Data structures and algorithms for topological analysis
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | Data structures and algorithms for topological analysis |
| Type de publication | Conference Paper |
| Year of Publication | 2014 |
| Auteurs | Cane J-M, Tzoumas GM, Michelucci D, Hidalgo M, Foufou S |
| Conference Name | 2014 SCIENCE AND INFORMATION CONFERENCE (SAI) |
| Publisher | Microsoft; RK Trans2Cloud; Springer; IEEE Comp Soc, UKRI Sect; IEEE Computat Intelligence Soc, UKRI Sect; IEEE |
| Conference Location | 345 E 47TH ST, NEW YORK, NY 10017 USA |
| ISBN Number | 978-0-9893193-1-7 |
| Mots-clés | Betti numbers, CIA and HIA algorithms, Euler characteristic, Homology, Homotopy, Morse-Smale complex, Topology |
| Résumé | 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. |