Sven/maing01_06
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Band 2 Grafiken bis 2.4

Browse Source
This commit is contained in:
Sven Riwoldt
2026-03-28 12:25:05 +01:00
parent cfc360f1fc
commit 843fda0210
8 changed files with 1344 additions and 380 deletions
Download Patch File Download Diff File Expand all files Collapse all files

72
Band2/Grafiken/B2.1.typ
View File

@@ -0,0 +1,72 @@
#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot
#cetz.canvas(length: 1.25cm,{
import cetz.draw: *
plot.plot(
//definitionen
name: "plot",
size: (6, 6),
x-tick-step: none,
y-tick-step: none,
axis-style: "school-book",
x-label: $x$,
y-label: $y$,
x-ticks: ((0.5, $1/2$),(1.25, $x$),),
y-ticks: ((0.25, $1/4$),(1.5625, $x^2$),),
{
//berechnungen und plot
let f = x => calc.pow(x, 2)
let x0 = 0.5
let y0 = f(x0)
let x1 = 1.25
let y1 = f(x1)
// Berechnung der Steigung m = (y1 - y0) / (x1 - x0)
let m = (y1 - y0) / (x1 - x0)
// Sekantenfunktion: s(x) = m * (x - x0) + y0
let s = x => m * (x - x0) + y0
let x1_1 = x1 + 0.1
let x0_1 = x0 - 0.2
let y0_1 = y0 + 0.2
let x2 = ((x1 - x0)/2) + x0
let y3 = ((y1 - y0)/2) +y0
plot.add(x => calc.pow(x, 2), domain: (-1.4, 1.8))
//Sekante
plot.add(s, domain: (0.3, 1.7), style: (stroke: red))
plot.add-anchor("pt1", (-1.4,y1))
plot.add-anchor("P", (x1_1,y1))
plot.add-anchor("P0", (x0_1,y0_1))
plot.add-anchor("F1", (x2,0.14))
plot.add-anchor("F2", (x1+0.1,y3))
plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((0, y1), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((0, y0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((x0, y0), (x1, y0)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
plot.add(((x1, y0), (x1, y1)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
plot.add(((x0, y0),), mark: "o")
plot.add(((x1, y1),), mark: "o")
}
)
//Der Plot muss einen Namen haben
content("plot.pt1", text(0.85em)[$y=x^2$], anchor: "east", name: "pt")
content("plot.P", text(0.75em)[$P$], anchor: "west", name: "p")
content("plot.P0", text(0.75em)[$P_0$], anchor: "west", name: "p0")
content("plot.F1", text(0.75em)[$x- 1/2$], anchor: "center", name: "f1")
content("plot.F2", text(0.75em)[$x^2- 1/4$], anchor: "west", name: "f2")
})

48
Band2/Grafiken/B2.2.typ
View File

@@ -0,0 +1,48 @@
#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot
#cetz.canvas({
import cetz.draw: *
set-style(
axes: (
// Basisstil beibehalten
stroke: (thickness: 0.5pt),
// x-Achse: stealth-Pfeil am Ende
x: (mark: (end: "stealth", fill: black)),
// y-Achse: stealth-Pfeil am Ende
y: (mark: (end: "stealth", fill: black)),
),
)
plot.plot(
name: "plot",
size: (5, 5),
x-tick-step: none,
y-tick-step: none,
axis-style: "school-book",
x-label: $x$,
y-label: $y$,
x-ticks: ((0.5, $1/2$),),
y-ticks: ((1, $1$),),
//definitionen
{
let f = x => if x != 0.5 { (calc.pow(x, 2) - 0.25) / (x - 0.5) } else { none }
let x0 = 0.5
let y0 = 1
plot.add(f, domain: (-0.6, 0.75), style: (stroke: blue))
plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((0, y0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
plot.add(((x0, y0),), mark: "o")
plot.add-anchor("F1", (-.7,0.5))
plot.add-anchor("F2", (-.7,0.35))
}
)
content("plot.F1", text(0.85em)[$y=(x^2-1/4)/(x-1/2)$], anchor: "west", name: "pt")
content("plot.F2", text(0.85em)[$(x eq.not 1/2)$], anchor: "west", name: "pt")
})

135
Band2/Grafiken/B2.3.typ
View File

@@ -0,0 +1,135 @@
#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot
#cetz.canvas(length: 1.25cm,{
import cetz.draw: *
set-style(
axes: (
// Basisstil beibehalten
stroke: (thickness: 0.5pt),
// x-Achse: stealth-Pfeil am Ende
x: (mark: (end: "stealth", fill: black)),
// y-Achse: stealth-Pfeil am Ende
y: (mark: (end: "stealth", fill: black)),
),
)
plot.plot(
//definitionen
name: "plot",
size: (6, 6),
ymin: -2,
ymax: 6,
x-tick-step: none,
y-tick-step: none,
axis-style: "school-book",
x-label: $x$,
y-label: $y$,
x-ticks: ((0.5, $1/2$),(1.25, $x$),),
y-ticks: ((0, $0$),),
{
//berechnungen und plot
plot.add(x => (calc.pow(x, 2) -2), domain: (-1.4, 1.8))
plot.add(x => (calc.pow(x, 2) +2), domain: (-1.4, 1.8))
}
)
})
#let linspace(start, end, n)=range(0,n).map(x => x / n * (end - start) + start)
#cetz.canvas({
import cetz.draw: *
line((-5,0), (5,0), mark: (end: "stealth", fill: black))
content((), block(inset: 0.2em)[$x$], anchor: "west")
line((0,-5), (0,5), mark: (end: "stealth", fill: black))
content((), block(inset: 0.2em)[$p^0$], anchor: "east")
let pe = linspace(-2, 2, 200).map(x => (calc.pow(x,2) +2, x))
line(..pe, stroke: olive)
// let draw-point(pos, text, color, anchor) = {
// circle(pos, radius: 0.1, fill: color, stroke: none)
// content((), block(inset: 0.3em)[#text], anchor: anchor)
//}
// draw-point((0, 3), "(a)", red, "east")
// draw-point((0, -3), "(b)", blue, "east")
// draw-point((1, 1), "(c)", red, "south-east")
// draw-point((1, -1), "(d)", blue, "north-east")
// draw-point((3, 0), "(e)", olive, "north-east")
// draw-point((0, 0), "(f)", olive, "east")
})
#let linspace(start, end, n)=range(0,n).map(x => x / n * (end - start) + start)
#cetz.canvas({
import cetz.draw: *
line((0,0), (5,0), mark: (end: "stealth", fill: black))
content((), block(inset: 0.2em)[$abs(bold(p))$], anchor: "west")
line((0,-5), (0,5), mark: (end: "stealth", fill: black))
content((), block(inset: 0.2em)[$p^0$], anchor: "east")
let pa = linspace(0, 4, 100).map(x => (x, calc.sqrt(9+x*x)))
line(..pa, stroke: red)
let pb = linspace(0, 4, 100).map(x => (x, -calc.sqrt(9+x*x)))
line(..pb, stroke: blue)
line((0,0), (5,5), stroke: red)
line((0,0), (5,-5), stroke: blue)
let pe = linspace(-4, 4, 100).map(x => (calc.sqrt(9+x*x), x))
line(..pe, stroke: olive)
let draw-point(pos, text, color, anchor) = {
circle(pos, radius: 0.1, fill: color, stroke: none)
content((), block(inset: 0.3em)[#text], anchor: anchor)
}
draw-point((0, 3), "(a)", red, "east")
draw-point((0, -3), "(b)", blue, "east")
draw-point((1, 1), "(c)", red, "south-east")
draw-point((1, -1), "(d)", blue, "north-east")
draw-point((3, 0), "(e)", olive, "north-east")
draw-point((0, 0), "(f)", olive, "east")
})
#import "@preview/cetz:0.3.2"
#import "@preview/cetz-plot:0.1.1"
#cetz.canvas(
{
import cetz.draw: *
import cetz-plot: *
plot.plot(
//size: (5,5),
xmin: -2cm,
xmax: 2cm,
ymin: -2cm,
ymax: 4cm,
x-tick-step: none,
y-tick-step: none,
axis-style: "school-book",
x-label: $x$,
y-label: $y$,
//x-ticks: ((0.5, $1/2$),(1.25, $x$),),
y-ticks: ((2, $2$),(1, $1$)),
plot.add(
domain: (-5,5),
x => calc.pow(x, 2)+2
)
)
}
)
#import "@preview/cetz:0.4.1"
#import "@preview/cetz-plot:0.1.2"
#cetz.canvas({
import cetz.draw: *
import cetz-plot: *
let f = x => (calc.pow(x,2)+2)
plot.plot(size: (6,9), axis-style: "school-book", x-tick-step:none, y-tick-step:none, x-label: $x$,
y-label: $y$,
x-ticks: ((0.5, $1/2$),(1.25, $x$),),
y-ticks: ((2, $2$),), {
plot.add(domain: (-1.5, 1.5), f)
// Hilfslinie damit Koordinatensystem nicht verrutscht
plot.add(((0, 0), (0, 0.1)), style: (stroke: none))
})
})

281
Band2/Grafiken/Grafiken.typ → Band2/Grafiken/Grafiken_Beispiele.typ
View File

@@ -506,12 +506,14 @@
)
})
#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot
#cetz.canvas(length: 1.25cm,{
import cetz.draw: *
set-style(
set-style(
axes: (
// Basisstil beibehalten
stroke: (thickness: 0.5pt),
@@ -635,3 +637,280 @@
content("plot.F2", text(0.85em)[$(x eq.not 1/2)$], anchor: "west", name: "pt")
})
#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot
#cetz.canvas({
import cetz.draw: *
plot.plot(
//definitionen
{
//berechnungen und plot
}
)
})
#import "@preview/cetz:0.4.1"
#import "@preview/cetz-plot:0.1.2"
#cetz.canvas({
import cetz.draw: *
import cetz-plot: *
set-style(
axes: (
stroke: (thickness: 0.5pt),
x: (mark: (end: "stealth", fill: black)),
y: (mark: (end: "stealth", fill: black)),
),
)
let f = x => (calc.pow(x,3)+0.5)
let x1 = 0.35
let x3 = 0.5
let x0 = 0.7
let x2 = 0.8
let y1 = f(x1)
plot.plot(size: (6,7), name: "plot", axis-style: "school-book", x-tick-step:none, y-tick-step:none, x-label: $x$,
y-label: $y$,
x-ticks: ((x1, $x_1$),(x3, $x_3$),(x0, $x_0$),(x2, $x_2$),),
y-ticks: ((f(x1), $f(x_1)$),(f(x2), $f(x_2)$),(f(x0), $g$),(f(x3), $f(x_3)$)), {
plot.add(domain: (0.25, 1), f, style: (stroke: red))
plot.add(((x1, 0), (x1, f(x1))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((0, f(x1)), (x1, f(x1))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((x3, 0), (x3, f(x3))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((0, f(x3)), (x3, f(x3))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((x0, 0), (x0, f(x0))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((0, f(x0)), (x0, f(x0))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((x2, 0), (x2, f(x2))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
plot.add(((0, f(x2)), (x2, f(x2))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
// Hilfslinie damit Koordinatensystem nicht verrutscht
plot.add(((0, 0), (0, 0.1)), style: (stroke: none))
//circle((x1, y1), radius: 0.05, fill: black)
plot.add(((x1, f(x1)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))
plot.add(((x3, f(x3)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))
plot.add(((x0, f(x0)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: white))
plot.add(((x2, f(x2)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))
plot.add-anchor("F", (x2 - 0.05,f(x2)+0.1))
})
content("plot.F", text(0.85em)[$y=f(x)$], anchor: "east", name: "pt")
})
#import "@preview/cetz:0.4.2"
#align(center,
cetz.canvas({
import cetz-plot: *
import cetz.palette
import cetz.draw: *
plot.plot(size: (5,5),
name: "plot",
x-tick-step: 2,
x-minor-tick-step: 1,
y-tick-step: 2,
y-minor-tick-step: 1,
axis-style: "school-book", {
plot.add(domain: (-1, 2.5),
x => x - 1,
style: (color: red))
plot.add(domain: (-1, 2.5),
x => x - 1 + calc.exp(-x),
style: (color: yellow))
plot.add(domain: (-1, 2.5),
x => x - 1 - calc.exp(-x),
style: (color: red))
plot.add-anchor("pt1", (1,1.3))
plot.add-anchor("pt2", (1.8,-2))
plot.add-anchor("exp1", (1, calc.exp(-1)+0.2))
plot.add-anchor("exp2", (0.5, 0.5-1-calc.exp(-0.58)-0.2))
})
content("plot.pt1", [$y=t-1+e^(-t)$], anchor: "south", name: "prb")
line("plot.exp1", "prb", mark: (start: ">"))
content("plot.pt2", [$y=t-1-e^(-t)$], anchor: "north", name: "curve2")
line("plot.exp2", "curve2", mark: (start: ">"))
})
)
#import "@preview/cetz-plot:0.1.3": plot
#let intersection(plotA, plotB, style: (stroke: red + 2pt)) = {
let dataA = plotA.first().data
let dataB = plotB.first().data
let points = dataA.filter(x => x in dataB)
for ((i, point)) in points.enumerate() {
plot.add-anchor("i_" + str(i),point )
}
plotA
plotB
}
#canvas(
length: 1cm,
{
import draw: *
plot.plot(
name: "my_plot",
size: (5, 5),
axis-style: "school-book",
x-label: [$x$],
y-label: [$y$],
{
intersection(
plot.add(
style: (stroke: black + 1.5pt),
domain: (-1, 1),
x => calc.pow(x, 4) - 2 * calc.pow(x, 2) + 1,
),
plot.add(
style: (stroke: black + 1.5pt),
domain: (-1, 1),
x => -(calc.pow(x, 4) - 2 * calc.pow(x, 2) + 1),
)
)
}
)
// reference the point with {plot name}.i_{number}
line("my_plot.i_1", ((), "|-", (0,3.5)), mark: (start: ">"), name: "line")
content("line.end", [Here], anchor: "south", padding: .1)
},
)
#let intersection(plotA, plotB, style: (stroke: red + 2pt)) = {
import draw: *
let dataA = plotA.first().data
let dataB = plotB.first().data
plot.annotate({
hide({
intersections("i", line(..plotA.first().data), line(..plotB.first().data))
})
for-each-anchor("i", (name) => {
circle("i." + name, radius: 0.05, fill: red)
})
})
plotA
plotB
}
#canvas(
length: 1cm,
{
import draw: *
plot.plot(
name: "plot",
size: (10, 10),
axis-style: "school-book",
x-label: [$x$],
y-label: [$y$],
{
intersection(
plot.add(
style: (stroke: black + 1.5pt),
domain: (-1, 1),
x => calc.pow(x, 4) - 2 * calc.pow(x, 2) + 1,
),
plot.add(
style: (stroke: black + 1.5pt),
domain: (-1, 1),
x => -(calc.pow(x, 4) - 2 * calc.pow(x, 2) + 0.5),
),
)
},
)
},
)
#import "@preview/cetz:0.4.0"
#import "@preview/cetz-plot:0.1.2"
#let my-plot = cetz-plot.plot.plot.with(axis-style: "school-book")
#cetz.canvas({
import cetz.draw: *
import cetz-plot: *
set-style(
axes: (
stroke: (dash: "dotted", paint: gray),
x: (mark: (start: ">", end: ">"), padding: 1),
y: (mark: none),
tick: (stroke: gray + .5pt),
),
)
my-plot(
size: (5, 4),
y-tick-step: none,
{
plot.add(calc.sin, domain: (0, calc.pi * 2))
},
)
})
#let plot-cfg = (size: (5, 4), axis-style: "school-book")
#cetz.canvas({
import cetz.draw: *
import cetz-plot: *
plot.plot(..plot-cfg, {
plot.add(calc.sin, domain: (0, calc.pi * 2))
})
})
#import "@preview/simple-plot:0.3.0": plot
//#set page(width: auto, height: auto, margin: 0.5cm)
// Showcases: major grid only, grid-label-break, axis extension, integer ticks
#plot(
xmin: -3.1, xmax: 3.1,
ymin: -1, ymax: 9,
xlabel: $x$,
ylabel: $y$,
//show-grid: "major",
(fn: x => calc.pow(x, 2), stroke: blue + 1.5pt, label: $x^2$, label-pos: 0.7, label-side: "below-right"),
)
#plot(
xmin: -2 * calc.pi, xmax: 2 * calc.pi,
ymin: -2, ymax: 2,
width: 10, height: 5,
show-grid: "major",
xtick: (-2*calc.pi, -calc.pi, 0, calc.pi, 2*calc.pi),
xtick-labels: ($-2pi$, $-pi$, $0$, $pi$, $2pi$),
(fn: x => calc.sin(x), stroke: blue + 1.2pt),
(fn: x => calc.cos(x), stroke: red + 1.2pt),
)
#plot(
xmin: -2, xmax: 5,
ymin: 0, ymax: 32,
show-grid: true,
(fn: x => calc.pow(2, x), stroke: blue + 1.5pt, label: $2^x$),
(fn: x => calc.pow(3, x), stroke: red + 1.5pt, label: $3^x$),
)