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.
The Generalized Indexed data structure with Adjacencies (IA * ) REF generalizes such representations and is capable of encoding non-manifold simplicial complexes of any dimension.
IA*: An Adjacency-Based Representation for Non-Manifold Simplicial Shapes in Arbitrary Dimensions
Comput. Graph.
Comput. Graph.
Computer Science