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Reports Year : 2003

An Effective Condition for Sampling Surfaces with Guarantees

Jean-Daniel Boissonnat
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Steve Oudot
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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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Dates and versions

inria-00071520 , version 1 (23-05-2006)


  • HAL Id : inria-00071520 , version 1


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