一种基于图的平面点集Delaunay三角剖分算法

马小虎; 董军; 潘志庚; 石教英

doi:10.11834/jig.19970115

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一种基于图的平面点集Delaunay三角剖分算法
A Graph-Based Algorithm for Generating theDelaunay Triangulation of a Planar Point Set
1997年2卷第1期页码：7
纸质出版：1997
DOI： 10.11834/jig.19970115
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马小虎, 董军, 潘志庚, 石教英. 一种基于图的平面点集Delaunay三角剖分算法[J]. 中国图象图形学报, 1997,2(1):7. DOI： 10.11834/jig.19970115.

A Graph-Based Algorithm for Generating theDelaunay Triangulation of a Planar Point Set[J]. Journal of Image and Graphics, 1997, 2(1): 7. DOI： 10.11834/jig.19970115.

摘要

本文提出了一种基于图的平面点集Delaunay三角剖分算法。该算法首先求出平面点集的欧几里得最小生成树，然后逐次加入一边构造三角形网格，最后按最小内角最大的三角化准则，通过局部变换，得到平面点集的Delaunay三角剖分。本文同时阐述了它的对偶图；平面点集的Voronoi图的概念和性质。

Abstract

A graph-based algorithm for generating the Delaunay triangulation of aplanar point set is presented in this paper. The first step is to calculate the Euclidean Minimum Spanning Tree (EM ST) of the given points. The EM ST is then augumented to triangle mesh. Finally the Delaunay Triangulation of the given points is obtained by local tranformation acording to Max-M in angle criteria. The concepts and properties of Vorono i diagram of a planar point set are slso discussed in the paper.