We propose a compact, dimension-independent data structure for manifold, non-manifold and non-regular simplicial complexes, that we call the Generalized Indexed Data structure with Adjacencies (IA* data structure). It encodes only top simplices, i.e. the ones that are not on the boundary of any other simplex, plus a suitable subset of the adjacency relations. We describe the IA* data structure in arbitrary dimensions, and compare the storage requirements of its two-dimensional and three-dimensional instances with both dimension-specific and dimension-independent representations. We show that the IA* data structure is more cost effective than other dimension-independent representations and is even slightly more compact than the existing dimension-specific ones. We present efficient algorithms for navigating a simplicial complex described as an IA* data structure. This shows that the IA* data structure allows retrieving all topological relations of a given simplex by considering only its local neighborhood and thus it is a more efficient alternative to incidence-based representations when information does not need to be encoded for boundary simplices

IA*: an adjacency-based representation for non-manifold simplicial shapes in arbitrary dimensions

DE FLORIANI, LEILA;
2012-01-01

Abstract

We propose a compact, dimension-independent data structure for manifold, non-manifold and non-regular simplicial complexes, that we call the Generalized Indexed Data structure with Adjacencies (IA* data structure). It encodes only top simplices, i.e. the ones that are not on the boundary of any other simplex, plus a suitable subset of the adjacency relations. We describe the IA* data structure in arbitrary dimensions, and compare the storage requirements of its two-dimensional and three-dimensional instances with both dimension-specific and dimension-independent representations. We show that the IA* data structure is more cost effective than other dimension-independent representations and is even slightly more compact than the existing dimension-specific ones. We present efficient algorithms for navigating a simplicial complex described as an IA* data structure. This shows that the IA* data structure allows retrieving all topological relations of a given simplex by considering only its local neighborhood and thus it is a more efficient alternative to incidence-based representations when information does not need to be encoded for boundary simplices
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/351302
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