凸多胞形的保顶单纯剖分  

The Vertex-preserving Simplicial Dissectionof Convex Polytopes

作　　者：王见勇[1] 闫萍[1] 

机构地区：[1]常熟理工学院数学系,江苏常熟215500

出　　处：《数学的实践与认识》2008年第7期158-164,共7页Mathematics in Practice and Theory

基　　金：江苏省教育厅自然科学基金(05KJB110001)

摘　　要：通过引进凸多胞形对其外部一点的阴面、阳面与平射面等概念,借助两个屏蔽引理证明Rn中任何n维凸多胞形都可以剖分为内部互不相交、以原凸多胞形的顶点集的子集为顶点集的有限个n维单纯形之并,克服了相关文献中剖分的不足,为单纯形算法提供了一种比较理想的剖分工具.Via the new concepts of sunny facets, shady facets and flat projective facets of a convex polytope to an outer point and two shield lemmas, it is proved that any n-polytope in R＂ can be dissected into a finite union of n-simplices with the vertices coincide with the original polytope and no pair of small simplices has an interior point in common. This improves the corresponding results of relevant literature, and a new dissection toolfor the simplicial method is supplied.

关 键 词：保顶单纯剖分 阳面 阴面 平射面 屏蔽引理 

分 类 号：O186.1[理学—数学]