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31
tikz/neighbourhood-topology-open/Makefile Normal file
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SOURCE = neighbourhood-topology-open
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/neighbourhood-topology-open/Readme.md Normal file
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Compiled example
----------------
![Example](neighbourhood-topology-open.png)

75
tikz/neighbourhood-topology-open/neighbourhood-topology-open.tex Normal file
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\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=middle,
axis y line=middle,
%width=9cm,
%height=4.5cm,
xmin=-1, % start the diagram at this x-coordinate
xmax= 5, % 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
xlabel=$Y$,
ylabel=$X$,
ticks=none,
enlargelimits=true,
after end axis/.code={
\draw [decorate,decoration={brace,mirror,raise=15pt}, orange] (axis cs:0,3.6) -- (axis cs:0,2.5) node [midway,left=20pt,orange] {$V_{x,y}$};
\draw [decorate,decoration={brace,mirror,raise=12pt}, green] (axis cs:1.5,0) -- (axis cs:2.5,0) node [midway,below=16pt,green] {$U_{x,y}$};
}]
\addplot[mark=none, red, smooth cycle, thick, fill=red!30] coordinates {(1,1) (2,0.5) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.9, 2.5)};
\node[red] at (axis cs:4,4) [anchor=south] {$W_i$};
% Draw help lines
%\addplot[dashed] coordinates {(1.5,0) (1.5,3.6)};
%\addplot[dashed] coordinates {(2.5,0) (2.5,3.6)};
%\addplot[dashed] coordinates {(0,2.5) (2.5,2.5)};
%\addplot[dashed] coordinates {(0,3.6) (2.5,3.6)};
% Draw solid square
\addplot[mark=none, orange, thick] coordinates {(2.5,2.5) (2.5,3.6)};
\addplot[mark=none, green, thick] coordinates {(2.5,3.6) (1.5,3.6)};
\addplot[mark=none, orange, thick] coordinates {(1.5,3.6) (1.5,2.5)};
\addplot[mark=none, green, thick] coordinates {(1.5,2.5) (2.5,2.5)};
\addplot[mark=none, orange, thick] coordinates {(3.0,1.5) (3.0,2.6)};
\addplot[mark=none, green, thick] coordinates {(3.0,2.6) (1.1,2.6)};
\addplot[mark=none, orange, thick] coordinates {(1.1,1.5) (1.1,2.6)};
\addplot[mark=none, green, thick] coordinates {(1.1,1.5) (3.0,1.5)};
\addplot[mark=none, orange, thick] coordinates {(3.0,1.5) (3.0,2.6)};
\addplot[mark=none, green, thick] coordinates {(3.0,2.6) (1.1,2.6)};
\addplot[mark=none, orange, thick] coordinates {(1.1,1.5) (1.1,2.6)};
\addplot[mark=none, green, thick] coordinates {(1.1,1.5) (3.0,1.5)};
\addplot[mark=none, blue, thick, dashed] coordinates {((1.8,0) (1.8,5)};
\addplot[mark=none, blue, thick, dashed] coordinates {((2.2,0) (2.2,5)};
% Draw x and annotation
\node at (axis cs:2,3) [anchor=-90] {$x$};
\addplot[mark=*] coordinates {(2,3)};
% Draw ticks of help lines
\addplot[mark=none, green, thick] coordinates {(1.5, -0.1) (1.5,0.1)};
\addplot[mark=none, green, thick] coordinates {(2.5, -0.1) (2.5,0.1)};
\addplot[mark=none, green, thick] coordinates {(1.5, 0) (2.5,0)};
\addplot[mark=none, orange, thick] coordinates {(-0.1, 2.5) (0.1,2.5)};
\addplot[mark=none, orange, thick] coordinates {(-0.1, 3.6) (0.1,3.6)};
\addplot[mark=none, orange, thick] coordinates {(0, 2.5) (0,3.6)};
% Draw axis text
\node at (axis cs:0,3) [anchor=east] {$y$};
\node at (axis cs:2,0) [anchor=north] {$x$};
\end{axis}
\end{tikzpicture}
\end{document}

31
tikz/topology-1/Makefile Normal file
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SOURCE = topology-1
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-1/Readme.md Normal file
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Compiled example
----------------
![Example](topology-1.png)

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41
tikz/topology-1/topology-1.tex Normal file
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\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=none,
axis y line=none,
%width=9cm,
%height=4.5cm,
xmin= 0, % start the diagram at this x-coordinate
xmax= 5, % end the diagram at this x-coordinate
ymin= 0, % start the diagram at this y-coordinate
ymax= 5, % end the diagram at this y-coordinate
xlabel=$Y$,
ylabel=$X$,
ticks=none,
enlargelimits=true]
\addplot[mark=none, red, smooth cycle, thick, fill=red!30] coordinates {(0,0) (2,0.2) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.2, 2.5)};
\node[red] at (axis cs:4,4) [anchor=south] {$X_i$};
% Draw solid square
\addplot[mark=none, thick] coordinates {(1.5,2.0) (2.5,2.0) (2.5,3.6) (1.5,3.6) (1.5,2.0)};
\node at (axis cs:2.7,3.2) [anchor=90] {$K$};
% Draw x and annotation
\node at (axis cs:1.8,3.2) [anchor=-90] {$x$};
\draw (axis cs:1.8,3.2) circle[radius=0.6];
\addplot[mark=*] coordinates {(1.8,3.2)};
\node at (axis cs:0.8,1.2) [anchor=-90] {$y$};
\draw (axis cs:0.8,1.2) circle[radius=0.6];
\addplot[mark=*] coordinates {(0.8,1.2)};
\end{axis}
\end{tikzpicture}
\end{document}