/rf /rectfill where {pop /rectfill}{/*rf} ifelse load def +/rs /rectstroke where {pop /rectstroke}{/*rs} ifelse load def +/rc /rectclip where {pop /rectclip}{/*rc} ifelse load def + +% Emulation of the selectfont operator. This includes a 20% increase in +% the fontsize which is necessary to get sizes similar to the Java fonts. +/*sf {exch findfont exch + dup type /arraytype eq {makefont}{scalefont} ifelse setfont} bind def +/sf /selectfont where {pop {1.2 mul selectfont}}{{1.2 mul *sf}} ifelse def + +% Special version of stroke which allows the dash pattern to continue +% across path segments. (This may be needed for PostScript although +% modern printers seem to do this correctly.) +/vg&stroke { + currentdash pop length 0 eq + {stroke} + { + currentdash /vg&doffset exch def pop + flattenpath + {m vg&resetdash} + {2 copy + currentpoint + 3 -1 roll sub dup mul + 3 1 roll sub dup mul + add sqrt + 3 1 roll l + currentdash 3 -1 roll add setdash} + {} + {h vg&resetdash} + pathforall + stroke + vg&resetdash + } ifelse +} def +/vg&resetdash {currentdash pop vg&doffset setdash} def + +% Initialize variables for safety. +/delta 0 def +/xv 0 def /yv 0 def /width 0 def /height 0 def + +% Initialize to portrait INTERNATIONAL (Letter-height, A4-width) page. +/pw 595 def /ph 791 def /po true def /ftp false def + +% Initialize margins to 20 points. +/ml 20 def /mr 20 def /mt 20 def /mb 20 def + +% Temporary matrices. +/smatrix 0 def /nmatrix 0 def + +% set page size (usage: setpagesize) +/setpagesize {/ph exch def /pw exch def} def + +% set page orientation (usage: portrait or landscape) +/portrait {/po true def} def +/landscape {/po false def} def + +% force natural size for image (usage: naturalsize) +/naturalsize {/ftp false def} def + +% resize image to fill page (usage: fittopage) +/fittopage {/ftp true def} def + +% set margins of the page (usage: setmargins) +/setmargins {/mr exch def /mt exch def /mb exch def /ml exch def} def + +% set the graphic's size (usage: setsize) +/setsize {/gh exch def /gw exch def} def + +% set the graphic's origin (usage: setorigin) +/setorigin {/gy exch def /gx exch def} def + +% calculate image center +/imagecenter {pw ml sub mr sub 2 div ml add + ph mt sub mb sub 2 div mb add} def + +% calculate the necessary scaling +/imagescale {po {gw}{gh} ifelse pw ml sub mr sub div + po {gh}{gw} ifelse ph mt sub mb sub div + 2 copy lt {exch} if pop + ftp not {1 2 copy lt {exch} if pop} if + 1 exch div /sfactor exch def + /gw gw sfactor mul def /gh gh sfactor mul def} def + +% calculate image origin +/imageorigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div po {add}{sub} ifelse} def + +% calculate the clipping origin +/cliporigin {pw ml sub mr sub 2 div ml add + po {gw}{gh} ifelse 2 div sub floor + ph mt sub mb sub 2 div mb add + po {gh}{gw} ifelse 2 div sub floor} def + +% Set the clipping region to the bounding box. +/cliptobounds {cliporigin po {gw}{gh} ifelse 1 add + po {gh}{gw} ifelse 1 add rc} def + +% set the base transformation matrix (usage: setbasematrix) +/setbasematrix {imageorigin translate + po {0}{90} ifelse rotate + sfactor sfactor neg scale + /defaultmatrix matrix currentmatrix def} def + +% The lower-right bias in drawing 1 pt. wide lines. +/bias {q 0.5 0.5 translate} def +/unbias {Q} def + +% Draw a line. (x0 y0 x1 y1 line) +/L {bias n m l S unbias} def + +% Polyline primitive. +/polyline {n m 1 exch 1 exch + {pop currentfile token pop currentfile token pop l} for + } def + +% Draw a polyline (n x0 y0 OPL x1 y1 x2 y2 ... ... xn yn) +/OPL {bias polyline S unbias} def + +% Draw a closed polyline (n x0 y0 CPL x1 y1 x2 y2 ... ... xn yn) +/CPL {bias polyline s unbias} def + +% Draw a filled polyline (n x0 y0 FPL x1 y1 x2 y2 ... ... xn yn) +/FPL {polyline h f*} def + +% Draw an oval. (x y w h OVL) +/OVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width currentlinewidth sub 2 div + height currentlinewidth sub 2 div neg + scale n 0 0 1 5 -2 roll arc + smatrix setmatrix S} def + +% Draw a filled oval. (x y w h FOVL) +/FOVL {matrix currentmatrix /smatrix exch def + /height exch def /width exch def + /yv exch def /xv exch def + width 2 div xv add height 2 div yv add translate + width 2 div + height 2 div neg + scale n 0 0 m 0 0 1 5 -2 roll arc + h smatrix setmatrix f} def + +% Draw a rounded rectangle. (x y w h arcwidth archeight RREC) +/RREC {matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + s} def + +% Draw a filled rounded rectangle. (x y w h arcwidth archeight FRREC) +/FRREC{matrix currentmatrix /smatrix exch def + 2 div /ah exch def + 2 div /aw exch def + /height exch def /width exch def + /yv exch def /xv exch def + aw ah scale matrix + currentmatrix /nmatrix exch def + smatrix setmatrix + n xv width add aw sub yv m + nmatrix setmatrix + currentpoint exch 1 add exch + currentpoint 1 add exch 1 add exch + 1 arct smatrix setmatrix + xv width add yv height add ah sub l + nmatrix setmatrix + currentpoint 1 add + currentpoint exch 1 sub exch 1 add + 1 arct smatrix setmatrix + xv aw add yv height add l + nmatrix setmatrix + currentpoint exch 1 sub exch + currentpoint exch 1 sub exch 1 sub + 1 arct smatrix setmatrix + xv yv ah add l + nmatrix setmatrix + currentpoint 1 sub + currentpoint exch 1 add exch 1 sub + 1 arct smatrix setmatrix + h f} def + +% Draw a string. (string x y STR) +/STR {q m 1 -1 scale recshow Q} def + +% Define basic plot symbols. +/xys {/siz exch def /yv exch def /xv exch def} def +/hline {xys n xv siz 2. div sub yv m siz 0 rlineto S} def +/vline {xys n xv yv siz 2. div sub m 0 siz rlineto S} def +/plus {xys n xv yv siz 2. div sub m 0 siz rlineto + xv siz 2. div sub yv m siz 0 rlineto S} def +/dot {n 2. div 0 360 arc s} def +/fdot {n 2. div 0 360 arc h f} def +/box {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rs} def +/fbox {xys n xv siz 2 sqrt div 2 div sub yv siz 2 sqrt div 2 div sub + siz 2 sqrt div dup rf} def +/tridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto s} def +/ftridn{xys n xv yv siz 3 sqrt div add m + siz 2. div neg 3 sqrt 2. div siz mul neg rlineto + siz 0 rlineto h f} def + +% Symbols defined in terms of the others. +/star {3 copy cross plus} def +/cross {xys q xv yv translate 45 rotate 0 0 siz plus Q} def +/diamond {xys q xv yv translate 45 rotate 0 0 siz box Q} def +/fdiamond {xys q xv yv translate 45 rotate 0 0 siz fbox Q} def +/triup {xys q xv yv translate 180 rotate 0 0 siz tridn Q} def +/ftriup {xys q xv yv translate 180 rotate 0 0 siz ftridn Q} def + +% Define the composite fonts used to print Unicode strings. +% Undefine particular values in an encoding array. +/vg&undef { {exch dup 3 -1 roll /.notdef put} forall } def +/vg&redef { {3 -1 roll dup 4 2 roll put} forall } def + +% usage: key encoding basefontname vg&newbasefont font +/vg&newbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + currentdict + end +definefont +} def + +% usage: key encoding basefontname vg&newskewedbasefont font +/vg&newskewedbasefont { +findfont dup length dict copy + begin + currentdict /FID undef + /Encoding exch def + dup /FontName exch def + exch FontMatrix exch matrix concatmatrix /FontMatrix exch def + currentdict + end +definefont +} def + +% usage: basekey suffix vg&nconcat name +/vg&nconcat { + 2 {dup length string cvs exch} repeat + dup length 3 -1 roll dup length 3 -1 roll add string + dup 0 4 -1 roll dup length 5 1 roll putinterval + dup 4 -2 roll exch putinterval cvn +} def + +%usage: fontname vg&skewmatrix matrix +/vg&skewmatrix { +findfont dup /FontInfo known + { + /FontInfo get dup /ItalicAngle known + { + [ 1 0 4 -1 roll /ItalicAngle get neg dup sin exch cos div 1 0 0 ] + } + {pop matrix} ifelse + } + {pop matrix} ifelse +} def + +% usage: newfontname basefontname vg&newcompositefont -- +/vg&newcompositefont { +/vg&fstyle exch def +/vg&bfont exch def +/vg&fname exch def +<< +/FontStyleBits vg&fstyle +/FontType 0 +/FontMatrix matrix +/FontName vg&fname +/FMapType 2 +/Encoding [ 0 1 255 {pop 6} for ] + dup 16#00 0 put % Latin + dup 16#03 1 put % Greek + dup 16#20 2 put % Punctuation + dup 16#21 3 put % Arrows + dup 16#22 4 put % MathOps + dup 16#27 5 put % Dingbats + +/FDepVector [ +vg&bfont /-UC-Latin vg&nconcat UCLatinEncoding +vg&bfont vg&newbasefont + +vg&bfont vg&skewmatrix +vg&bfont /-UC-Greek vg&nconcat UCGreekEncoding +/Symbol vg&newskewedbasefont + +vg&bfont /-UC-Punctuation vg&nconcat UCPunctuationEncoding +vg&bfont vg&newbasefont + +/Arrows-UC findfont +/MathOps-UC findfont +/Dingbats-UC findfont +/Undefined-UC findfont ] +>> +vg&fname exch definefont pop +} def + +% Null encoding vector (all elements set to .notdef) +/NullEncoding [ 256 {/.notdef} repeat ] def + +% Unicode Latin encoding (unicode codes \u0000-\u00ff) +/UCLatinEncoding + ISOLatin1Encoding dup length array copy + dup 16#60 /grave put + [ 16#90 16#91 16#92 16#93 16#94 16#95 16#96 + 16#97 16#98 16#9a 16#9b 16#9d 16#9e 16#9f + ] vg&undef + def + +% Unicode Greek encoding (unicode codes \u0370-\u03ff) +/UCGreekEncoding + NullEncoding dup length array copy + << 16#91 /Alpha 16#92 /Beta 16#93 /Gamma 16#94 /Delta + 16#95 /Epsilon 16#96 /Zeta 16#97 /Eta 16#98 /Theta + 16#99 /Iota 16#9a /Kappa 16#9b /Lambda 16#9c /Mu + 16#9d /Nu 16#9e /Xi 16#9f /Omicron 16#a0 /Pi + 16#a1 /Rho 16#a3 /Sigma 16#a4 /Tau 16#a5 /Upsilon + 16#a6 /Phi 16#a7 /Chi 16#a8 /Psi 16#a9 /Omega + 16#b1 /alpha 16#b2 /beta 16#b3 /gamma 16#b4 /delta + 16#b5 /epsilon 16#b6 /zeta 16#b7 /eta 16#b8 /theta + 16#b9 /iota 16#ba /kappa 16#bb /lambda 16#bc /mu + 16#bd /nu 16#be /xi 16#bf /omicron 16#c0 /pi + 16#c1 /rho 16#c2 /sigma1 16#c3 /sigma 16#c4 /tau + 16#c5 /upsilon 16#c6 /phi1 16#c7 /chi 16#c8 /psi + 16#c9 /omega 16#7e /semicolon 16#87 /dotmath 16#d1 /theta1 + 16#d2 /Upsilon1 16#d5 /phi 16#d6 /omega1 + >> vg&redef + def + +% Unicode punctuation encoding (unicode codes \u2000-\u206f) +/UCPunctuationEncoding + NullEncoding dup length array copy + << 16#10 /hyphen 16#11 /hyphen 16#12 /endash + 16#13 /emdash 16#18 /quoteleft 16#19 /quoteright + 16#1a /quotesinglbase 16#1b /quotesingle 16#1c /quotedblleft + 16#1d /quotedblright 16#1e /quotedblbase 16#1f /quotedbl + 16#20 /dagger 16#21 /daggerdbl 16#22 /bullet + 16#24 /period 16#26 /ellipsis 16#27 /periodcentered + 16#30 /perthousand 16#44 /fraction + 16#70 /zerosuperior 16#74 /foursuperior 16#75 /fivesuperior + 16#76 /sixsuperior 16#77 /sevensuperior 16#78 /eightsuperior + 16#79 /ninesuperior 16#7b /hyphensuperior 16#7d /parenleftsuperior + 16#7e /parenrightsuperior + 16#80 /zeroinferior 16#84 /fourinferior 16#85 /fiveinferior + 16#81 /oneinferior 16#82 /twoinferior 16#83 /threeinferior + 16#86 /sixinferior 16#87 /seveninferior 16#88 /eightinferior + 16#89 /nineinferior 16#8b /hypheninferior 16#8d /parenleftinferior + 16#8e /parenrightinferior + >> vg&redef + def + +% Unicode mathematical operators encoding (unicode codes \u2200-\u22ff) +/UCMathOpsEncoding + NullEncoding dup length array copy + << 16#00 /universal 16#02 /partialdiff 16#03 /existential + 16#05 /emptyset 16#06 /Delta 16#07 /gradient + 16#08 /element 16#09 /notelement 16#0b /suchthat + 16#0f /product 16#11 /summation 16#12 /minus + 16#15 /fraction 16#17 /asteriskmath 16#19 /bullet + 16#1a /radical 16#1d /proportional 16#1e /infinity + 16#20 /angle 16#23 /bar 16#27 /logicaland + 16#28 /logicalor 16#29 /intersection 16#2a /union + 16#2b /integral 16#34 /therefore 16#36 /colon + 16#3c /similar 16#45 /congruent 16#48 /approxequal + 16#60 /notequal 16#61 /equivalence 16#64 /lessequal + 16#65 /greaterequal 16#82 /propersubset 16#83 /propersuperset + 16#86 /reflexsubset 16#87 /reflexsuperset 16#95 /circleplus + 16#97 /circlemultiply 16#a5 /perpendicular 16#03 /existential + 16#c0 /logicaland 16#c1 /logicalor 16#c2 /intersection + 16#c3 /union 16#c4 /diamond 16#c5 /dotmath + >> vg&redef + def + +% Unicode arrows encoding (unicode codes \u2190-\u21ff) +% Also includes those "Letterlike" unicode characters +% which are available in the symbol font. (unicode codes \u2100-\u214f) +/UCArrowsEncoding + NullEncoding dup length array copy + << 16#11 /Ifraktur 16#1c /Rfraktur 16#22 /trademarkserif + 16#35 /aleph + 16#90 /arrowleft 16#91 /arrowup 16#92 /arrowright + 16#93 /arrowdown 16#94 /arrowboth 16#d0 /arrowdblleft + 16#d1 /arrowdblup 16#d2 /arrowdblright 16#d3 /arrowdbldown + 16#d4 /arrowdblboth + >> vg&redef + def + +/ZapfDingbats findfont /Encoding get +dup length array copy /UCDingbatsEncoding exch def +16#20 1 16#7f { + dup 16#20 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +16#a0 1 16#ff { + dup 16#40 sub exch + UCDingbatsEncoding exch get + UCDingbatsEncoding 3 1 roll put +} for +UCDingbatsEncoding [ 16#c0 1 16#ff {} for ] vg&undef +[ 16#00 16#05 16#0a 16#0b 16#28 16#4c 16#4e 16#53 16#54 16#55 16#57 16#5f + 16#60 16#68 16#69 16#6a 16#6b 16#6c 16#6d 16#6e 16#6f 16#70 16#71 16#72 + 16#73 16#74 16#75 16#95 16#96 16#97 16#b0 16#bf +] vg&undef pop + +% Define the base fonts which don't change. +/Undefined-UC NullEncoding /Helvetica vg&newbasefont pop +/MathOps-UC UCMathOpsEncoding /Symbol vg&newbasefont pop +/Arrows-UC UCArrowsEncoding /Symbol vg&newbasefont pop +/Dingbats-UC UCDingbatsEncoding /ZapfDingbats vg&newbasefont pop + +% Make the SansSerif composite fonts. +/SansSerif /Helvetica 16#00 vg&newcompositefont +/SansSerif-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/SansSerif-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/SansSerif-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Serif composite fonts. +/Serif /Times-Roman 16#00 vg&newcompositefont +/Serif-Bold /Times-Bold 16#01 vg&newcompositefont +/Serif-Italic /Times-Italic 16#02 vg&newcompositefont +/Serif-BoldItalic /Times-BoldItalic 16#03 vg&newcompositefont + +% Make the Monospaced composite fonts. +/Monospaced /Courier 16#00 vg&newcompositefont +/Monospaced-Bold /Courier-Bold 16#01 vg&newcompositefont +/Monospaced-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Monospaced-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + +% Make the Dialog composite fonts. +/Dialog /Helvetica 16#00 vg&newcompositefont +/Dialog-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/Dialog-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/Dialog-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the DialogInput composite fonts. +/DialogInput /Helvetica 16#00 vg&newcompositefont +/DialogInput-Bold /Helvetica-Bold 16#01 vg&newcompositefont +/DialogInput-Italic /Helvetica-Oblique 16#02 vg&newcompositefont +/DialogInput-BoldItalic /Helvetica-BoldOblique 16#03 vg&newcompositefont + +% Make the Typewriter composite fonts (JDK 1.1 only). +/Typewriter /Courier 16#00 vg&newcompositefont +/Typewriter-Bold /Courier-Bold 16#01 vg&newcompositefont +/Typewriter-Italic /Courier-Oblique 16#02 vg&newcompositefont +/Typewriter-BoldItalic /Courier-BoldOblique 16#03 vg&newcompositefont + + +/cfontH { + dup /fontsize exch def /SansSerif exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHB { + dup /fontsize exch def /SansSerif-Bold exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHI { + dup /fontsize exch def /SansSerif-Italic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def +/cfontHBI { + dup /fontsize exch def /SansSerif-BoldItalic exch sf + /vg&fontstyles [{cfontH} {cfontHB} {cfontHI} {cfontHBI}] def +} def + +/cfontT { + dup /fontsize exch def /Serif exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTB { + dup /fontsize exch def /Serif-Bold exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTI { + dup /fontsize exch def /Serif-Italic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def +/cfontTBI { + dup /fontsize exch def /Serif-BoldItalic exch sf + /vg&fontstyles [{cfontT} {cfontTB} {cfontTI} {cfontTBI}] def +} def + +/cfontC { + dup /fontsize exch def /Typewriter exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCB { + dup /fontsize exch def /Typewriter-Bold exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCI { + dup /fontsize exch def /Typewriter-Italic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def +/cfontCBI { + dup /fontsize exch def /Typewriter-BoldItalic exch sf + /vg&fontstyles [{cfontC} {cfontCB} {cfontCI} {cfontCBI}] def +} def + +% Darken or lighten the current color. +/darken {0.7 exch exp 3 copy + q 4 -1 roll vg&C + currentrgbcolor 3 {4 -2 roll mul} repeat + 3 array astore Q} def + +/displayColorMap +<< /Cr [1.00 0.00 0.00] /Cg [0.00 1.00 0.00] + /Cb [0.00 0.00 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.00 0.00] /CGg [0.00 1.00 0.00] + /CGb [0.00 0.00 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.00 0.00] /CIg [0.00 1.00 0.00] + /CIb [0.00 0.00 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/printColorMap +<< /Cr [1.00 0.33 0.33] /Cg [0.33 1.00 0.33] + /Cb [0.33 0.33 1.00] /Cc [1.00 0.00 0.00 0.00] + /Cm [0.00 1.00 0.00 0.00] /Cy [0.00 0.00 1.00 0.00] + /Co [1.00 0.78 0.00] /Cp [1.00 0.67 0.67] + /Cw [1 ] /Cgrl [0.75] + /Cgr [0.50] /Cgrd [0.25] + /Ck [0 ] + /CGr [1.00 0.33 0.33] /CGg [0.33 1.00 0.33] + /CGb [0.33 0.33 1.00] /CGc [1.00 0.00 0.00 0.00] + /CGm [0.00 1.00 0.00 0.00] /CGy [0.00 0.00 1.00 0.00] + /CGo [1.00 0.78 0.00] /CGp [1.00 0.67 0.67] + /CGw [1 ] /CGgrl [0.75] + /CGgr [0.50] /CGgrd [0.25] + /CGk [0 ] + /CIr [1.00 0.33 0.33] /CIg [0.33 1.00 0.33] + /CIb [0.33 0.33 1.00] /CIc [1.00 0.00 0.00 0.00] + /CIm [0.00 1.00 0.00 0.00] /CIy [0.00 0.00 1.00 0.00] + /CIo [1.00 0.78 0.00] /CIp [1.00 0.67 0.67] + /CIw [1 ] /CIgrl [0.75] + /CIgr [0.50] /CIgrd [0.25] + /CIk [0 ] +>> def + +/grayColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [0.75] /CGg [1 ] + /CGb [0.50] /CGc [0.75] + /CGm [0.50] /CGy [1 ] + /CGo [0.75] /CGp [1 ] + /CGw [0 ] /CGgrl [0.25] + /CGgr [0.50] /CGgrd [0.75] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +/bwColorMap +<< /Cr [0 ] /Cg [0 ] + /Cb [0 ] /Cc [0 ] + /Cm [0 ] /Cy [0 ] + /Co [0 ] /Cp [0 ] + /Cw [0 ] /Cgrl [0 ] + /Cgr [0 ] /Cgrd [0 ] + /Ck [0 ] + /CGr [1 ] /CGg [1 ] + /CGb [1 ] /CGc [1 ] + /CGm [1 ] /CGy [1 ] + /CGo [1 ] /CGp [1 ] + /CGw [0 ] /CGgrl [1 ] + /CGgr [1 ] /CGgrd [1 ] + /CGk [1 ] + /CIr [1 ] /CIg [1 ] + /CIb [1 ] /CIc [1 ] + /CIm [1 ] /CIy [1 ] + /CIo [1 ] /CIp [1 ] + /CIw [1 ] /CIgrl [1 ] + /CIgr [1 ] /CIgrd [1 ] + /CIk [1 ] +>> def + +% +% The following routines handle the alignment of and printing of +% tagged strings. +% + +% Predefine the bounding box values. +/bbllx 0 def /bblly 0 def /bburx 0 def /bbury 0 def + +% This routine pops the first unicode character off of a string and returns +% the remainder of the string, the character code of first character, +% and a "true" if the string was non-zero length. +% popfirst +% popfirst +/popfirst { + dup length 1 gt + {dup 0 get /vg&fbyte exch def + dup 1 get /vg&cbyte exch def + dup length 2 sub 2 exch getinterval true} + {pop false} ifelse +} def + +% This routine shows a single unicode character given the font and +% character codes. +% unicharshow -- +/unicharshow { + 2 string + dup 0 5 -1 roll put + dup 1 4 -1 roll put + internalshow +} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and showing the string for recshow. +% internalshow -- +/internalshow {show} def + +% This is an internal routine to alternate between determining the +% bounding box for stringsize and stroking various ornaments. +% internalstroke -- +/internalstroke {S} def + +% Sets up internalshow to use the null device to determine string size. +% -- nullinternalshow -- +/nullinternalshow {/internalshow {false charpath flattenpath + pathbbox updatebbox} def} def + +% Sets up internalstroke to use the null device to determine string size. +% -- nullinternalstroke -- +/nullinternalstroke { + /internalstroke {flattenpath pathbbox updatebbox} def} def + +% This routine tests to see if the character code matches the first +% character of a string. +% testchar +/testchar {exch dup 3 -1 roll 0 get eq} def + +% Raise the text baseline for superscripts. +% -- raise -- +/raise { + 0 fontsize 2 div rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-raise the text baseline for superscripts. +% -- unraise -- +/unraise { + /fontsize fontsize 1.5 mul def + 0 fontsize 2 div neg rmoveto +} def + +% Lower the text baseline for subscripts. +% -- lower -- +/lower { + 0 fontsize 3 div neg rmoveto + /fontsize fontsize 2 mul 3 div def + currentfont /FontName get fontsize sf +} def + +% Un-lower the text baseline for subscripts. +% -- unlower -- +/unlower { + /fontsize fontsize 1.5 mul def + 0 fontsize 3 div rmoveto +} def + +% Compare the top two elements on the stack and leave only the +% larger one. +/maxval {2 copy gt {pop} {exch pop} ifelse} def + +% Tokenize a string. Do not use the usual PostScript token because +% parentheses will not be interpreted correctly because of rescanning +% of the string. +/vg&token {/vg&string exch def /vg&index -1 def /vg&level 0 def +0 2 vg&string length 2 sub { + dup dup 1 add exch vg&string exch get 8 bitshift vg&string 3 -1 roll get or + dup 16#f0fe eq {pop 1}{16#f0ff eq {-1}{0} ifelse} ifelse + /vg&level exch vg&level add def + vg&level 0 eq {/vg&index exch def exit} if pop +} for +vg&index 0 ge { + vg&string vg&index 2 add dup vg&string length exch sub getinterval + vg&index 2 gt {vg&string 2 vg&index 2 sub getinterval}{()} ifelse + true} +{false} ifelse +} bind def + +% Recursively show an unicode string. +% recshow -- +/recshow { + popfirst + { + % Test to see if this is a string attribute. + vg&fbyte 16#f0 and 16#e0 eq + { + q + + % Font style. + currentfont dup /FontStyleBits known {/FontStyleBits get}{pop 0} ifelse + vg&cbyte or vg&fontstyles exch get fontsize exch exec + + vg&token pop recshow currentpoint Q m recshow + } + { + vg&fbyte 16#F8 and 16#F0 eq { + + % Superscript and/or subscript. + vg&cbyte 16#00 eq { + vg&token pop exch vg&token pop 3 -1 roll + q raise recshow unraise currentpoint pop Q exch + q lower recshow unlower currentpoint pop Q + maxval currentpoint exch pop m recshow } if + + % Strikeout. + vg&cbyte 16#01 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll fontsize 3 div add moveto + fontsize 3 div add lineto internalstroke Q + recshow} if + + % Underline. + vg&cbyte 16#02 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dashed underline. + vg&cbyte 16#03 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J [ vg&uthick 5 mul vg&uthick 2 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Dotted underline. + vg&cbyte 16#04 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 1 J [ 0 vg&uthick 3 mul] 0 d + vg&underline vg&uthick w + currentpoint 4 -2 roll vg&uoffset add moveto + vg&uoffset add lineto internalstroke Q + recshow} if + + % Thick underline. + vg&cbyte 16#05 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Gray thick underline. + vg&cbyte 16#06 eq { + vg&token pop currentpoint 3 -1 roll recshow + q 0 J vg&underline vg&uthick 2 mul w 0.5 setgray + currentpoint 4 -2 roll vg&uoffset vg&uthick 2 div sub add moveto + vg&uoffset vg&uthick 2 div sub add lineto internalstroke Q + recshow} if + + % Overbar. + vg&cbyte 16#07 eq { + vg&token pop dup stringsize relative 4 1 roll pop pop exch + 3 -1 roll recshow + q 0 J vg&underline vg&uthick w + vg&uoffset neg add dup currentpoint pop exch m l internalstroke Q + recshow} if + } + { + vg&fbyte vg&cbyte unicharshow recshow + } ifelse + } ifelse + } if +} def + +% Get the underline position and thickness from the current font. +/vg&underline { + +currentfont dup /FontType get 0 eq {/FDepVector get 0 get} if +dup dup /FontInfo known { + /FontInfo get dup + dup /UnderlinePosition known { + /UnderlinePosition get /vg&uoffset exch def + } + { + pop /vg&uoffset 0 def + } ifelse + dup /UnderlineThickness known { + /UnderlineThickness get /vg&uthick exch def + } + { + pop /vg&uthick 0 def + } ifelse +} +{ + pop /vg&uoffset 0 def /vg&uthick 0 def +} ifelse +/FontMatrix get +currentfont dup /FontType get 0 eq +{/FontMatrix get matrix concatmatrix}{pop} ifelse +dup 0 vg&uoffset 3 -1 roll transform /vg&uoffset exch def pop +0 vg&uthick 3 -1 roll transform /vg&uthick exch def pop +} def + +% Make a frame with the coordinates on the stack. +% frame -- +/frame {4 copy m 3 1 roll exch l 4 -2 roll l l h} def + +% Resets the accumulated bounding box to a degenerate box at the +% current point. +% -- resetbbox -- +/resetbbox { + currentpoint 2 copy + /bbury exch def + /bburx exch def + /bblly exch def + /bbllx exch def +} def + +% Update the accumulated bounding box. +% updatebbox -- +/updatebbox { + dup bbury gt {/bbury exch def} {pop} ifelse + dup bburx gt {/bburx exch def} {pop} ifelse + dup bblly lt {/bblly exch def} {pop} ifelse + dup bbllx lt {/bbllx exch def} {pop} ifelse +} def + +% Set the bounding box to the values on the stack. +% updatebbox -- +/restorebbox { + /bbury exch def /bburx exch def /bblly exch def /bbllx exch def +} def + +% Push the accumulated bounding box onto the stack. +% -- pushbbox +/pushbbox {bbllx bblly bburx bbury} def + +% Make the relative bounding box relative to the currentpoint. +% inflate +/inflate { + 2 {fontsize 0.2 mul add 4 1 roll} repeat + 2 {fontsize 0.2 mul sub 4 1 roll} repeat +} def + +% Make the relative bounding box relative to the currentpoint. +% relative +/relative { + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll + currentpoint 3 -1 roll add 3 1 roll add exch 4 2 roll +} def + +% Returns the size of a string appropriate for recshow. +% stringsize +/stringsize { + pushbbox /internalshow load /internalstroke load 7 -1 roll + q + nulldevice 0 0 m + nullinternalshow nullinternalstroke + resetbbox + recshow + /internalstroke exch def /internalshow exch def + pushbbox 8 -4 roll restorebbox + Q +} def + +% Calculate values for string positioning. +/calcval {4 copy + 3 -1 roll sub /widy exch def sub neg /widx exch def + pop pop /dy exch def /dx exch def} def + +% Utilities to position a string. +% First letter (U=upper, C=center, B=baseline, L=lower) +% Second letter (L=left, C=center, R=right) +/align [ +{calcval dx neg widy dy add neg rmoveto} % UL +{calcval dx neg widy 2 div dy add neg rmoveto} % CL +{calcval dx neg 0 rmoveto} % BL +{calcval dx neg dy neg rmoveto} % LL +{calcval widx dx add neg widy dy add neg rmoveto} 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a/Q1_1.tex b/Q1_1.tex new file mode 100644 index 0000000..deecd87 --- /dev/null +++ b/Q1_1.tex @@ -0,0 +1,84 @@ +\section*{Aufgabe 1} + +Welche der folgenden Intervalle sind im Bereich der Funktion $\sqrt{2 x-x^3}$ enthalten? Wählen Sie alle zutreffenden Antworten aus $\ldots$ + + + \begin{itemize} + \item $\mathbf{[0, \sqrt{2}]}$ + \item $[\sqrt{2},+\infty)$ + \item $[-\sqrt{2}, 0]$ + \item $\mathbf{(-\infty,-\sqrt{2}]}$ + \end{itemize} + +\subsection*{Bestimmen des Definitionsbereiches} + +\begin{flalign*} +f(x) &= \sqrt{2 x-x^3}\\ +\sqrt{2 x-x^3} & \geq 0\qquad \vert ^2 \\ +2x-x^3 & \geq 0\qquad| x\text{ ausklammern}\\ +x\left(2-x^2\right) & \geq 0\\ +x_1 & \geq 0\\ +2-x^2 & \geq 0 \qquad \vert -2\\ +-x^2 & \geq -2 \qquad \vert \div (-1)\\ +x^2 & \leq 2 \qquad \vert \sqrt{ }\\ +x_2 & \leq \sqrt{2}\\ +x_3 & \leq -\sqrt{2} +\end{flalign*} + +Damit ergeben sich die folgenden Intervalle: +\begin{itemize} + \item $(-\infty,-\sqrt{2}]$ + \item $[0,\sqrt{2}]$ +\end{itemize} + + +\subsection*{Bestimmen der Nullstellen} +\begin{flalign*} +x\left(2-x^2\right) & = 0\\ +x_1 &= 0\\ +2-x^2 & = 0 \qquad \vert -2\\ +-x^2 & = -2 \qquad \vert \div (-1)\\ +x^2 & = 2 \qquad \vert \sqrt{ }\\ +x_2 & = \sqrt{2}\\ +x_3 & = -\sqrt{2} +\end{flalign*} + +\vspace{2pt} +\begin{figure}[ht] + \centering +\begin{tikzpicture} + \begin{axis}[ + domain=-4:3, % Bereich, in dem die Funktion definiert ist + samples=1000, % Anzahl der Abtastpunkte + xlabel={$x$}, + ylabel={$y$}, + axis lines=middle, + xtick={-4,-3,-1.414, 0, 1, 1.414,3}, + xticklabels={-4,-3,-$\sqrt{2}$, 0, 1, $\sqrt{2}$,3}, + ytick={0, 1,2,3}, + ymin=-0.1, ymax=3.5, + xmin=-4, xmax=3, + legend pos=outer north east, + %grid=both, + %major grid style={line width=.2pt,draw=gray!50}, + %minor grid style={line width=.1pt,draw=gray!50}, + ] + \addplot [ + domain=0:1.414, + samples=500, + thick, + red, + ] {sqrt(2*x - x^3)}; + \addplot [ + domain=-4:-1, + samples=500, + thick, + red, + ] {sqrt(2*x - x^3)}; + \addlegendentry{$\sqrt{2x - x^3}$} + \end{axis} +\end{tikzpicture} +% %\caption{} + \label{fig:q2} +\end{figure} + diff --git a/Q1_2.tex b/Q1_2.tex new file mode 100644 index 0000000..f97be65 --- /dev/null +++ b/Q1_2.tex @@ -0,0 +1,98 @@ +\section*{Aufgabe 2} +Welche der folgenden Intervalle sind im Bereich der Funktion $\frac{x-3}{x^2-4} \ln x$ enthalten? Wählen Sie alle zutreffenden Antworten aus... + +\begin{itemize} + \item $(2,+\infty)$ + \item $(-\infty,-2)$ + \item $(-2,0)$ + \item $(0,2)$ +\end{itemize} + +Untersuchung des Nenners (wann gibt es eine Division durch Null): +\begin{align*} + x^2-4=0 & \qquad \vert{} +4 \\ + x^2=4 & \qquad \vert{} \sqrt{\quad} \\ + x_1=-2 \\ + x_2=2 +\end{align*} + +Somit sind die Bereiche $(2,+\infty)$ und $(-\infty,-2)$ + +\textcolor{red}{\textbf{Dies stellt mich aber noch nicht zufrieden, das kann einfach nicht alles sein}} + +\textcolor{blue}{\textbf{Hier hatte ich im ersten Versuch den Fehler gemacht, das ich das $\ln x$ übersah}} + + +\begin{figure}[h] + \centering + + \begin{tikzpicture} + \begin{axis}[ + domain=0.1:4.9, % Bereich, in dem die Funktion definiert ist (z.B. nahe bei 0 und 2 ausgespart) + samples=100, % Anzahl der Abtastpunkte + xlabel={$x$}, + ylabel={$f(x)$}, + axis lines=middle, + xtick={0, 1, 2, 3, 4}, + ytick={-2, -1, 0, 1, 2}, + ymin=-2.5, ymax=2.5, + xmin=0, xmax=5, + legend pos=outer north east, + grid=both, + major grid style={line width=.2pt,draw=gray!50}, + minor grid style={line width=.1pt,draw=gray!50}, + restrict y to domain=-2.5:2.5, % Begrenze y-Werte für bessere Darstellung + ] + \addplot [ + domain=0.1:1.9999, + samples=500, + thick, + blue + ] {(x-3)/(x^2-4) * ln(x)}; + \addlegendentry{$\left(\frac{x-3}{x^2-4}\right) \ln(x)$} + + \addplot [ + domain=2.00001:5, + samples=500, + thick, + blue + ] {(x-3)/(x^2-4) * ln(x)}; + \end{axis} +\end{tikzpicture} +% \includegraphics[width=0.75\linewidth]{Grafiken/Q1_2.png} + %\caption{Enter Caption} + \label{fig:enter-label} +\end{figure} + + + +Um die Intervalle zu bestimmen, in denen die Funktion $h(x)=\left(\frac{x-3}{x^2-4}\right) \ln (x)$ definiert ist, muss man die Punkte betrachten, an denen die Funktion nicht definiert ist. Diese Punkte sind: + +\begin{enumerate} + \item Nullstellen des Nenners $x^2-4$ + \item Punkte, an denen der Logarithmus $\ln (x)$ nicht definiert ist (insbesondere $x \leq 0$ ) +\end{enumerate} + +\subsection{Nullstellen des Nenners} +\begin{flalign*} +x^2-4&=0 \\ +x^2&=4 \\ +x&= \pm 2 +\end{flalign*} + + +Die Funktion hat also Pole (nicht definierte Punkte) bei $x=2$ und $x=-2$. +2. Definitionsbereich des Logarithmus: +$\ln (x)$ ist nur für $x>0$ definiert. +Zusammenführung der Bedingungen: +- Der Nenner darf nicht null sein: $x \neq 2$ und $x \neq-2$. +- Der Logarithmus ist nur für $x>0$ definiert. + +Schlussfolgerung: +Die Funktion $h(x)=\left(\frac{x-3}{x^2-4}\right) \ln (x)$ ist definiert für $x>0$, ausgenommen $x=2$. Somit sind die Intervalle, in denen die Funktion definiert ist: +$$ +(0,2) \cup(2, \infty) +$$ + +Diese Intervalle umfassen alle Werte, für die der Ausdruck sowohl im Nenner als auch im Logarithmus definiert und nicht null ist. + diff --git a/Q1_3.tex b/Q1_3.tex new file mode 100644 index 0000000..9a6fd2d --- /dev/null +++ b/Q1_3.tex @@ -0,0 +1,71 @@ +\begin{itemize} +\item Was ist der Bereich der Funktion $\arcsin \frac{x-2}{3}$ ? +\begin{itemize} + \item $[-2,3]$ + \item \textcolor{red}{$[-1,5]$} + \item $[2-3 \pi, 2+3 \pi]$ + \item $[-2,2]$ + \item $\mathbb{R}=(-\infty,+\infty)$ + \item $\left[\frac{2}{3}, \frac{5}{3}\right]$ +\end{itemize} +\end{itemize} + + +%\begin{figure}[h] +% \centering +% \includegraphics[width=0.5\linewidth]%{Grafiken/A10.png} + %\caption{Enter Caption} + %\label{fig:enter-label} +%\end{figure} + +\begin{tikzpicture} + \begin{axis}[ + domain=-1:5, + samples=500, + axis lines*=middle, + xtick={-1,1,2,3,4,5}, ytick={-1.57,1.57}, + yticklabels={$-\pi$/2,$\pi$/2}] + \addplot[color = red] {asin((x-2)/3)/180*pi}; + \addlegendentry{$\arcsin\left(\frac{x-2}{3}\right)$} + \end{axis} +\end{tikzpicture} + + +Um den Wertebereich der Funktion $h(x)=\arcsin \left(\frac{x-2}{3}\right)$ zu bestimmen, müssen wir sicherstellen, dass der Ausdruck $\frac{x-2}{3}$ im Definitionsbereich der Arkussinusfunktion liegt. Die Arkussinusfunktion, $\arcsin (y)$, ist nur für $-1 \leq y \leq 1$ definiert und ihr Wertebereich ist $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ +1. Bedingung für den Argumentbereich von arcsin: +$$ +-1 \leq \frac{x-2}{3} \leq 1 +$$ +2. Lösen der Ungleichung: +Multiplizieren wir alle Teile der Ungleichung mit 3: +$$ +-3 \leq x-2 \leq 3 +$$ + +Addieren wir 2 zu allen Teilen der Ungleichung: +$$ +-1 \leq x \leq 5 +$$ + +Das bedeutet, dass $x$ im Intervall $[-1,5]$ liegen muss, damit der Ausdruck $\frac{x-2}{3}$ im Bereich $[-1,1]$ liegt und arcsin definiert ist. +3. Bestimmung des Wertebereichs: +Nun betrachten wir die Extremwerte des Ausdrucks $\frac{x-2}{3}$ : +- Für $x=-1$ : +$$ +\frac{-1-2}{3}=\frac{-3}{3}=-1 +$$ +- Für $x=5$ : +$$ +\frac{5-2}{3}=\frac{3}{3}=1 +$$ + +Die Funktion $\arcsin \left(\frac{x-2}{3}\right)$ nimmt also ihre Extremwerte bei $\arcsin (-1)$ und $\arcsin (1)$ an: +- $\arcsin (-1)=-\frac{\pi}{2}$ +- $\arcsin (1)=\frac{\pi}{2}$ + +Da die Arkussinusfunktion stetig und streng monoton ist, nimmt sie alle Werte zwischen diesen Extremwerten an. + +Der Wertebereich der Funktion $h(x)=\arcsin \left(\frac{x-2}{3}\right)$ ist daher: +$$ +\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] +$$ \ No newline at end of file diff --git a/Quiz1.tex b/Quiz1.tex new file mode 100644 index 0000000..22a20e4 --- /dev/null +++ b/Quiz1.tex @@ -0,0 +1,128 @@ + \chapter{Quiz Woche 1} + +%\input{Q1_1} +%\newpage +\input{Q1_2} +\newpage +\input{Q1_3} + + + + +\newpage +\begin{itemize} +\item Was ist der Bereich der Funktion $-x^2+1$ ? +\begin{itemize} + \item $(-\infty, 0]$ + \item $[1,+\infty)$ + \item $[0,1]$ + \item $[0,+\infty)$ + \item $(-\infty, 1]$ + \item $\mathbb{R}=(-\infty,+\infty)$ + \end{itemize} + \end{itemize} + +\begin{figure}[h] + \centering + \includegraphics[width=0.5\linewidth]{Grafiken/A11.png} + %\caption{Enter Caption} + \label{fig:enter-label} +\end{figure} + +$-x^2+1$ + +Nullstellen + +$-x^2+1=0$ + +$-x^2=-1$ + +$x^2=1$ + +$x_1=-1$ und $x_2=1$ + +Muss ich nun den Scheitelpunkt berechnen? \textcolor{red}{Ja} + +Hier gibt es verschiedene Wege: + +\begin{enumerate} + \item per Differentialrechnung + \begin{itemize} + \item Bilden der ersten Ableitung + $f(x)=-x^2+1 $ + + $f'(x)=-2x$ + \item $x=0$ setzen + + $-2x=0$ + + $x=0$ + + \item $y$ berechnen, $x$ in $f(x)$ einsetzen + $f(x)=-x^2+1 $ + + $f(0)=-0^2+1$ + + $f(0)=1$ + + + \end{itemize} + + \item per quadratischer Ergänzung + + + + +\end{enumerate} + +\newpage + + \begin{itemize} +\item Was ist der Bereich der Funktion $\ln \left(1+x^2\right)$ ? +\begin{itemize} + \item $[1,+\infty)$ +\item $\mathbb{R}=(-\infty,+\infty)$ +\item $(-\infty, 0]$ +\item $(-\infty, 1]$ +\item $[0,+\infty)$ +\item $[-1,+\infty)$ + \end{itemize} + \end{itemize} + +\begin{figure}[h] + \centering + \includegraphics[width=0.5\linewidth]{Grafiken/A12.png} + %\caption{Enter Caption} + \label{fig:enter-label} +\end{figure} + + + + \newpage + 6. Wie groß ist der Bereich der Funktion $\arctan \cos x$ (d.h. die Umkehrung der Tangensfunktion mit dem Parameter $\cos x) ?$ + $[0,+\infty)$ + $\mathbb{R}=(-\infty,+\infty)$ + $[-\pi, \pi]$ + $\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]$ + $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ + $(-\infty, 0]$ + + +\newpage + + 7. Wenn $f(x)=4 x^3+1$ und $g(x)=\sqrt{x+3}$, berechnen Sie $(f \circ g)(x)$ und $(g \circ f)(x)$. + $(f \circ g)(x)=(g \circ f)(x)=\left(4 x^3+1\right) \sqrt{x+3}$ + $(f \circ g)(x)=(g \circ f)(x)=4 x^3+1+\sqrt{x+3}$ + $(f \circ g)(x)=4(x+3)^{3 / 2}+1$ und $(g \circ f)(x)=2 \sqrt{x^3+1}$ + $(f \circ g)(x)=2 \sqrt{x^3+1}$ und $(g \circ f)(x)=4(x+3)^{3 / 2}+1$ + + +\newpage + + 8. Was ist die Umkehrung der Funktion $f(x)=e^{2 x}$ ? Wählen Sie alle, die richtig sind. + Die Exponentialfunktion ist ihre eigene Inverse, also $f^{-1}(x)=e^{2 x}$ + $f^{-1}(x)=\log _2 x$ + $f^{-1}(x)=\ln x^2$ + $f^{-1}(x)=\frac{1}{e^{2 x}}$ + $f^{-1}(x)=\frac{1}{2} \ln x$. + $f^{-1}(x)=\ln \sqrt{x}$ \ No newline at end of file