Abstract
In this paper we consider the problem of decomposing a nonmanifold n-dimensional object described by an abstract simplicial complex into an assembly of ‘more-regular’ components. Manifolds, which would be natural candidates for components, cannot be used to this aim in high dimensions because they are not decidable sets. Therefore, we define d-quasi-manifolds, a decidable superset of the class of combinatorial d-manifolds that coincides with d-manifolds in dimension less or equal than two. We first introduce the notion of d-quasi-manifold complexes, then we sketch an algorithm to decompose an arbitrary complex into an assembly of quasi-manifold components abutting at non-manifold joints. This result provides a rigorous starting point for our future work, which includes designing efficient data structures for non-manifold modeling, as well as defining a notion of measure of shape complexity of such models.
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Keywords
- Arbitrary Dimension
- Abstract Simplicial Complex
- Singular Vertex
- Combinatorial Topology
- Combinatorial Manifold
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De Floriani, L., Mesmoudi, M.M., Morando, F., Puppo, E. (2002). Non-manifold Decomposition in Arbitrary Dimensions. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_6
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DOI: https://doi.org/10.1007/3-540-45986-3_6
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