Non-manifold Decomposition in Arbitrary Dimensions

  • Leila De Floriani
  • Mostefa Mohammed Mesmoudi
  • Franco Morando
  • Enrico Puppo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

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.

Keywords

Arbitrary Dimension Abstract Simplicial Complex Singular Vertex Combinatorial Topology Combinatorial Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Leila De Floriani
    • 1
  • Mostefa Mohammed Mesmoudi
    • 1
  • Franco Morando
    • 1
  • Enrico Puppo
    • 1
  1. 1.Department of Computer and Information SciencesUniversità di GenovaGenovaItaly

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