From a14385eccb4fa12d22c88f2955b39bee7ee482c7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 12:51:42 +0200 Subject: Funktionsauswahl --- .../110-elliptisch/images/ellselection.tex | 122 +++++++++++++++++++++ 1 file changed, 122 insertions(+) create mode 100644 buch/chapters/110-elliptisch/images/ellselection.tex (limited to 'buch/chapters/110-elliptisch/images/ellselection.tex') diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex new file mode 100644 index 0000000..9e822ec --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -0,0 +1,122 @@ +% +% ellselection.tex -- Wahl einer elliptischen Funktion +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\l{0.45} +\pgfmathparse{\l*72/2.54} +\xdef\L{\pgfmathresult} + +\def\sx{4.1} +\pgfmathparse{\sx*72/2.54} +\xdef\Sx{\pgfmathresult} + +\def\sy{3.2} +\pgfmathparse{\sy*72/2.54} +\xdef\Sy{\pgfmathresult} + +\pgfmathparse{\sx/2-\l} +\xdef\linksx{\pgfmathresult} +\pgfmathparse{\sy/2-\l} +\xdef\linksy{\pgfmathresult} + +\pgfmathparse{\sx/2+2*\l} +\xdef\rechtsx{\pgfmathresult} +\pgfmathparse{\sy/2} +\xdef\rechtsy{\pgfmathresult} + +\fill[color=red!20] ({-\sx},0) rectangle (\sx,\sy); +\fill[color=blue!20] ({-\sx},{-\sy}) rectangle (\sx,0); +\fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); + +\draw (-\sx,-\sy) rectangle (\sx,\sy); + +\draw[->] ({-1.4*\sx},0) -- ({1.4*\sx},0) coordinate[label={$\Re u$}]; +\draw[->] (0,{-\sy-1}) -- (0,{\sy+1}) coordinate[label={right:$\Im u$}]; + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\draw[->,line width=1.9pt,color=darkgreen] + (\sx,0) to[out=180,in=-79] (\linksx,\linksy); +\draw[->,line width=1.9pt,color=darkgreen] + (\sx,{\sy-\l}) to[out=-90,in=0] (\rechtsx,\rechtsy); + +\def\rect#1#2{ + \fill[color=white] (-\l,-\l) rectangle (\l,\l); + #2 + \draw (-\l,-\l) rectangle (\l,\l); + \node at (0,0) {\Huge #1\strut}; +} + +\def\kreuz{ + \begin{scope} + \clip ({-\l},{-\l}) rectangle ({\l},{\l}); + \fill[color=white] ({-2*\l},{-2*\l}) rectangle ({2*\l},{2*\l}); + \draw[color=darkgreen!30,line width=3pt] (-\l,-\l) -- (\l,\l); + \draw[color=darkgreen!30,line width=3pt] (-\l,\l) -- (\l,-\l); + \end{scope} +} + +\def\kreis{ + \begin{scope} + \clip ({-\l},{-\l}) rectangle ({\l},{\l}); + \fill[color=white] ({-2*\l},{-2*\l}) rectangle ({2*\l},{2*\l}); + \draw[color=darkgreen!30,line width=3pt] + (0,0) circle[radius={\l*(\L-1.5)/\L}]; + \end{scope} +} + +\begin{scope}[xshift={0},yshift={0}] + \rect{s}{} +\end{scope} + +\begin{scope}[xshift={\Sx},yshift={0}] + \rect{c}{\kreis} +\end{scope} + +\begin{scope}[xshift={\Sx},yshift={\Sy}] + \rect{d}{\kreuz} +\end{scope} + +\begin{scope}[xshift={0},yshift={\Sy}] + \rect{n}{} +\end{scope} + +\node at ({-\l+0.1},{\sy+\l-0.1}) [above left] {$iK'\mathstrut$}; +\node at ({-\l+0.1},{-\l+0.1}) [below left] {$0\mathstrut$}; +\node at ({\sx+\l-0.1},{-\l+0.1}) [below right] {$K\mathstrut$}; +\node at ({\sx+\l-0.1},{\sy+\l-0.1}) [above right] {$K+iK'\mathstrut$}; +\node at ({-\sx},0) [below left] {$-K\mathstrut$}; +\node at (0,{-\sy+0.05}) [below left] {$-iK'\mathstrut$}; +\node at ({\sx-0.1},{-\sy+0.1}) [below right] {$K-iK'\mathstrut$}; +\node at ({-\sx+0.1},{-\sy+0.1}) [below left] {$-K-iK'\mathstrut$}; +\node at ({-\sx+0.1},{\sy-0.1}) [above left] {$-K+iK'\mathstrut$}; + +\begin{scope}[xshift={-\L+0.5*\Sx},yshift={0.5*\Sy}] + \node at ({-\l},{\l-0.1}) [above] {Nullstelle\strut}; + \kreis + \node[color=darkgreen] at (0,0) {\Huge c\strut}; + \draw[line width=0.2pt] (-\l,-\l) rectangle (\l,\l); +\end{scope} + +\begin{scope}[xshift={\L+0.5*\Sx},yshift={0.5*\Sy}] + \node at ({\l},{\l-0.1}) [above] {Pol\strut}; + \kreuz + \node[color=darkgreen] at (0,0) {\Huge d\strut}; + \draw[line width=0.2pt] (-\l,-\l) rectangle (\l,\l); +\end{scope} + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1 From 3a7e2cef27bd78a96b20751db2a53f7291fcd2a6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 20:18:48 +0200 Subject: add grid to images --- buch/chapters/110-elliptisch/images/ellselection.tex | 15 ++++++++++++--- 1 file changed, 12 insertions(+), 3 deletions(-) (limited to 'buch/chapters/110-elliptisch/images/ellselection.tex') diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex index 9e822ec..0dd1e04 100644 --- a/buch/chapters/110-elliptisch/images/ellselection.tex +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -14,15 +14,22 @@ \def\skala{1} \begin{tikzpicture}[>=latex,thick,scale=\skala] +\input{rechteckpfade2.tex} + \def\l{0.45} \pgfmathparse{\l*72/2.54} \xdef\L{\pgfmathresult} +\pgfmathparse{4.1/\xmax} +\xdef\dx{\pgfmathresult} +\xdef\dy{\dx} + \def\sx{4.1} \pgfmathparse{\sx*72/2.54} \xdef\Sx{\pgfmathresult} -\def\sy{3.2} +\pgfmathparse{\dx*\ymax} +\xdef\sy{\pgfmathresult} \pgfmathparse{\sy*72/2.54} \xdef\Sy{\pgfmathresult} @@ -36,8 +43,10 @@ \pgfmathparse{\sy/2} \xdef\rechtsy{\pgfmathresult} -\fill[color=red!20] ({-\sx},0) rectangle (\sx,\sy); -\fill[color=blue!20] ({-\sx},{-\sy}) rectangle (\sx,0); +\hintergrund +\netz{0.7pt} +\fill[color=red!14,opacity=0.7] ({-\sx},0) rectangle (\sx,\sy); +\fill[color=blue!14,opacity=0.7] ({-\sx},{-\sy}) rectangle (\sx,0); \fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); \draw (-\sx,-\sy) rectangle (\sx,\sy); -- cgit v1.2.1 From e1e6149b020ef102e257adb9898d5ba5242bac05 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 20:47:33 +0200 Subject: more improvements --- buch/chapters/110-elliptisch/images/ellselection.tex | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) (limited to 'buch/chapters/110-elliptisch/images/ellselection.tex') diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex index 0dd1e04..d8afeb1 100644 --- a/buch/chapters/110-elliptisch/images/ellselection.tex +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -43,8 +43,18 @@ \pgfmathparse{\sy/2} \xdef\rechtsy{\pgfmathresult} -\hintergrund -\netz{0.7pt} +\begin{scope} + \clip (-\sx,-\sy) rectangle (\sx,\sy); + \begin{scope}[xshift={-\Sx}] + \hintergrund + \netz{0.7pt} + \end{scope} + \begin{scope}[xshift={\Sx}] + \hintergrund + \netz{0.7pt} + \end{scope} +\end{scope} + \fill[color=red!14,opacity=0.7] ({-\sx},0) rectangle (\sx,\sy); \fill[color=blue!14,opacity=0.7] ({-\sx},{-\sy}) rectangle (\sx,0); \fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); -- cgit v1.2.1