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A Dimension-Independent Data Structure forSimplicial Complexes

Leila De Floriani, Annie Hui, Daniele Panozzo, and David Canino

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.403-420, October 3-6 2010


19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Department of Computer Science, University of Genova, Italy.
Department of Computer Science, University of Maryland, MD, USA.

We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes. To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient navigation and topological modifications. The IS data structure has the same expressive power and exibits performances in query and update operations as the incidence graph, a widely-used representation for general cell complexes, but it is much more compact. Here, we describe the IS data structure and we evaluate its storage cost. Moreover, we present efficient algorithms for navigating and for generating a simplicial complex described as an IS data structure. We compare the IS data structure with the incidence graph and with dimension-specific representations for simplicial complexes.

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