Data structures and algorithms for topological analysis

被引：0

作者：

Cane, Jean-Marc ^{[1
]}

Tzoumas, George M. ^{[1
]}

Michelucci, Dominique ^{[1
]}

Hidalgo, Marta ^{[2
]}

Foufou, Sebti ^{[3
]}

机构：

[1] Univ Burgundy, Le2i, Dijon, France

[2] Univ Politcn Catalunya, Grp Informt Engn, Barcelona, Spain

[3] Qatar Univ, Comp Sci, Doha, Qatar

来源：

2014 SCIENCE AND INFORMATION CONFERENCE (SAI) | 2014年

关键词：

Topology; Homotopy; Homology; Betti numbers; Euler characteristic; Morse-Smale complex; CIA and HIA algorithms; COMPUTATION; SET;

D O I：

暂无

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

One of the steps of geometric modeling is to know the topology and/or the geometry of the objects considered. This paper presents different data structures and algorithms used in this study. We are particularly interested by algebraic structures, eg homotopy and homology groups, the Betti numbers, the Euler characteristic, or the Morse-Smale complex. We have to be able to compute these data structures, and for (homotopy and homology) groups, we also want to compute their generators. We are also interested in algorithms CIA and HIA presented in the thesis of Nicolas DELANOUE, which respectively compute the connected components and the homotopy type of a set defined by a CSG (constructive solid geometry) tree. We would like to generalize these algorithms to sets defined by projection.

引用

页码：302 / 312

页数：11

共 20 条

[1]

Audin M., 2010, THEORIE MORSE HOMOLO

[2]

Boissonnat Jean-Daniel, 2006, Effective computational geometry for curves and surfaces

[3] An iterative algorithm for homology computation on simplicial shapes [J].