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added many images

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Martin Thoma 2013-12-03 14:59:22 +01:00
parent 8654f2d45e
commit a8e6ccd140
24 changed files with 357 additions and 7 deletions
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10
documents/GeoTopo/figures/topology-circle-two-paths.tex Normal file
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\begin{tikzpicture}
\tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\draw [red, thick,domain=90:-90, samples=100] plot ({cos(\x)}, {sin(\x)});
\draw [green,thick,domain=-90:-270,samples=100] plot ({cos(\x)}, {sin(\x)});
\node (a)[point,label=90:$a$] at (0,-1cm) {};
\node (b)[point,label=-90:$b$] at (0, 1cm) {};
\node at (1,0) [anchor=180, red] {$\gamma_1$};
\node at (-1,0) [anchor=0, green] {$\gamma_2$};
\end{tikzpicture}

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documents/GeoTopo/figures/topology-homotop-paths.tex Normal file
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\begin{tikzpicture}
\tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\node (a)[point,label=180:$a$] at (0,0) {};
\node (b)[point,label=0:$b$] at (3, 0) {};
\draw [rounded corners] (a) .. controls (0.8,0.8) .. (1.5,0.8) .. controls (2.2,1) .. (b);
\draw [rounded corners] (a) .. controls (0.6,0.6) .. (1.3,0.6) .. controls (2.0,0.8) .. (b);
\draw [rounded corners] (a) .. controls (0.3,0.3) .. (1.0,0.3) .. controls (2.0,0.4) .. (b);
\draw [rounded corners] (a) -- (b);
\draw [rounded corners] (a) .. controls (1,-0.8) .. (2,-0.4) .. controls (2.2,-0.9) .. (b);
\draw [rounded corners] (a) .. controls (1,-0.6) .. (2,-0.2) .. controls (2.2,-0.5) .. (b);
\draw [rounded corners] (a) .. controls (1,-0.3) .. (2,-0.05) .. controls (2.2,-0.2) .. (b);
\draw [rounded corners,->, thick, red] (a) .. controls (1,1) .. (2,1) .. controls (2.5,1) .. (b);
\draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b);
\node at (1,1.2) [red] {$\gamma_1$};
\node at (0.5,-0.8) [blue] {$\gamma_2$};
\end{tikzpicture}

10
documents/GeoTopo/figures/topology-non-homotop-paths.tex Normal file
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\begin{tikzpicture}
\tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\node (a)[point,label=180:$a$] at (0,0) {};
\node (b)[point,label=0:$b$] at (3, 0) {};
\draw[orange,pattern color=orange,pattern=north east lines] (1.5,0) circle (0.3cm);
\draw [rounded corners,->, thick, red] (a) .. controls (1,1) .. (2,1) .. controls (2.5,1) .. (b);
\draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b);
\node at (1,1.2) [red] {$\gamma_1$};
\node at (0.5,-0.8) [blue] {$\gamma_2$};
\end{tikzpicture}

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documents/GeoTopo/figures/topology-paths-in-r2.tex Normal file
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\begin{tikzpicture}
\begin{axis}[
legend pos=south west,
axis x line=middle,
axis y line=middle,
%grid = major,
width=9cm,
height=9cm,
grid style={dashed, gray!30},
xmin=-2, % start the diagram at this x-coordinate
xmax= 1, % end the diagram at this x-coordinate
ymin=-1, % start the diagram at this y-coordinate
ymax= 5, % end the diagram at this y-coordinate
%axis background/.style={fill=white},
%xlabel=$x$,
%ylabel=$y$,
ticks=none,
%tick align=outside,
%minor tick num=-3,
enlargelimits=true,
tension=0.08]
\addplot[mark=none, orange, smooth cycle, thick, tension=1, dashed] coordinates {%
(0,0) (-1,1) (-2,2) (-1,3) (0, 3) (1, 4)};
\addplot[mark=none, blue, smooth cycle, thick, tension=3] coordinates {%
(0,0) (-1,1) (-2,2) (-1,3) (0, 3) (1, 4)};
\end{axis}
\end{tikzpicture}