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File:Directed medial graph example.svg

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Summary

Description
English: Example of a plane graph (in blue) and its directed medial graph (in red).
Date
Source 
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds,positioning}

\begin{document}
 \def\nodeDist{2.5cm}
 \def\arrowType{triangle 60}
 \def\fillColor{black!20}
 \def\position{0.6}
 \tikzstyle{origVertex}      = [draw, blue, fill, shape=circle]
 \tikzstyle{newVertex}       = [draw, red , fill, shape=circle]
 \tikzstyle{invisibleVertex} = [shape=circle]
 \tikzstyle{origEdge}      = [blue]
 \tikzstyle{newEdge}       = [red, densely dashed]
 \tikzstyle{invisibleEdge} = [draw opacity=0]
 
 \begin{tikzpicture}[node distance=\nodeDist,>=\arrowType,semithick]
  \node[origVertex] (0)              {};
  \node[origVertex] (1) [right of=0] {};
  \node[origVertex] (2) [below of=1] {};
  \node[origVertex] (3) [left  of=2] {};
  \path (0) edge[origEdge] node[invisibleVertex] (m0) {} (1)
        (1) edge[origEdge] node[invisibleVertex] (m1) {} (2)
        (2) edge[origEdge] node[invisibleVertex] (m2) {} (3)
        (3) edge[origEdge] node[invisibleVertex] (m3) {} (0);
  \path (m0) edge[invisibleEdge]                                                                                       (m1)
             edge[invisibleEdge, out=  45, in=  45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e0) {} (m1)
        (m1) edge[invisibleEdge]                                                                                       (m2)
             edge[invisibleEdge, out= -45, in= -45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e1) {} (m2)
        (m2) edge[invisibleEdge]                                                                                       (m3)
             edge[invisibleEdge, out=-135, in=-135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e2) {} (m3)
        (m3) edge[invisibleEdge]                                                                                       (m0)
             edge[invisibleEdge, out= 135, in= 135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e3) {} (m0);
   \node[invisibleVertex, below=0cm of e0] {};
   \node[invisibleVertex, left =0cm of e1] {};
   \node[invisibleVertex, above=0cm of e2] {};
   \node[invisibleVertex, right=0cm of e3] {};
 \end{tikzpicture}
 \qquad
 \begin{tikzpicture}[node distance=\nodeDist,>=\arrowType,semithick]
  \node[origVertex] (0)              {};
  \node[origVertex] (1) [right of=0] {};
  \node[origVertex] (2) [below of=1] {};
  \node[origVertex] (3) [left  of=2] {};
  \path (0) edge[origEdge] node[newVertex] (m0) {} (1)
        (1) edge[origEdge] node[newVertex] (m1) {} (2)
        (2) edge[origEdge] node[newVertex] (m2) {} (3)
        (3) edge[origEdge] node[newVertex] (m3) {} (0);
  \path (m0) edge[->, newEdge]                                                                                       (m1)
             edge[<-, newEdge, out=  45, in=  45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e0) {} (m1)
        (m1) edge[->, newEdge]                                                                                       (m2)
             edge[<-, newEdge, out= -45, in= -45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e1) {} (m2)
        (m2) edge[->, newEdge]                                                                                       (m3)
             edge[<-, newEdge, out=-135, in=-135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e2) {} (m3)
        (m3) edge[->, newEdge]                                                                                       (m0)
             edge[<-, newEdge, out= 135, in= 135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e3) {} (m0);
   \node[invisibleVertex, below=0cm of e0] {};
   \node[invisibleVertex, left =0cm of e1] {};
   \node[invisibleVertex, above=0cm of e2] {};
   \node[invisibleVertex, right=0cm of e3] {};
  \begin{scope}[on background layer, overlay]
   \fill[fill=\fillColor] (m0.  45) to [out=  45, in=  45, looseness=3] (m1.  45) to (m1.center) to (m0.center) to (m0.  45);
   \fill[fill=\fillColor] (m1. -45) to [out= -45, in= -45, looseness=3] (m2. -45) to (m2.center) to (m1.center) to (m1. -45);
   \fill[fill=\fillColor] (m2.-135) to [out=-135, in=-135, looseness=3] (m3.-135) to (m3.center) to (m2.center) to (m2.-135);
   \fill[fill=\fillColor] (m3. 135) to [out= 135, in= 135, looseness=3] (m0. 135) to (m0.center) to (m3.center) to (m3. 135);
  \end{scope}
 \end{tikzpicture}
 \qquad
 \begin{tikzpicture}[node distance=\nodeDist,>=\arrowType,semithick]
  \node[invisibleVertex] (0)              {};
  \node[invisibleVertex] (1) [right of=0] {};
  \node[invisibleVertex] (2) [below of=1] {};
  \node[invisibleVertex] (3) [left  of=2] {};
  \path (0) edge[invisibleEdge] node[draw opacity=100, newVertex] (m0) {} (1)
        (1) edge[invisibleEdge] node[draw opacity=100, newVertex] (m1) {} (2)
        (2) edge[invisibleEdge] node[draw opacity=100, newVertex] (m2) {} (3)
        (3) edge[invisibleEdge] node[draw opacity=100, newVertex] (m3) {} (0);
  \path (m0) edge[->, newEdge]                                                                                       (m1)
             edge[<-, newEdge, out=  45, in=  45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e0) {} (m1)
        (m1) edge[->, newEdge]                                                                                       (m2)
             edge[<-, newEdge, out= -45, in= -45, looseness=3, overlay] node[invisibleVertex, pos=\position] (e1) {} (m2)
        (m2) edge[->, newEdge]                                                                                       (m3)
             edge[<-, newEdge, out=-135, in=-135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e2) {} (m3)
        (m3) edge[->, newEdge]                                                                                       (m0)
             edge[<-, newEdge, out= 135, in= 135, looseness=3, overlay] node[invisibleVertex, pos=\position] (e3) {} (m0);
   \node[invisibleVertex, below=0cm of e0] {};
   \node[invisibleVertex, left =0cm of e1] {};
   \node[invisibleVertex, above=0cm of e2] {};
   \node[invisibleVertex, right=0cm of e3] {};
  \begin{scope}[on background layer, overlay]
   \fill[fill=\fillColor] (m0.  45) to [out=  45, in=  45, looseness=3] (m1.  45) to (m1.center) to (m0.center) to (m0.  45);
   \fill[fill=\fillColor] (m1. -45) to [out= -45, in= -45, looseness=3] (m2. -45) to (m2.center) to (m1.center) to (m1. -45);
   \fill[fill=\fillColor] (m2.-135) to [out=-135, in=-135, looseness=3] (m3.-135) to (m3.center) to (m2.center) to (m2.-135);
   \fill[fill=\fillColor] (m3. 135) to [out= 135, in= 135, looseness=3] (m0. 135) to (m0.center) to (m3.center) to (m3. 135);
  \end{scope}
 \end{tikzpicture}
\end{document}
Author Self

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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inception

26 March 2013

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Date/TimeThumbnailDimensionsUserComment
current19:03, 26 March 2013Thumbnail for version as of 19:03, 26 March 2013510 × 146 (30 KB)Bender2k14Edits to remove white space
16:06, 26 March 2013Thumbnail for version as of 16:06, 26 March 2013598 × 203 (30 KB)Bender2k14{{Information |Description ={{en|1=Example of a plane graph (in blue) and its directed medial graph (in red).}} |Source =<source lang="latex"> \documentclass{article} \thispagestyle{empty} \usepackage{fullpage} \usepackage{tikz} \usetikzlibr...

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