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DOI:
Journal of Software:2009.20(9):2407-2416

二维黎曼流形的Voronoi图生成算法
程丹,杨钦,李吉刚,蔡强
(北京航空航天大学 计算机学院,北京 100191;北京工商大学 计算机学院,北京 100048)
Algorithm for Creating Voronoi Diagrams for Two-Dimensional Riemannian Manifolds
HENG Dan,YANG Qin,LI Ji-Gang,CAI Qiang
()
Abstract
Chart / table
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Received:March 01, 2008    Revised:January 04, 2009
> 中文摘要: 提出采用黎曼流形描述研究对象和基于坐标卡生成Voronoi图的算法思路.讨论了黎曼流形上研究Voronoi图的难点,并给出了存在定理,该定理说明了坐标卡上Voronoi图的存在条件.按照算法思路和存在定理,详细描述了二维黎曼流形上创建坐标卡的算法,并给出流形上转换函数和混合函数的定义方法.最后描述了基于坐标卡生成Voronoi图的算法,并给出了具体实例.
Abstract:This paper describes objects by Riemannian manifolds and creates Voronoi diagrams based on charts. Difficulties in studying Voronoi diagrams for Riemannian manifolds are discussed. A theorem in existence is given, which demonstrates the present condition of Voronoi diagrams for Riemannian manifolds in a chart. According to the idea and theorem, this paper describes the algorithm of creating charts for two-dimensional Riemannian manifolds and presents the definitions of transition and blend functions. Finally, the algorithm of creating Voronoi diagrams based on charts is given, and some examples are provided.
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基金项目:Supported by the Beijing Municipal Natural Science Foundation of China under Grant No.4062010 (北京市自然科学基金) Supported by the Beijing Municipal Natural Science Foundation of China under Grant No.4062010 (北京市自然科学基金)
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程丹,杨钦,李吉刚,蔡强.二维黎曼流形的Voronoi图生成算法.软件学报,2009,20(9):2407-2416

HENG Dan,YANG Qin,LI Ji-Gang,CAI Qiang.Algorithm for Creating Voronoi Diagrams for Two-Dimensional Riemannian Manifolds.Journal of Software,2009,20(9):2407-2416