Triangulating topological spaces

被引：83

作者：

Edelsbrunner, H

Shah, NR

机构：

[1] UNIV ILLINOIS, DEPT COMP SCI, URBANA, IL 61801 USA

[2] MENTOR GRAPH CORP, SAN JOSE, CA 95131 USA

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS | 1997年 / 7卷 / 04期

关键词：

combinatorial topology; geometric modeling; grid generation; topological spaces; manifolds; coverings; nerves; regular complexes; simplicial complexes; triangulations; Voronoi cells; Delaunay complexes; homotopy equivalence; homeomorphisms;

D O I：

10.1142/S0218195997000223

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Given a subspace X subset of or equal to R-d and a finite set S subset of or equal to R-d, we introduce the Delaunay complex, D-X, restricted by X. Its simplices are spanned by subsets T subset of or equal to S for which the common intersection of Voronoi cells meets X in a non-empty set. By the nerve theorem, boolean OR D-X and X are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for boolean OR D-X and X be homeomorphic.

引用

页码：365 / 378

页数：14

共 24 条

[1]

Bott R., 1982, Graduate Texts in Mathematics

[2] REPRESENTING GEOMETRIC STRUCTURES IN D-DIMENSIONS - TOPOLOGY AND ORDER [J].