diff --git a/documents/GeoTopo/Arbeitszeit.md b/documents/GeoTopo/Arbeitszeit.md index a9be3c4..c118ec8 100644 --- a/documents/GeoTopo/Arbeitszeit.md +++ b/documents/GeoTopo/Arbeitszeit.md @@ -73,4 +73,5 @@ in dem Erstellen dieses Skripts steckt: |07.02.2014 | 19:30 - 21:20 | Textsetzung, kleine Fehler und Verbesserung eines Bildes |10.02.2014 | 10:30 - 11:05 | Formulierung in Definitionen vereinfacht; Textsetzung |10.02.2014 | 11:05 - 11:20 | Verbesserungen von Marco, Email vom 10.02.2014, eingefügt. -|10.02.2014 | 11:40 - 13:20 | Verbesserungen von Jérôme Urhausen, Email vom 10.02.2014, eingefügt. \ No newline at end of file +|10.02.2014 | 11:40 - 13:20 | Verbesserungen von Jérôme Urhausen, Email vom 10.02.2014, eingefügt. +|11.02.2014 | 05:30 - 06:00 | TikZ'en eines Bildes mit Hilfe von Jérôme Urhausen (Email vom 10.02.2014) \ No newline at end of file diff --git a/documents/GeoTopo/GeoTopo.pdf b/documents/GeoTopo/GeoTopo.pdf index 1abbd23..64ba1a1 100644 Binary files a/documents/GeoTopo/GeoTopo.pdf and b/documents/GeoTopo/GeoTopo.pdf differ diff --git a/documents/GeoTopo/Kapitel2.tex b/documents/GeoTopo/Kapitel2.tex index 7cecc66..c962cd8 100644 --- a/documents/GeoTopo/Kapitel2.tex +++ b/documents/GeoTopo/Kapitel2.tex @@ -775,8 +775,8 @@ Differenzierbare Mannigfaltigkeiten der Klasse $C^\infty$ werden auch \parbox[c][3cm]{4cm}{\centering\input{figures/topology-graph-k-3-3.tex}} \label{fig:k-3-3} }% - \label{fig:graphen-beispiele} \caption{Beispiele für Graphen} + \label{fig:graphen-beispiele} \end{figure} \begin{bemerkung} @@ -824,8 +824,8 @@ Differenzierbare Mannigfaltigkeiten der Klasse $C^\infty$ werden auch \parbox{4cm}{\centering\input{figures/topology-graph-tetraeder-area-2.tex}} \label{fig:topology-simplizial-complex-k-division} }% - \label{fig:simplex-unterteilung-beispiel} \caption{Beispiel für \cref{kor:simplex-unterteilung}.} + \label{fig:simplex-unterteilung-beispiel} \end{figure} \begin{beweis} @@ -849,12 +849,14 @@ Differenzierbare Mannigfaltigkeiten der Klasse $C^\infty$ werden auch \item Sind $P_1$ und $P_2$ konvexe Polygone und $T_1, T_2$ die zugehörigen Triangulierungen von $S^2$, so gibt es eine eine Triangulierungen $T$, die sowohl um $T_1$ als - auch um $T_2$ Verfeinerung ist. + auch um $T_2$ Verfeinerung ist (vgl. \cref{fig:topology-3}). - \begin{center} + \begin{figure}[htp] \centering - \input{figures/topology-3.tex}\todo{Was bedeutet diese Zeichnung?} - \end{center} + \input{figures/topology-3.tex} + \caption{$T$ ist eine Triangulierung, die für $T_1$ und $T_2$ eine Verfeinerung ist.} + \label{fig:topology-3} + \end{figure} Nach \cref{kor:simplex-unterteilung} ist $\chi(\partial P_1) = \chi(T_1) = \chi(T) = \chi(T_2) = \chi(\partial P_2) = 2$, diff --git a/documents/GeoTopo/figures/topology-3.tex b/documents/GeoTopo/figures/topology-3.tex index 51a47a4..415e903 100644 --- a/documents/GeoTopo/figures/topology-3.tex +++ b/documents/GeoTopo/figures/topology-3.tex @@ -28,48 +28,59 @@ \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground} \begin{tikzpicture} - \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt] - \tikzstyle{smallpoint}=[circle,thick,draw=red,fill=red,inner sep=0pt,minimum width=3pt,minimum height=3pt] - \begin{pgfonlayer}{foreground} - \node (a)[point] at (0,0) {}; - \node (b)[point] at (2,0) {}; - \node (c)[point] at (3,0.5) {}; - \node (d)[point] at (0,3) {}; - \node (e)[point] at (2,3) {}; - \node (f)[point] at (3,1.5) {}; - \node (g)[point] at (2,2.5) {}; - \node (h)[point] at (1,1.5) {}; - \end{pgfonlayer} + \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black] - \draw (h.center) -- (e.center) -- (f.center) -- (b.center) -- cycle; - \draw (h.center) -- (f.center); - - \draw[green, densely dashed] (a.center) -- (d.center) -- (g.center) -- (c.center) -- cycle; - \draw[green, densely dashed] (a.center) -- (g.center); + \tkzDefPoints{0/0/A, 2/0/B, 3/0.5/C, 0/3/D, 2/3/E, 3/1.5/F, 2/2/G, 1/1.5/H} \begin{pgfonlayer}{foreground} - \node (x)[point, red,fill=red] at (1.79,0.31) {}; - \node (x1)[smallpoint] at (1.2,1.5) {}; - \node (x2)[smallpoint] at (1.71,2.56) {}; - \node (x3)[smallpoint] at (2.5,1.5) {}; - \node (x4)[smallpoint] at (2.72,1.06) {}; - \end{pgfonlayer} - \draw[blue, densely dotted] (x.center) -- (x1.center); - \draw[blue, densely dotted] (x.center) -- (x2.center); - \draw[blue, densely dotted] (x.center) -- (x3.center); - \draw[blue, densely dotted] (x.center) -- (x4.center); + %Get intersections + \tkzInterLL(B,H)(A,C) \tkzGetPoint{I} + \tkzInterLL(B,F)(A,C) \tkzGetPoint{J} + \tkzInterLL(A,G)(B,H) \tkzGetPoint{K} + \tkzInterLL(A,G)(H,F) \tkzGetPoint{L} + \tkzInterLL(C,G)(B,F) \tkzGetPoint{M} + \tkzInterLL(C,G)(H,F) \tkzGetPoint{N} + \tkzInterLL(G,D)(H,E) \tkzGetPoint{O} + \tkzDrawPoints[color=green,fill=green](A,C,G,D) + \tkzDrawPoints[color=blue,fill=blue](B,F,E,H) + \tkzDrawPoints[color=red,fill=red](I,J,K,L,M,N,O) + \end{pgfonlayer} + + \tkzDrawPolygon[blue,very thick](H,E,F,B) + \tkzDrawSegment[blue,very thick](H,F) + + \tkzDrawPolygon[green,very thick](A,D,G,C) + \tkzDrawSegment[green,very thick](A,G) + + \tkzDrawSegments[red,very thick](I,M I,N I,L A,H H,D L,O N,E G,E) + + % \tkzLabelPoint(A){A} + % \tkzLabelPoint(B){B} + % \tkzLabelPoint(C){C} + % \tkzLabelPoint(D){D} + % \tkzLabelPoint(E){E} + % \tkzLabelPoint(F){F} + % \tkzLabelPoint(G){G} + % \tkzLabelPoint(H){H} + % \tkzLabelPoint(I){I} + % \tkzLabelPoint(J){J} + % \tkzLabelPoint(K){K} + % \tkzLabelPoint(L){L} + % \tkzLabelPoint(M){M} + % \tkzLabelPoint(N){N} + % \tkzLabelPoint(O){O} \begin{customlegend}[ legend entries={ $T_1$, $T_2$, - $?$ + $T$ }, legend style={at={(4.5,3.5)},font=\footnotesize}] % <= to define position and font legend % the following are the "images" and numbers in the legend - \addlegendimage{black} - \addlegendimage{green,densely dashed} - \addlegendimage{blue, densely dotted} + \addlegendimage{blue,very thick} + \addlegendimage{green,very thick} + \addlegendimage{red,very thick} \end{customlegend} -\end{tikzpicture} +\end{tikzpicture} \ No newline at end of file diff --git a/tikz/topology-3/topology-3.png b/tikz/topology-3/topology-3.png index ebe1779..79d743c 100644 Binary files a/tikz/topology-3/topology-3.png and b/tikz/topology-3/topology-3.png differ diff --git a/tikz/topology-3/topology-3.tex b/tikz/topology-3/topology-3.tex index aef0d50..d3f54e5 100644 --- a/tikz/topology-3/topology-3.tex +++ b/tikz/topology-3/topology-3.tex @@ -1,10 +1,11 @@ \documentclass[varwidth=true, border=2pt]{standalone} \usepackage{tikz} +\usepackage{tkz-euclide} \usetikzlibrary{calc,shadings} \usepackage{pgfplots} \begin{document} - +\usetkzobj{all} \newenvironment{customlegend}[1][]{% \begingroup % inits/clears the lists (which might be populated from previous @@ -35,49 +36,60 @@ \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground} \begin{tikzpicture} - \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt] - \tikzstyle{smallpoint}=[circle,thick,draw=red,fill=red,inner sep=0pt,minimum width=3pt,minimum height=3pt] - \begin{pgfonlayer}{foreground} - \node (a)[point] at (0,0) {}; - \node (b)[point] at (2,0) {}; - \node (c)[point] at (3,0.5) {}; - \node (d)[point] at (0,3) {}; - \node (e)[point] at (2,3) {}; - \node (f)[point] at (3,1.5) {}; - \node (g)[point] at (2,2.5) {}; - \node (h)[point] at (1,1.5) {}; - \end{pgfonlayer} + \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black] - \draw (h.center) -- (e.center) -- (f.center) -- (b.center) -- cycle; - \draw (h.center) -- (f.center); - - \draw[green, densely dashed] (a.center) -- (d.center) -- (g.center) -- (c.center) -- cycle; - \draw[green, densely dashed] (a.center) -- (g.center); + \tkzDefPoints{0/0/A, 2/0/B, 3/0.5/C, 0/3/D, 2/3/E, 3/1.5/F, 2/2/G, 1/1.5/H} \begin{pgfonlayer}{foreground} - \node (x)[point, red,fill=red] at (1.79,0.31) {}; - \node (x1)[smallpoint] at (1.2,1.5) {}; - \node (x2)[smallpoint] at (1.71,2.56) {}; - \node (x3)[smallpoint] at (2.5,1.5) {}; - \node (x4)[smallpoint] at (2.72,1.06) {}; - \end{pgfonlayer} - \draw[blue, densely dotted] (x.center) -- (x1.center); - \draw[blue, densely dotted] (x.center) -- (x2.center); - \draw[blue, densely dotted] (x.center) -- (x3.center); - \draw[blue, densely dotted] (x.center) -- (x4.center); + %Get intersections + \tkzInterLL(B,H)(A,C) \tkzGetPoint{I} + \tkzInterLL(B,F)(A,C) \tkzGetPoint{J} + \tkzInterLL(A,G)(B,H) \tkzGetPoint{K} + \tkzInterLL(A,G)(H,F) \tkzGetPoint{L} + \tkzInterLL(C,G)(B,F) \tkzGetPoint{M} + \tkzInterLL(C,G)(H,F) \tkzGetPoint{N} + \tkzInterLL(G,D)(H,E) \tkzGetPoint{O} + \tkzDrawPoints[color=green,fill=green](A,C,G,D) + \tkzDrawPoints[color=blue,fill=blue](B,F,E,H) + \tkzDrawPoints[color=red,fill=red](I,J,K,L,M,N,O) + \end{pgfonlayer} + + \tkzDrawPolygon[blue,very thick](H,E,F,B) + \tkzDrawSegment[blue,very thick](H,F) + + \tkzDrawPolygon[green,very thick](A,D,G,C) + \tkzDrawSegment[green,very thick](A,G) + + \tkzDrawSegments[red,very thick](I,M I,N I,L A,H H,D L,O N,E G,E) + + % \tkzLabelPoint(A){A} + % \tkzLabelPoint(B){B} + % \tkzLabelPoint(C){C} + % \tkzLabelPoint(D){D} + % \tkzLabelPoint(E){E} + % \tkzLabelPoint(F){F} + % \tkzLabelPoint(G){G} + % \tkzLabelPoint(H){H} + % \tkzLabelPoint(I){I} + % \tkzLabelPoint(J){J} + % \tkzLabelPoint(K){K} + % \tkzLabelPoint(L){L} + % \tkzLabelPoint(M){M} + % \tkzLabelPoint(N){N} + % \tkzLabelPoint(O){O} \begin{customlegend}[ legend entries={ $T_1$, $T_2$, - $?$ + $T$ }, legend style={at={(4.5,3.5)},font=\footnotesize}] % <= to define position and font legend % the following are the "images" and numbers in the legend - \addlegendimage{black} - \addlegendimage{green,densely dashed} - \addlegendimage{blue, densely dotted} + \addlegendimage{blue,very thick} + \addlegendimage{green,very thick} + \addlegendimage{red,very thick} \end{customlegend} \end{tikzpicture} \end{document}