diff --git a/documents/GeoTopo/Arbeitszeit.txt b/documents/GeoTopo/Arbeitszeit.txt index 29bc717..1cae279 100644 --- a/documents/GeoTopo/Arbeitszeit.txt +++ b/documents/GeoTopo/Arbeitszeit.txt @@ -3,4 +3,4 @@ in dem erstellen dieses Skripts steckt Datum | Uhrzeit --------------------------------------------------------------------- -03.12.2013 | 11:00 - 12:00 +03.12.2013 | 11:00 - 12:00, 13:10 - 15:00 diff --git a/documents/GeoTopo/GeoTopo.pdf b/documents/GeoTopo/GeoTopo.pdf index aee9017..9e36335 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 80423ec..e20501f 100644 --- a/documents/GeoTopo/Kapitel2.tex +++ b/documents/GeoTopo/Kapitel2.tex @@ -867,7 +867,9 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. \end{korollar} \begin{beispiel} - \input{figures/topology-oriented-triangle.tex} + \begin{figure}[h!] + \input{figures/topology-oriented-triangle.tex} + \end{figure} $a < b < c$ @@ -907,17 +909,19 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. \end{enumerate} \end{definition} +\begin{minipage}{\textwidth}%don't break this theorem! \begin{satz} Für jeden endlichen Simplizialkomplex $K$ der Dimension $d$ gilt: \[\sum_{k=0}^d (-1)^k b_k (K) = \sum_{k=0}^d (-1)^k a_k(K) = \chi(K) \] \end{satz} +\end{minipage} \begin{bemerkung} Es gilt \underline{nicht} $a_k = b_k\;\forall k \in \mdn_0$. \end{bemerkung} -\begin{beweis} +\begin{beweis}\leavevmode \begin{itemize} \item Dimensionsformel für $d_n$: $a_n = \dim Z_n + \dim B_{n-1}$ für $n \geq 1$ \item Dimensionsformel für $Z_n \rightarrow H_n = Z_n / B_n: \dim Z_n = b_n + \dim B_n$ diff --git a/documents/GeoTopo/Kapitel3.tex b/documents/GeoTopo/Kapitel3.tex index 0af9fc1..1dac904 100644 --- a/documents/GeoTopo/Kapitel3.tex +++ b/documents/GeoTopo/Kapitel3.tex @@ -3,6 +3,21 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Fundamentalgruppe und Überlagerungen} \section{Homotopie von Wegen} +\begin{figure}[ht] + \centering + \subfloat[$\gamma_1$ und $\gamma_2$ sind homotop, da man sie + \enquote{zueinander verschieben} kann.]{ + \input{figures/topology-homotop-paths.tex} + \label{fig:homotope-wege-anschaulich} + }\hspace{1em}% + \subfloat[$\gamma_1$ und $\gamma_2$ sind wegen dem Hindernis nicht homotop.]{ + \input{figures/topology-non-homotop-paths.tex} + \label{fig:nicht-homotope-wege-anschaulich} + } + \label{Formen} + \caption{Beispiele für Wege $\gamma_1$ und $\gamma_2$} +\end{figure} + \begin{definition} Sei $X$ ein topologischer Raum, $a, b \in X$, $\gamma_1, \gamma_2: [0,1] \rightarrow X$ Wege von $a$ nach $b$, @@ -26,7 +41,7 @@ Wege in $X$ von $a$ nach $b$. \end{korollar} -\begin{beweis} +\begin{beweis}\leavevmode \begin{itemize} \item reflexiv: $H(t,s) = \gamma(t)$ für alle $t,s \in I \times I$ \item symmetrisch: $H'(t,s) = H(t,1-s)$ für alle $t,s \in I \times I$ @@ -34,8 +49,8 @@ nach $\gamma_2$ bzw. von $\gamma_2$ nach $\gamma_3$. Dann sei $H(t,s) := \begin{cases} - H'(t, 2s) &\text{, falls } 0 \leq s \leq \frac{1}{2}\\ - H''(t, 2s-1) &\text{, falls } \frac{1}{2} \leq s \leq 1\end{cases}$ + H'(t, 2s) &\text{falls } 0 \leq s \leq \frac{1}{2}\\ + H''(t, 2s-1) &\text{falls } \frac{1}{2} \leq s \leq 1\end{cases}$ $\Rightarrow$ $H$ ist stetig und Homotopie von $\gamma_1$ nach $\gamma_2$ @@ -43,7 +58,46 @@ $\qed$ \end{beweis} -\todo[inline]{Noch ca. eine halbe seite mit 3 Beispielen} +\begin{beispiel} + \begin{enumerate}[label=\arabic*)] + \item Sei $X = S^1$. $\gamma_1$ und $\gamma_2$ aus + Abb.~\ref{fig:circle-two-paths} nicht homöotop. + \begin{figure} + \centering + \input{figures/topology-circle-two-paths.tex} + \caption{Kreis mit zwei Wegen} + \label{fig:circle-two-paths} + \end{figure} + \item Sei $X = T^2$. $\gamma_1, \gamma_2$ und $\gamma_3$ + aus Abb.~\ref{fig:torus-three-paths} sind paarweise + nicht homöotop. + \begin{figure} + \centering + \input{figures/todo.tex} + \caption{Torus mit drei Wegen} + \label{fig:torus-three-paths} + \end{figure} + \item Sei $X = \mdr^2$ und $a=b=(0,0)$. + + Je zwei Wege im $\mdr^2$ mit Anfangs- und Enpunkt $(0,0)$ + sind homöotop. + + \begin{figure} + \centering + \input{figures/topology-paths-in-r2.tex} + \caption{Zwei Wege im $\mdr^2$ mit Anfangs- und Enpunkt $(0,0)$} + \label{fig:torus-three-paths} + \end{figure} + + Sei $\gamma_0: I \rightarrow \mdr^2$ der konstante Weg + $\gamma_0(t) = 0 \; \forall t \in I$. Sei + $\gamma(0) = \gamma(1) = 0$. + + $H(t,s) := (1-s) \gamma(t)$ ist stetig, + $H(t,0) = \gamma(t)\; \forall t \in I$ und + $H(t,1) = 0 \; \forall t \in I$ + \end{enumerate} +\end{beispiel} % Die Übungsaufgaben sollen ganz am Ende des Kapitels sein. \input{Kapitel3-UB} diff --git a/documents/GeoTopo/figures/topology-circle-two-paths.tex b/documents/GeoTopo/figures/topology-circle-two-paths.tex new file mode 100644 index 0000000..927d1f8 --- /dev/null +++ b/documents/GeoTopo/figures/topology-circle-two-paths.tex @@ -0,0 +1,10 @@ +\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} diff --git a/documents/GeoTopo/figures/topology-homotop-paths.tex b/documents/GeoTopo/figures/topology-homotop-paths.tex new file mode 100644 index 0000000..93c70fd --- /dev/null +++ b/documents/GeoTopo/figures/topology-homotop-paths.tex @@ -0,0 +1,16 @@ +\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} diff --git a/documents/GeoTopo/figures/topology-non-homotop-paths.tex b/documents/GeoTopo/figures/topology-non-homotop-paths.tex new file mode 100644 index 0000000..12a8a99 --- /dev/null +++ b/documents/GeoTopo/figures/topology-non-homotop-paths.tex @@ -0,0 +1,10 @@ +\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} diff --git a/documents/GeoTopo/figures/topology-paths-in-r2.tex b/documents/GeoTopo/figures/topology-paths-in-r2.tex new file mode 100644 index 0000000..6534e97 --- /dev/null +++ b/documents/GeoTopo/figures/topology-paths-in-r2.tex @@ -0,0 +1,27 @@ +\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} diff --git a/tikz/topology-circle-two-paths/Makefile b/tikz/topology-circle-two-paths/Makefile new file mode 100644 index 0000000..ae7fade --- /dev/null +++ b/tikz/topology-circle-two-paths/Makefile @@ -0,0 +1,31 @@ +SOURCE = topology-circle-two-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 diff --git a/tikz/topology-circle-two-paths/Readme.md b/tikz/topology-circle-two-paths/Readme.md new file mode 100644 index 0000000..1bab764 --- /dev/null +++ b/tikz/topology-circle-two-paths/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](topology-circle-two-paths.png) diff --git a/tikz/topology-circle-two-paths/topology-circle-two-paths.png b/tikz/topology-circle-two-paths/topology-circle-two-paths.png new file mode 100644 index 0000000..671ad7c Binary files /dev/null and b/tikz/topology-circle-two-paths/topology-circle-two-paths.png differ diff --git a/tikz/topology-circle-two-paths/topology-circle-two-paths.tex b/tikz/topology-circle-two-paths/topology-circle-two-paths.tex new file mode 100644 index 0000000..fa9061b --- /dev/null +++ b/tikz/topology-circle-two-paths/topology-circle-two-paths.tex @@ -0,0 +1,18 @@ +\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] + \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} +\end{document} diff --git a/tikz/topology-homotop-paths/Makefile b/tikz/topology-homotop-paths/Makefile new file mode 100644 index 0000000..7cd4c43 --- /dev/null +++ b/tikz/topology-homotop-paths/Makefile @@ -0,0 +1,31 @@ +SOURCE = topology-homotop-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 diff --git a/tikz/topology-homotop-paths/Readme.md b/tikz/topology-homotop-paths/Readme.md new file mode 100644 index 0000000..ab49332 --- /dev/null +++ b/tikz/topology-homotop-paths/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](topology-homotop-paths.png) diff --git a/tikz/topology-homotop-paths/topology-homotop-paths.png b/tikz/topology-homotop-paths/topology-homotop-paths.png new file mode 100644 index 0000000..f3532c2 Binary files /dev/null and b/tikz/topology-homotop-paths/topology-homotop-paths.png differ diff --git a/tikz/topology-homotop-paths/topology-homotop-paths.tex b/tikz/topology-homotop-paths/topology-homotop-paths.tex new file mode 100644 index 0000000..5cde660 --- /dev/null +++ b/tikz/topology-homotop-paths/topology-homotop-paths.tex @@ -0,0 +1,23 @@ +\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] (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} +\end{document} diff --git a/tikz/topology-non-homotop-paths/Makefile b/tikz/topology-non-homotop-paths/Makefile new file mode 100644 index 0000000..ee369dc --- /dev/null +++ b/tikz/topology-non-homotop-paths/Makefile @@ -0,0 +1,31 @@ +SOURCE = topology-non-homotop-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 diff --git a/tikz/topology-non-homotop-paths/Readme.md b/tikz/topology-non-homotop-paths/Readme.md new file mode 100644 index 0000000..8efd5d4 --- /dev/null +++ b/tikz/topology-non-homotop-paths/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](topology-non-homotop-paths.png) diff --git a/tikz/topology-non-homotop-paths/topology-non-homotop-paths.png b/tikz/topology-non-homotop-paths/topology-non-homotop-paths.png new file mode 100644 index 0000000..f3c84c2 Binary files /dev/null and b/tikz/topology-non-homotop-paths/topology-non-homotop-paths.png differ diff --git a/tikz/topology-non-homotop-paths/topology-non-homotop-paths.tex b/tikz/topology-non-homotop-paths/topology-non-homotop-paths.tex new file mode 100644 index 0000000..320bb3f --- /dev/null +++ b/tikz/topology-non-homotop-paths/topology-non-homotop-paths.tex @@ -0,0 +1,18 @@ +\documentclass[varwidth=true, border=2pt]{standalone} + +\usepackage{pgfplots} +\usepackage{tikz} +\usetikzlibrary{patterns} + +\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[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} +\end{document} diff --git a/tikz/topology-paths-in-r2/Makefile b/tikz/topology-paths-in-r2/Makefile new file mode 100644 index 0000000..2e25c4c --- /dev/null +++ b/tikz/topology-paths-in-r2/Makefile @@ -0,0 +1,31 @@ +SOURCE = topology-paths-in-r2 +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 diff --git a/tikz/topology-paths-in-r2/Readme.md b/tikz/topology-paths-in-r2/Readme.md new file mode 100644 index 0000000..f8e70f5 --- /dev/null +++ b/tikz/topology-paths-in-r2/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](topology-paths-in-r2.png) diff --git a/tikz/topology-paths-in-r2/topology-paths-in-r2.png b/tikz/topology-paths-in-r2/topology-paths-in-r2.png new file mode 100644 index 0000000..ef01119 Binary files /dev/null and b/tikz/topology-paths-in-r2/topology-paths-in-r2.png differ diff --git a/tikz/topology-paths-in-r2/topology-paths-in-r2.tex b/tikz/topology-paths-in-r2/topology-paths-in-r2.tex new file mode 100644 index 0000000..cd514ad --- /dev/null +++ b/tikz/topology-paths-in-r2/topology-paths-in-r2.tex @@ -0,0 +1,34 @@ +\documentclass[varwidth=true, border=2pt]{standalone} + +\usepackage{pgfplots} +\usepackage{tikz} + +\begin{document} +\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} +\end{document}