tex-projects/LaTeX-examples
2
0
Fork 0
mirror of https://github.com/MartinThoma/LaTeX-examples.git synced 2025-04-19 11:38:05 +02:00
Code Activity

TikZ'en von Bildern

Browse source
This commit is contained in:
Martin Thoma 2014-02-02 18:42:22 +01:00
parent abdf6ef315
commit 23eed4cd24
15 changed files with 163 additions and 16 deletions
Download patch file Download diff file Expand all files Collapse all files

1
documents/GeoTopo/Arbeitszeit.md
View file

@ -56,3 +56,4 @@ in dem Erstellen dieses Skripts steckt:
|30.01.2014 | 15:45 - 17:00 | Digitalisieren der Vorlesung von 30.01.2014
|30.01.2014 | 19:30 - 21:30 | Textsetzung
|01.02.2014 | 15:40 - 15:50 | Beweis "Möbiustransformation ist Gruppenoperation" hinzugefügt
|02.02.2014 | 17:00 - 18:00 | TikZ'en von Bildern

BIN
documents/GeoTopo/GeoTopo.pdf
View file

Binary file not shown.

2
documents/GeoTopo/Kapitel2.tex
View file

@ -879,7 +879,7 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$.
\begin{figure}[h!]
\centering
\input{figures/topology-oriented-triangle.tex}
\caption{TODO}
\caption{Simplizialkomplex mit Totalordnung}
\end{figure}
$a < b < c$

13
documents/GeoTopo/Kapitel3.tex
View file

@ -269,7 +269,7 @@ Für einen Weg $\gamma$ sei $[\gamma]$ seine \textbf{Homotopieklasse}\xindex{Hom
\begin{figure}[htp]
\centering
\input{figures/todo.tex}
\input{figures/topology-paths.tex}
\caption{Situation aus \cref{kor:gruppenisomorphismus-wege}}.
\label{fig:situation-gruppenisomorphismus-wege}
\end{figure}
@ -826,12 +826,11 @@ $p|V_j: V_j \rightarrow U$ Homöomorphismus.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Mitschrieb vom 19.12.2013 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{bemerkung}%Vorlesung: Folgerung 12.12
\todo{Hier stimmt was mit den Tilden nicht}
Sind $p:X \rightarrow X$ und $y: \tilde{Y} \rightarrow X$
\begin{folgerung}%Vorlesung: Folgerung 12.12
Sind $p:\tilde{X} \rightarrow X$ und $q: \tilde{Y} \rightarrow X$
universelle Überlagerungen, so sind $\tilde{X}$ und $\tilde{Y}$
homöomorph.
\end{bemerkung}
\end{folgerung}
\begin{beweis}
Seien $x_0 \in X, \tilde{x_0} \in \tilde{X}$ mit
@ -848,8 +847,8 @@ $p|V_j: V_j \rightarrow U$ Homöomorphismus.
$p:\tilde{X} \rightarrow X$ mit $(g \circ f) (\tilde{x_0}) = \tilde{x_0}$.
Da auch $\id_{\tilde{x}}$ diese Eigenschaft hat, folgt mit
\cref{kor:12.4}: $g \circ f = \id_{\tilde{X}}$.
Analog $f \circ g = \id_{\tilde{Y}}$. $\qed$
\cref{kor:12.4}: $g \circ f = \id_{\tilde{X}}$.\\
Analog gilt $f \circ g = \id_{\tilde{Y}}$. $\qed$
\end{beweis}
Die Frage, wann es eine universelle Überlagerung gibt, beantwortet

14
documents/GeoTopo/Kapitel4.tex
View file

@ -600,8 +600,7 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}.
\end{beweis}
\section{Weitere Eigenschaften einer euklidischen Ebene}
\subsection{Strahlensatz}
\begin{satz}
\begin{satz}[Strahlensatz]
In ähnlichen Dreiecken sind Verhältnisse entsprechender Seiten gleich.
\end{satz}
@ -612,9 +611,8 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}.
\label{fig:bild-2}
\end{figure}
\begin{beweis}
TODO
\end{beweis}
Der Beweis wird hier nicht geführt. Für Beweisvorschläge wäre ich
dankbar.
\begin{figure}[htp]
\centering
@ -632,11 +630,11 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}.
\begin{figure}[ht]
\centering
\subfloat[TODO]{
\subfloat[Zwei kongruente Dreiecke]{
\input{figures/rectangle-2.1.tex}
\label{fig:bild-4}
}%
\subfloat[TODO]{
\subfloat[Zwei weitere kongruente Dreiecke]{
\input{figures/rectangle-2.2.tex}
\label{fig:bild-5}
}%
@ -648,7 +646,7 @@ Der Flächeninhalt eines Dreiecks ist $\nicefrac{1}{2} \cdot \text{Grundseite} \
\begin{figure}[htp]
\centering
\input{figures/todo.tex}
\input{figures/triangle-4.tex}
\caption{Flächenberechnung im Dreiecks}
\label{fig:flaechenberechnung-dreieck}
\end{figure}

8
documents/GeoTopo/figures/topology-paths.tex Normal file
View file

@ -0,0 +1,8 @@
\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,->, thick, red] (a) .. controls (0.5,2) .. (2,1) .. controls (2,0.5) .. (a);
\draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b);
\node at (1,1.2) [red] {$\gamma$};
\end{tikzpicture}

25
documents/GeoTopo/figures/triangle-4.tex Normal file
View file

@ -0,0 +1,25 @@
\begin{tikzpicture}
\tkzSetUpPoint[shape=circle,size=10,color=black,fill=black]
\tkzSetUpLine[line width=1]
\tkzDefPoints{0/0/A, 4/0/B, -2/3/C}
\tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper}
\tkzInterLL(B,C)(A,helper) \tkzGetPoint{La}
\tkzMarkAngle[arc=l,size=0.4cm,color=red,fill=red!20](A,La,B)
\tkzLabelAngle[pos=0.25](A,La,B){$\cdot$}
\tkzDrawPolygon(A,B,C)
\node at ($(A)+(-0.47,-0.2)$){$A$};
\node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough
\node at ($(C)+(0.05,0.3)$) {$C$};
\node[green] at ($(La)+(-0.4,-0.1)$) {$L_A$};
\tkzDrawSegments[red](A,La)
\tkzDrawSegments[blue](B,C)
\tkzLabelSegment[right,red](A,La){$h_a$}
\tkzLabelSegment[above,blue](B,C){$c$}
\tkzDrawPoints(A,B,C)
\tkzDrawPoints[color=green,fill=green](La)
\end{tikzpicture}

31
tikz/topology-paths/Makefile Normal file
View file

@ -0,0 +1,31 @@
SOURCE = topology-paths
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

3
tikz/topology-paths/Readme.md Normal file
View file

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

BIN
tikz/topology-paths/topology-paths.png Normal file
View file

Binary file not shown.
Side by side

After

Width:  |  Height:  |  Size: 15 KiB

15
tikz/topology-paths/topology-paths.tex Normal file
View file

@ -0,0 +1,15 @@
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{pgfplots}
\usepackage{tikz}
\begin{document}
\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,->, thick, red] (a) .. controls (0.5,2) .. (2,1) .. controls (2,0.5) .. (a);
\draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b);
\node at (1,1.2) [red] {$\gamma$};
\end{tikzpicture}
\end{document}

31
tikz/triangle-4/Makefile Normal file
View file

@ -0,0 +1,31 @@
SOURCE = triangle-4
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

3
tikz/triangle-4/Readme.md Normal file
View file

@ -0,0 +1,3 @@
Compiled example
----------------
![Example](triangle-4.png)

BIN
tikz/triangle-4/triangle-4.png Normal file
View file

Binary file not shown.
Side by side

After

Width:  |  Height:  |  Size: 12 KiB

33
tikz/triangle-4/triangle-4.tex Normal file
View file

@ -0,0 +1,33 @@
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tkz-euclide}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\usetkzobj{all}
\begin{tikzpicture}
\tkzSetUpPoint[shape=circle,size=10,color=black,fill=black]
\tkzSetUpLine[line width=1]
\tkzDefPoints{0/0/A, 4/0/B, -2/3/C}
\tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper}
\tkzInterLL(B,C)(A,helper) \tkzGetPoint{La}
\tkzMarkAngle[arc=l,size=0.4cm,color=red,fill=red!20](A,La,B)
\tkzLabelAngle[pos=0.25](A,La,B){$\cdot$}
\tkzDrawPolygon(A,B,C)
\node at ($(A)+(-0.47,-0.2)$){$A$};
\node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough
\node at ($(C)+(0.05,0.3)$) {$C$};
\node[green] at ($(La)+(-0.4,-0.1)$) {$L_A$};
\tkzDrawSegments[red](A,La)
\tkzDrawSegments[blue](B,C)
\tkzLabelSegment[right,red](A,La){$h_a$}
\tkzLabelSegment[above,blue](B,C){$c$}
\tkzDrawPoints(A,B,C)
\tkzDrawPoints[color=green,fill=green](La)
\end{tikzpicture}
\end{document}