TY - JOUR
T1 - An iterative algorithm for homology computation on simplicial shapes
JF - Computer-Aided Design
Y1 - 2011
A1 - Boltcheva,Dobrina
A1 - Canino,David
A1 - Merino Aceituno,Sara
A1 - Léon,Jean-Claude
A1 - De Floriani, Leila
A1 - Hétroy,Franck
KW - Computational topology
KW - Generators
KW - Mayer–Vietoris sequence
KW - shape decomposition
KW - simplicial complexes
KW - Z -homology
AB - 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.
VL - 43
SN - 0010-4485
UR - http://www.sciencedirect.com/science/article/pii/S0010448511002144
CP - 11
M3 - 10.1016/j.cad.2011.08.015
ER -