A Boundary Operator for Computing the Homology of Cellular Structures

Sylvie Alayrangues (1) , Guillaume Damiand (2) , Pascal Lienhardt (1) , Samuel Peltier (1)

1 SIC
2 M2DisCo - Geometry Processing and Constrained Optimization

The paper focuses on homology computation over cellular structures through the computation of incidence numbers. Roughly speaking, if two cells are incident, then their incidence number characterizes how they are attached. Having these numbers naturally leads to the definition of a boundary operator, which induces a cellular homology. More precisely, the two main families of cellular structures (incidence graphs and ordered models) are studied through various models. A boundary operator is then proposed for the most general structure, and is optimized for the other structures. It is proved that, under specific conditions, the cellular boundary operator proposed in this paper defines a cellular homology equivalent to the simplicial one.

Mots clés: cellular homology computation; boundary operator; incidence graph-based representations; ordered models

Domaines: Géométrie algorithmique [cs.CG]

Sylvie Alayrangues, Guillaume Damiand, Pascal Lienhardt, Samuel Peltier. A Boundary Operator for Computing the Homology of Cellular Structures. [Research Report] Université de poitiers. 2011. ⟨hal-00683031v2⟩