added image

documents/GeoTopo/Arbeitszeit.txt

@@ -10,4 +10,4 @@ Datum      | Uhrzeit
 14.12.2013 | 13:00 - 14:45
 15.12.2013 | 20:30 - 21:20
 16.12.2013 | 15:00 - 15:30
-17.12.2013 | 07:30 - 07:45, 14:30 - 15:40, 16:30 - 
+17.12.2013 | 07:30 - 07:45, 14:30 - 15:40, 16:30 - 18:00

documents/GeoTopo/Kapitel3.tex

@@ -492,7 +492,7 @@ Für einen Weg $\gamma$ sei $[\gamma]$ seine \textbf{Homotopieklasse}\xindex{Hom
             \label{fig:ueberlappung-kaestchen-torus}
         }%
         \subfloat[$t \mapsto (\cos 4 \pi t, \sin 4 \pi t)$]{
-            \includegraphics[width=0.3\linewidth, keepaspectratio]{figures/todo/liftung-s-s.jpg}
+            \resizebox{0.3\linewidth}{!}{\input{figures/topology-ueberlagerung.tex}}
             \label{fig:liftung-s1-s1}
         }%
         \label{Formen}

documents/GeoTopo/figures/topology-ueberlagerung.tex

@@ -0,0 +1,51 @@
+\newcommand\markangle[6]{% origin X Y radius radiusmark mark
+  % fill red circle
+  \begin{scope}
+    \path[clip] (#1) -- (#2) -- (#3);
+    \fill[color=red,fill opacity=0.5,draw=red,name path=circle]
+    (#1) circle (#4);
+  \end{scope}
+  % middle calculation
+  \path[name path=line one] (#1) -- (#2);
+  \path[name path=line two] (#1) -- (#3);
+  \path[%
+  name intersections={of=line one and circle, by={inter one}},
+  name intersections={of=line two and circle, by={inter two}}
+  ] (inter one) -- (inter two) coordinate[pos=.5] (middle);
+  % put mark
+  \node at ($(#1)!#5!(middle)$) {#6};
+}
+
+\begin{tikzpicture}
+    \newcommand{\R}{2}
+    \draw (0,0) circle (\R);
+    \draw[->, thick] ({-(\R+0.2)},0) -- ({\R+0.2},0);
+    \draw[->, thick] (0,{-(\R+0.2)}) -- (0,{\R+0.2});
+    \draw[thick] (\R,-0.06) -- (\R,0.06) node[label=below:$1$] {};
+    \draw[thick] (-0.06,\R) -- (0.06,\R) node[label=left:$i$] {};
+    \draw (0,0) -- ({\R*cos(30)},{\R*sin(30)}) node[label=15:$z$] {};
+    \draw (0,0) -- ({\R*cos(60)},{\R*sin(60)}) node[label=35:$z^2$] {};
+
+    \coordinate (O) at (0,0);
+    \coordinate (X) at (1,0);
+    \coordinate (Y) at ({\R*cos(30)},{\R*sin(30)});
+    \coordinate (Z) at ({\R*cos(60)},{\R*sin(60)});
+    \markangle{O}{Y}{Z}{10mm}{7mm}{$\varphi$}
+    \markangle{O}{X}{Y}{10mm}{7mm}{$\varphi$}
+
+    \begin{scope}[xshift=4cm, yshift=-1.2cm]
+        \draw (0,0) circle (\R/2);
+        \newcommand{\x}{1}
+        \draw [red,thick,domain=-30:30] plot ({cos(\x)}, {sin(\x)});
+        \draw [red,thick,domain=210:150] plot ({cos(\x)}, {sin(\x)});
+    \end{scope}
+
+    \begin{scope}[xshift=4cm, yshift=+1.2cm]
+        \draw (0,0) circle (\R/2);
+        \newcommand{\x}{1}
+        \draw [red,thick,domain=-30:30] plot ({cos(\x)}, {sin(\x)});
+    \end{scope}
+
+    \coordinate (T) at (5.5,1);
+    \path[->] (5.5,-1) edge[bend right] node[label=right:$z^2$] {} (T);
+\end{tikzpicture}

tikz/topology-ueberlagerung/Makefile

@@ -0,0 +1,31 @@
+SOURCE = topology-ueberlagerung
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/topology-ueberlagerung/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](topology-ueberlagerung.png)

tikz/topology-ueberlagerung/topology-ueberlagerung.tex

@@ -0,0 +1,57 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{calc,intersections,automata, arrows} 
+
+\newcommand\markangle[6]{% origin X Y radius radiusmark mark
+  % fill red circle
+  \begin{scope}
+    \path[clip] (#1) -- (#2) -- (#3);
+    \fill[color=red,fill opacity=0.5,draw=red,name path=circle]
+    (#1) circle (#4);
+  \end{scope}
+  % middle calculation
+  \path[name path=line one] (#1) -- (#2);
+  \path[name path=line two] (#1) -- (#3);
+  \path[%
+  name intersections={of=line one and circle, by={inter one}},
+  name intersections={of=line two and circle, by={inter two}}
+  ] (inter one) -- (inter two) coordinate[pos=.5] (middle);
+  % put mark
+  \node at ($(#1)!#5!(middle)$) {#6};
+}
+
+\begin{document}
+\begin{tikzpicture}
+    \newcommand{\R}{2}
+    \draw (0,0) circle (\R);
+    \draw[->, thick] ({-(\R+0.2)},0) -- ({\R+0.2},0);
+    \draw[->, thick] (0,{-(\R+0.2)}) -- (0,{\R+0.2});
+    \draw[thick] (\R,-0.06) -- (\R,0.06) node[label=below:$1$] {};
+    \draw[thick] (-0.06,\R) -- (0.06,\R) node[label=left:$i$] {};
+    \draw (0,0) -- ({\R*cos(30)},{\R*sin(30)}) node[label=15:$z$] {};
+    \draw (0,0) -- ({\R*cos(60)},{\R*sin(60)}) node[label=35:$z^2$] {};
+
+    \coordinate (O) at (0,0);
+    \coordinate (X) at (1,0);
+    \coordinate (Y) at ({\R*cos(30)},{\R*sin(30)});
+    \coordinate (Z) at ({\R*cos(60)},{\R*sin(60)});
+    \markangle{O}{Y}{Z}{10mm}{7mm}{$\varphi$}
+    \markangle{O}{X}{Y}{10mm}{7mm}{$\varphi$}
+
+    \begin{scope}[xshift=4cm, yshift=-1.2cm]
+        \draw (0,0) circle (\R/2);
+        \newcommand{\x}{1}
+        \draw [red,thick,domain=-30:30] plot ({cos(\x)}, {sin(\x)});
+        \draw [red,thick,domain=210:150] plot ({cos(\x)}, {sin(\x)});
+    \end{scope}
+
+    \begin{scope}[xshift=4cm, yshift=+1.2cm]
+        \draw (0,0) circle (\R/2);
+        \newcommand{\x}{1}
+        \draw [red,thick,domain=-30:30] plot ({cos(\x)}, {sin(\x)});
+    \end{scope}
+
+    \coordinate (T) at (5.5,1);
+    \path[->] (5.5,-1) edge[bend right] node[label=right:$z^2$] {} (T);
+\end{tikzpicture}
+\end{document}