On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions. - Archive ouverte HAL Access content directly
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On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions.

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Abstract

It is a well-known fact that, under mild sampling conditions, the restricted Delaunay triangulation provides good topological approximations of 1- and 2-manifolds. We show that this is not the case for higher-dimensional manifolds, even under stronger sampling conditions. Specifically, it is not true that, for any compact closed submanifold M of R^n, and any sufficiently dense uniform sampling L of M, the Delaunay triangulation of L restricted to M is homeomorphic to M, or even homotopy equivalent to it. Besides, it is not true either that, for any sufficiently dense set W of witnesses, the witness complex of L relative to M contains or is contained in the restricted Delaunay triangulation of L.
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Dates and versions

inria-00260861 , version 1 (06-03-2008)
inria-00260861 , version 2 (09-03-2008)

Identifiers

  • HAL Id : inria-00260861 , version 2
  • ARXIV : 0803.1296

Cite

Steve Oudot. On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions.. 2006. ⟨inria-00260861v2⟩
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