二维黎曼流形的Voronoi图生成算法

Algorithm for Creating Voronoi Diagrams for Two-Dimensional Riemannian Manifolds

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.

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.