An iterative algorithm for homology computation on simplicial shapes

Dobrina Boltcheva 1, 2 David Canino 3 Sara Merino Aceituno 1 Jean-Claude Léon 4, 1 Leila De Floriani 3 Franck Hétroy 1, 5
1 EVASION - Virtual environments for animation and image synthesis of natural objects
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 G-SCOP_SIREP - SIREP
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
5 MORPHEO - Capture and Analysis of Shapes in Motion
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We propose a new iterative algorithm for computing the homology of arbitrary shapes discretized through simplicial complexes, We demonstrate how the simplicial homology of a shape can be effectively expressed in terms of the homology of its sub-components. The proposed algorithm retrieves the complete homological information of an input shape including the Betti numbers, the torsion coefficients and the representative homology generators. To the best of our knowledge, this is the first algorithm based on the constructive Mayer-Vietoris sequence, which relates the homology of a topological space to the homologies of its sub-spaces, i.e. the sub-components of the input shape and their intersections. We demonstrate the validity of our approach through a specific shape decomposition, based only on topological properties, which minimizes the size of the intersections between the sub-components and increases the efficiency of the algorithm.
Type de document :
Article dans une revue
Computer-Aided Design, Elsevier, 2011, Solid and Physical Modeling 2011, 43 (11), pp.1457-1467. 〈10.1016/j.cad.2011.08.015〉
Liste complète des métadonnées

Littérature citée [38 références]  Voir  Masquer  Télécharger


https://hal.inria.fr/hal-00644410
Contributeur : Franck Hétroy-Wheeler <>
Soumis le : lundi 28 novembre 2011 - 11:36:58
Dernière modification le : mercredi 11 avril 2018 - 01:59:23
Document(s) archivé(s) le : lundi 5 décembre 2016 - 03:05:50

Fichiers

CAD_homology.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Dobrina Boltcheva, David Canino, Sara Merino Aceituno, Jean-Claude Léon, Leila De Floriani, et al.. An iterative algorithm for homology computation on simplicial shapes. Computer-Aided Design, Elsevier, 2011, Solid and Physical Modeling 2011, 43 (11), pp.1457-1467. 〈10.1016/j.cad.2011.08.015〉. 〈hal-00644410v2〉

Partager

Métriques

Consultations de la notice

978

Téléchargements de fichiers

597