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平面图的尖形图

Pointed drawings of planar graphs.

作者信息

Aichholzer Oswin, Rote Günter, Schulz André, Vogtenhuber Birgit

机构信息

Institute for Software Technology, Graz University of Technology, Austria.

出版信息

Comput Geom. 2012 Nov;45(9):482-494. doi: 10.1016/j.comgeo.2010.08.001.

DOI:10.1016/j.comgeo.2010.08.001
PMID:23471372
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC3587405/
Abstract

We study the problem how to draw a planar graph crossing-free such that every vertex is incident to an angle greater than . In general a plane straight-line drawing cannot guarantee this property. We present algorithms which construct such drawings with either tangent-continuous biarcs or quadratic Bézier curves (parabolic arcs), even if the positions of the vertices are predefined by a given plane straight-line drawing of the graph. Moreover, the graph can be drawn with circular arcs if the vertices can be placed arbitrarily. The topic is related to non-crossing drawings of multigraphs and vertex labeling.

摘要

我们研究如何绘制一个无交叉的平面图，使得每个顶点都与一个大于 的角相关联。一般来说，平面直线图无法保证这一性质。我们提出了一些算法，这些算法可以使用切线连续的双圆弧或二次贝塞尔曲线（抛物弧）来构建这样的图，即使顶点的位置由图的给定平面直线图预先定义。此外，如果顶点可以任意放置，那么该图可以用圆弧绘制。该主题与多重图的无交叉图和顶点标记相关。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/4675a6789a95/gr015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/18fdb9df9205/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/06c02147c00e/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/dbb74f0ea222/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/102eecbdb275/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/97c9eab2f558/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/9c5cc8831c05/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/6ecc57146a90/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/f7a1736a2205/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/6691daf333da/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/7fa78317bf2d/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/20de6b79bbac/gr011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/ad03f16b1682/gr012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/8736b18a4c86/gr013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/1569ea8fcdbc/gr014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/4675a6789a95/gr015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/18fdb9df9205/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/06c02147c00e/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/dbb74f0ea222/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/102eecbdb275/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/97c9eab2f558/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/9c5cc8831c05/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/6ecc57146a90/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/f7a1736a2205/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/6691daf333da/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/7fa78317bf2d/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/20de6b79bbac/gr011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/ad03f16b1682/gr012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/8736b18a4c86/gr013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/1569ea8fcdbc/gr014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/10a1/3587405/4675a6789a95/gr015.jpg

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