On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions.

Steve Oudot 1, *
* Corresponding author
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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  • HAL Id : inria-00260861, version 2
  • ARXIV : 0803.1296

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

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