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authorAndreas Müller <andreas.mueller@ost.ch>2021-10-13 20:53:37 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-10-13 20:53:37 +0200
commita27efc4b9657ace8e18fbf58db4dc3c31cb73514 (patch)
tree96c1945d4e7c5318460f84a84b8cd4335872541f /buch/chapters/110-elliptisch/images
parentadd ellipsenumfang (diff)
downloadSeminarSpezielleFunktionen-a27efc4b9657ace8e18fbf58db4dc3c31cb73514.tar.gz
SeminarSpezielleFunktionen-a27efc4b9657ace8e18fbf58db4dc3c31cb73514.zip
ellipsenumfang komplett
Diffstat (limited to '')
-rw-r--r--buch/chapters/110-elliptisch/images/Makefile4
-rw-r--r--buch/chapters/110-elliptisch/images/ellipsenumfang.m7
-rw-r--r--buch/chapters/110-elliptisch/images/ellipsenumfang.pdfbin16542 -> 22986 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/ellipsenumfang.tex71
4 files changed, 64 insertions, 18 deletions
diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile
index e366988..327fed1 100644
--- a/buch/chapters/110-elliptisch/images/Makefile
+++ b/buch/chapters/110-elliptisch/images/Makefile
@@ -8,9 +8,9 @@ all: lemniskate.pdf ellipsenumfang.pdf
lemniskate.pdf: lemniskate.tex
pdflatex lemniskate.tex
-ellipsenumfang.pdf: ellipsenumfang.tex ekpath.tex
+ellipsenumfang.pdf: ellipsenumfang.tex ekplot.tex
pdflatex ellipsenumfang.tex
-ekpath.tex: ellipsenumfang.m
+ekplot.tex: ellipsenumfang.m
octave ellipsenumfang.m
diff --git a/buch/chapters/110-elliptisch/images/ellipsenumfang.m b/buch/chapters/110-elliptisch/images/ellipsenumfang.m
index 84022bc..9ac8fe2 100644
--- a/buch/chapters/110-elliptisch/images/ellipsenumfang.m
+++ b/buch/chapters/110-elliptisch/images/ellipsenumfang.m
@@ -11,4 +11,11 @@ for epsilon = (1:100) / 100
fprintf(f, "--({\\dx*%.4f},{\\dy*%.4f})\n", epsilon, e);
endfor
fprintf(f, "\n}\n");
+fprintf(f, "\\def\\punkte{\n");
+for epsilon = (0.05:0.1:0.95)
+ [k, e] = ellipke(epsilon^2);
+ fprintf(f, "\\fill[color=blue] ({\\dx*%.4f},{\\dy*%.4f}) circle[radius=0.08];\n", epsilon, e);
+ fprintf(f, "\\draw[color=blue,line width=0.2pt] ({\\dx*%.4f},{\\dy*%.4f}) -- ({\\dx*%.4f},{\\dy*1.85});\n", epsilon, e, epsilon);
+endfor
+fprintf(f,"}\n");
fclose(f);
diff --git a/buch/chapters/110-elliptisch/images/ellipsenumfang.pdf b/buch/chapters/110-elliptisch/images/ellipsenumfang.pdf
index b52d5f3..fc27f21 100644
--- a/buch/chapters/110-elliptisch/images/ellipsenumfang.pdf
+++ b/buch/chapters/110-elliptisch/images/ellipsenumfang.pdf
Binary files differ
diff --git a/buch/chapters/110-elliptisch/images/ellipsenumfang.tex b/buch/chapters/110-elliptisch/images/ellipsenumfang.tex
index 9f7c788..0d1b807 100644
--- a/buch/chapters/110-elliptisch/images/ellipsenumfang.tex
+++ b/buch/chapters/110-elliptisch/images/ellipsenumfang.tex
@@ -12,32 +12,71 @@
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\input{ekplot.tex}
-\def\skala{1}
+\def\skala{1.19}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
+\pgfkeys{/pgf/number format/.cd, fixed, fixed zerofill, precision=1}
+
\def\dx{10}
\def\dy{4}
-\draw[->] (0,-0.1) -- (0,6.8) coordinate[label={right:$E(\varepsilon)$}];
-\draw[->] (-0.1,0) -- (10.5,0) coordinate[label={$\varepsilon$}];
-\draw[line width=0.4pt] (0,\dy) -- (10,\dy);
-\draw[line width=0.4pt] (\dx,0) -- (10,\dy);
+%\draw[line width=0.4pt] (0,\dy) -- (10,\dy);
+%\draw[line width=0.4pt] (\dx,0) -- (10,\dy);
+
+\draw[->] (0,{\dy-0.1}) -- (0,7.0) coordinate[label={left:$E(k=\varepsilon)$}];
+\draw[->] (-0.1,\dy) -- (10.5,\dy) coordinate[label={$\varepsilon$}];
+
+\foreach \i in {0,...,10}{
+ \pgfmathparse{\i/10}
+ \xdef\wert{\pgfmathresult}
+ \draw (\i,{\dy-0.1}) -- (\i,{\dy+0.1});
+ \node at (\i,{\dy-0.1}) [below] {$\pgfmathprintnumber{\wert}$};
+}
\draw[color=red,line width=1.4pt] \ekpath;
-\fill[color=red] (\dx,\dy) circle[radius=0.05];
+\fill[color=red] (\dx,\dy) circle[radius=0.07];
-\foreach \y in {2,4,...,16}{
- \draw (-0.1,{\dy*\y/10}) -- (0.1,{\dy*\y/10});
- \pgfmathparse{\y/10}
- \xdef\v{\pgfmathresult}
- \node at (0,{\dy*\y/10}) [left] {$\v$};
+\foreach \y in {1.0,1.2,1.4}{
+ \draw (-0.1,{\dy*\y}) -- (0.1,{\dy*\y});
+ \node at (-0.1,{\dy*\y}) [left] {$\pgfmathprintnumber{\y}$};
}
-\foreach \i in {1,...,9}{
- \draw (\i,-0.1) -- (\i,0.1);
- \node at (\i,0) [below] {$0.\i$};
+
+\draw (-0.1,{\dy*3.14159/2}) -- (0.1,{\dy*3.14159/2});
+\node at (0,{\dy*3.14159/2}) [left] {$\displaystyle\frac{\pi}2$};
+
+
+\punkte
+
+\foreach \exzentrizitaet in {0.05,0.15,...,0.95}{
+ \pgfmathparse{sqrt(1-\exzentrizitaet*\exzentrizitaet)}
+ \xdef\halbachse{\pgfmathresult}
+
+ \pgfmathparse{\exzentrizitaet*\dx}
+ \xdef\mitte{\pgfmathresult}
+ %\node at (\mitte,1) {$\pgfmathprintnumber{\mitte}$};
+
+ \pgfmathparse{(1-\exzentrizitaet)}
+ \xdef\breite{\halbachse}
+ %\node at (\mitte,0.5) {$\pgfmathprintnumber{\breite}$};
+
+ \begin{scope}
+
+ \clip ({\mitte-(\breite/2)},{1.8*\dy})
+ rectangle ({\mitte+(\breite/2)+0.1},{1.8*\dy+1.1});
+ \fill[color=blue!20] ({\mitte-\breite/2},{1.8*\dy})
+ ellipse({\breite} and 1);
+ \draw[color=blue,line width=1.4pt]
+ ({\mitte-\breite/2},{1.8*\dy})
+ ellipse({\breite} and 1);
+ \draw[color=blue,line width=0.2pt]
+ ({\mitte-\breite/2},{1.8*\dy+1})
+ --
+ ({\mitte-\breite/2},{1.8*\dy})
+ --
+ ({\mitte+\breite/2},{1.8*\dy});
+ \end{scope}
}
-\draw (10,-0.1) -- (10,0.1);
-\node at (10,0) [below] {$1.0$};
+
\end{tikzpicture}
\end{document}