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An Effective Condition for Sampling Surfaces with Guarantees

Jean-Daniel Boissonnat 1 Steve Oudot
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The notion of -sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an -sample of a smooth surface S for a sufficiently small , then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an -sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose -sample. We show that the set of loose -samples contains and is asymptotically identical to the set of -samples. The main advantage of -samples over -samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes.
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Submitted on : Tuesday, May 23, 2006 - 5:49:50 PM
Last modification on : Friday, February 4, 2022 - 3:16:22 AM
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  • HAL Id : inria-00071520, version 1

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Jean-Daniel Boissonnat, Steve Oudot. An Effective Condition for Sampling Surfaces with Guarantees. RR-5064, INRIA. 2003. ⟨inria-00071520⟩

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