From 7ccd7614635d93f8968747712a9e342a43ad3b0e Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Thu, 12 Dec 2013 18:22:37 +0100 Subject: [PATCH] added image with mapping --- documents/GeoTopo/Arbeitszeit.txt | 2 +- documents/GeoTopo/GeoTopo.pdf | Bin 3847424 -> 3857020 bytes documents/GeoTopo/Kapitel3.tex | 2 +- .../figures/topology-r-spiral-covering-s.tex | 57 ++++++++++++++++++ 4 files changed, 59 insertions(+), 2 deletions(-) create mode 100644 documents/GeoTopo/figures/topology-r-spiral-covering-s.tex diff --git a/documents/GeoTopo/Arbeitszeit.txt b/documents/GeoTopo/Arbeitszeit.txt index 5ad02f4..730b04b 100644 --- a/documents/GeoTopo/Arbeitszeit.txt +++ b/documents/GeoTopo/Arbeitszeit.txt @@ -5,4 +5,4 @@ Datum | Uhrzeit --------------------------------------------------------------------- 03.12.2013 | 11:00 - 12:00, 13:10 - 15:00 05.12.2013 | 15:50 - 17:00 -12.12.2013 | 12:00 - 13:40, 16:23 - 17:25 +12.12.2013 | 12:00 - 13:40, 16:23 - 18:22 diff --git 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b/documents/GeoTopo/Kapitel3.tex index 036775b..0f6c7e8 100644 --- a/documents/GeoTopo/Kapitel3.tex +++ b/documents/GeoTopo/Kapitel3.tex @@ -477,7 +477,7 @@ Für einen Weg $\gamma$ sei $[\gamma]$ seine \textbf{Homotopieklasse}\xindex{Hom \item \begin{figure} \centering - \input{figures/todo.tex} + \input{figures/topology-r-spiral-covering-s.tex} \caption{$\mdr \rightarrow S^1$, $t \mapsto (\cos 2 \pi t, \sin 2 \pi t)$} \label{fig:ueberlappung-r1-spirale-s1} \end{figure} diff --git a/documents/GeoTopo/figures/topology-r-spiral-covering-s.tex b/documents/GeoTopo/figures/topology-r-spiral-covering-s.tex new file mode 100644 index 0000000..9382720 --- /dev/null +++ b/documents/GeoTopo/figures/topology-r-spiral-covering-s.tex @@ -0,0 +1,57 @@ +\begin{tikzpicture} +\draw[->, thick] (7,5) -- (7, 2) node [midway, right] {$p$}; +\node at (1,5.5) {$\mathbb{R}$} ; +\node at (6.4,0.7) {$\color{blue} S^1$}; +\node at (4.9,1.1){$x$}; +\begin{axis}[ + view={-30}{-45}, + axis lines=middle, + zmax=60, + height=8cm, + xtick=\empty, + ytick=\empty, + ztick=\empty, + enlarge y limits=true, + enlarge x limits=true, +] + +\addplot3+[->,ytick=\empty,yticklabel=\empty, + mark=none, + thick, + black, + domain=0:14.8*pi, + samples=400, + samples y=0, +] +({sin(deg(x))},{cos(deg(x)},{x+15}); +\addplot3+[ytick=\empty,yticklabel=\empty, + mark=none, + thick, + dotted, + black, + domain=-1:0, + samples=100, + samples y=0, +] +({sin(deg(x))},{cos(deg(x)},{x+15}); + +\addplot3+[,ytick=\empty,yticklabel=\empty, + mark=none, + thick, + blue, + domain=0:14.7*pi, + samples=400, + samples y=0, +] +({sin(deg(x))},{cos(deg(x)},{0}); + +%%%%%%%%%%%%% Point +\addplot3+[ + mark options={color=black}, + mark=* +] +coordinates {({sin(deg(45)},{cos(deg(45))},0)}; +%%%%%%%%%%%%% + +\end{axis} +\end{tikzpicture}