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Section: New Results

Topology computation on simplicial shapes

Participants : Dobrina Boltcheva, Franck Hétroy.

This work is a part of the BQR project IDEAL (see Section  8.1.1 ) which is performed in collaboration with Leila de Floriani from the University of Genova in Italy. The main goal of this project is to study non-manifold geometrical models and to find out features allowing to classify these models and criteria for determining their shape. We are interested in non-manifold models such as idealized industrial CAD models, since they are still ill-understood even if they are frequently used in computer graphics and many engineering applications.

We have developed an efficient method to compute the homology of a large (non-manifold) simplicial complex, from the homologies of its sub-complexes. Computed topological invariants play a crucial role in the field of shape description and analysis. This work has been published in the CAD journal [5] and presented at the SIAM conference on geometric and physical modeling (GD/SPM'11).