File:Medial graph example.svg

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Original file ‎(SVG file, nominally 531 × 224 pixels, file size: 29 KB)

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Description
English: Example of a plane graph (in blue) and its medial graph (in red).
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\documentclass{article}
\thispagestyle{empty}
\usepackage{tikz}

\def\nodeDist{2.5cm}
\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{document}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[origVertex] (0)              {};
 \node[origVertex] (1) [right of=0] {};
 \node[origVertex] (2) [above of=0] {};
 \node[origVertex] (3) [above of=1] {};
 \node[origVertex] (4) [above of=2] {};
 \path (0) edge[origEdge, out=-45, in=-135]               node[invisibleVertex] (m0) {} (1)
           edge[origEdge, out= 45, in= 135]               node[invisibleVertex] (m1) {} (1)
           edge[origEdge]                                 node[invisibleVertex] (m2) {} (2)
       (1) edge[origEdge]                                 node[invisibleVertex] (m3) {} (3)
       (2) edge[origEdge]                                 node[invisibleVertex] (m4) {} (3)
           edge[origEdge]                                 node[invisibleVertex] (m5) {} (4)
       (3) edge[origEdge, out=125, in=  55, looseness=30] node[invisibleVertex] (m6) {} (3);
 \path (m0) edge[invisibleEdge, out= 135, in=-135]                (m1)
            edge[invisibleEdge, out=  45, in= -45]                (m1)
            edge[invisibleEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[invisibleEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[invisibleEdge]                                   (m2)
            edge[invisibleEdge]                                   (m3)
       (m2) edge[invisibleEdge]                                   (m4)
            edge[invisibleEdge, out= 135, in=-135]                (m5)
       (m3) edge[invisibleEdge]                                   (m4)
            edge[invisibleEdge, out=  45, in=  15]                (m6)
       (m4) edge[invisibleEdge]                                   (m5)
            edge[invisibleEdge, out=  90, in= 165]                (m6)
       (m5) edge[invisibleEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[invisibleEdge, out=-125, in= -55, looseness=15]  (m6);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[origVertex] (0)              {};
 \node[origVertex] (1) [right of=0] {};
 \node[origVertex] (2) [above of=0] {};
 \node[origVertex] (3) [above of=1] {};
 \node[origVertex] (4) [above of=2] {};
 \path (0) edge[origEdge, out=-45, in=-135]               node[newVertex] (m0) {} (1)
           edge[origEdge, out= 45, in= 135]               node[newVertex] (m1) {} (1)
           edge[origEdge]                                 node[newVertex] (m2) {} (2)
       (1) edge[origEdge]                                 node[newVertex] (m3) {} (3)
       (2) edge[origEdge]                                 node[newVertex] (m4) {} (3)
           edge[origEdge]                                 node[newVertex] (m5) {} (4)
       (3) edge[origEdge, out=125, in=  55, looseness=30] node[newVertex] (m6) {} (3);
 \path (m0) edge[newEdge, out= 135, in=-135]                (m1)
            edge[newEdge, out=  45, in= -45]                (m1)
            edge[newEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[newEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[newEdge]                                   (m2)
            edge[newEdge]                                   (m3)
       (m2) edge[newEdge]                                   (m4)
            edge[newEdge, out= 135, in=-135]                (m5)
       (m3) edge[newEdge]                                   (m4)
            edge[newEdge, out=  45, in=  15]                (m6)
       (m4) edge[newEdge]                                   (m5)
            edge[newEdge, out=  90, in= 165]                (m6)
       (m5) edge[newEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[newEdge, out=-125, in= -55, looseness=15]  (m6);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[invisibleVertex] (0)              {};
 \node[invisibleVertex] (1) [right of=0] {};
 \node[invisibleVertex] (2) [above of=0] {};
 \node[invisibleVertex] (3) [above of=1] {};
 \node[invisibleVertex] (4) [above of=2] {};
 \path (0) edge[invisibleEdge, out=-45, in=-135]               node[newVertex] (m0) {} (1)
           edge[invisibleEdge, out= 45, in= 135]               node[newVertex] (m1) {} (1)
           edge[invisibleEdge]                                 node[newVertex] (m2) {} (2)
       (1) edge[invisibleEdge]                                 node[newVertex] (m3) {} (3)
       (2) edge[invisibleEdge]                                 node[newVertex] (m4) {} (3)
           edge[invisibleEdge]                                 node[newVertex] (m5) {} (4)
       (3) edge[invisibleEdge, out=125, in=  55, looseness=30] node[newVertex] (m6) {} (3);
 \path (m0) edge[newEdge, out= 135, in=-135]                (m1)
            edge[newEdge, out=  45, in= -45]                (m1)
            edge[newEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[newEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[newEdge]                                   (m2)
            edge[newEdge]                                   (m3)
       (m2) edge[newEdge]                                   (m4)
            edge[newEdge, out= 135, in=-135]                (m5)
       (m3) edge[newEdge]                                   (m4)
            edge[newEdge, out=  45, in=  15]                (m6)
       (m4) edge[newEdge]                                   (m5)
            edge[newEdge, out=  90, in= 165]                (m6)
       (m5) edge[newEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[newEdge, out=-125, in= -55, looseness=15]  (m6);
\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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Date/TimeThumbnailDimensionsUserComment
current19:02, 26 March 2013Thumbnail for version as of 19:02, 26 March 2013531 × 224 (29 KB)Bender2k14 (talk | contribs)Restoring previous version (apparently you can't undo file upload edits)
18:56, 26 March 2013Thumbnail for version as of 18:56, 26 March 2013510 × 146 (30 KB)Bender2k14 (talk | contribs)Edits to remove white space
05:07, 9 December 2012Thumbnail for version as of 05:07, 9 December 2012531 × 224 (29 KB)Bender2k14 (talk | contribs){{Information |Description ={{en|1=Example of a plane graph in blue and its medial graph in red.}} |Source =<source lang="latex"> \documentclass{article} \thispagestyle{empty} \usepackage{tikz} \def\scale{1} \def\nodeDist{2.5cm} \tikzstyle{...

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