A data structure for non-manifold simplicial d-complexes

Authors:
Leila De Floriani;David Greenfieldboyce;Annie Hui
Affiliations:
University of Genova, Via Dodecaneso, Genova (Italy);University of Maryland, MD;University of Maryland, MD
Venue:
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Year:
2004

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Abstract

We propose a data structure for d-dimensional simplicial complexes, that we call the Simplified Incidence Graph (SIG). The simplified incidence graph encodes all simplices of a simplicial complex together with a set of boundary and partial co-boundary topological relations. It is a dimension-independent data structure in the sense that it can represent objects of arbitrary dimensions. It scales well to the manifold case, i.e. it exhibits a small overhead when applied to simplicial complexes with a manifold domain, Here, we present efficient navigation algorithms for retrieving all topological relations from a SIG, and an algorithm for generating a SIG from a representation of the complex as an incidence graph. Finally, we compare the simplified incidence graph with the incidence graph, with a widely-used data structure for d-dimensional pseudo-manifold simplicial complexes, and with two data structures specific for two-and three-dimensional simplicial complexes.