pgfplots / Trigonometrische Kurve: Wie kann ich die x-Achse mit beliebigen Pi-Faktoren automatisch skalieren?

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Etwa bei trigonometrischen Kurven wünscht man oft eine Achsenskalierung mit Pi-Faktoren.

Meistens werden Pi-Ganze, Pi-Halbe oder Pi-Viertel Unterteilungen gewählt, das heißt "Unterteilungstiefe" 1 bzw. 2 bzw. 4.

Günstig wäre also ein Code, der eine beliebige Unterteilungstiefe erlaubt (also z.B. auch Skalierung mit Pi-Siebtel Faktoren) und dabei folgenden Darstellungskriterien genügt:

Wie kann man das umsetzen?

tikz pgfplots

gefragt 02 Mai '18, 20:33

cis
9.5k●102●460●491
Akzeptiert-Rate: 29%

Eine Antwort:

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Zunächst benötigt man eine Liste mit Werten (z.B. -pi, -3pi/4,..., 3pi)

Öffne in Overleaf

Code, hier editierbar zum Übersetzen:

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% Liste mit tick-Werten erstellen
\pgfmathsetmacro{\pinum}{3.142} % Rechengenauigkeit
\pgfmathtruncatemacro{\u}{4} % Unterteilungstiefe
% Reichweite der Ticks festlegen
\def\Range{-20,...,20}
% xticklist erstellen
\newcommand{\xticklist}{}% Name reservieren
\let\xticklist=\empty% Liste erstellen
\makeatletter
\foreach \n  in \Range
{
\pgfmathparse{\n*\pinum/\u}%
  \ifx\empty\xticklist{} \protected@xdef\xticklist{\pgfmathresult}%
  \else \protected@xdef\xticklist{\xticklist,\pgfmathresult}%
  \fi
}\makeatother
Anzeigen: \xticklist
 
 
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Für die gewünschten Darstellungskriterien

kann man, im Hinblick auf Zähler (Z) und Nenner (N) des Pi-Faktorenbruches, folgendes Ablaufdiagramm verwenden:

das setzt pgfmath so um:

Öffne in Overleaf

Code, hier editierbar zum Übersetzen:

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xtick/.expanded = {\xticklist},           
xticklabel={%
\pgfmathsetmacro{\p}{int(\tick*\u/\pinum)}% pi-Faktor
\pgfmathsetmacro{\Z}{int(\p/gcd(\p,\u))}% Zähler
  \pgfmathsetmacro{\Zabs}{int(abs(\Z))}% Zähler-Betrag
\pgfmathsetmacro{\N}{int(\u/gcd(\p,\u))}% Nenner
\pgfmathparse{%
\N == 1 ? (\Z==1 ? "\pi" : (\Z==-1 ? "-\pi" : "\Z\pi")) :% 
(\Z==1 ? "\frac{\pi}{\N}" : (\Z==-1 ? "-\frac{\pi}{\N}" :%
(\Z<0 ? "-\frac{\Zabs\pi}{\N}" : "\frac{\Z\pi}{\N}")%
))%
}
$\pgfmathresult$%
%$\frac{\Z}{\N}$% zum Testen
},
 
 
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Kleiner Warnhinweis: Die Rechengenauigkeit von pgfmath ist nicht beliebig; z.B. ab Pi-Neuntel Unterteilung kommen Fehler rein.

Im Ergebnis

Beispiel 1:

Öffne in Overleaf

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\pgfmathtruncatemacro{\u}{2} % Unterteilungstiefe
 
 
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Beispiel 2:

Öffne in Overleaf

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\pgfmathtruncatemacro{\u}{7} % Unterteilungstiefe
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Ganzer Code:

Öffne in Overleaf

Code, hier editierbar zum Übersetzen:

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%\documentclass[]{article}
\documentclass[border=5mm, tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\begin{document}
% Eingaben
\pgfmathsetmacro{\xStauchung}{0.58500055}% Stauchung x-Achse
% Liste mit tick-Werten erstellen
\pgfmathsetmacro{\pinum}{3.142} % Rechengenauigkeit
\pgfmathtruncatemacro{\u}{7} % Unterteilungstiefe
% Reichweite der Ticks festlegen
\def\Range{-20,...,20}
% xticklist erstellen
\newcommand{\xticklist}{}% Name reservieren
\let\xticklist=\empty% Liste erstellen
\makeatletter
\foreach \n  in \Range
{
\pgfmathparse{\n*\pinum/\u}%
  \ifx\empty\xticklist{} \protected@xdef\xticklist{\pgfmathresult}%
  \else \protected@xdef\xticklist{\xticklist,\pgfmathresult}%
  \fi
}\makeatother
%Anzeigen: \xticklist
% Zeichnen
\pgfmathsetmacro{\xScale}{\xStauchung*\u/pi}% 
\begin{tikzpicture}[]
\begin{axis}[
font=\footnotesize, 
x = \xScale cm, 
%y = 1cm, 
axis lines=middle, 
xlabel=$x$,xlabel style={anchor=north},
ylabel=$y$,ylabel style={anchor=east},
x axis line style = {-latex}, y axis line style = {-latex},
%
xtick/.expanded = {\xticklist},           
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Code für das Ablaufdiagramm:

Öffne in Overleaf

Code, hier editierbar zum Übersetzen:

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\documentclass[border=5pt]{standalone}
\usepackage{selinput}
\SelectInputMappings{adieresis={ä},germandbls={ß}}
\usepackage{tikz}
\usetikzlibrary{matrix,shapes}
\tikzset{%
treenode/.style = {%fill=gray!10, 
shape=rectangle, 
draw, anchor=center,
%text width=5em, 
align=center,
%draw=cyan, very thick,
text=black,
text width=1cm,
%inner sep=1ex
},
startstop/.style      = {treenode, rounded corners=7pt},
process/.style      = {treenode},
decision/.style = {treenode, diamond, inner sep=0pt},
output/.style={treenode, trapezium,trapezium left angle=60, trapezium right angle=120, font=\sffamily\slshape\tiny},
input/.style={treenode, trapezium,trapezium left angle=120, trapezium right angle=60},
predefprocess/.style  = {treenode,  path picture={\draw[treenode, -]
    ([xshift=1mm]path picture bounding box.north west)--([xshift=1mm]path picture bounding box.south west)
    ([xshift=-1mm]path picture bounding box.north east)--([xshift=-1mm]path picture bounding box.south east);}},
}%
\newcommand{\ja}{-| node [auto=left, near start] {ja}}
\newcommand{\nein}{-|  node [auto=right, near start]  {nein}}
\begin{document}
\begin{tikzpicture}[scale=0.5,
font=\sffamily\tiny,
>=latex, ->,  
%every path/.style={red, very thick}, 
]
%\pgfgettransform\mytrafo
\def\Start{|[decision]| N=1}
\def\ZEins{|[decision]| Z = 1}
\def\ZnegEins{|[decision]| Z = -1}
\def\Zneg{|[decision]| Z < 0}
\def\ZposI{|[startstop,  minimum height=0.85cm]| \frac{Z\pi}{N}}
 
 
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Permanenter link

beantwortet 02 Mai '18, 20:33

cis
9.5k●102●460●491
Akzeptiert-Rate: 29%

bearbeitet 03 Mai '18, 05:04

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gestellte Frage: 02 Mai '18, 20:33

Frage wurde gesehen: 7,944 Mal

zuletzt geändert: 03 Mai '18, 05:04

pgfplots / Trigonometrische Kurve: Wie kann ich die x-Achse mit beliebigen Pi-Faktoren automatisch skalieren?

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