HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

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.
Document type :
Complete list of metadata

Cited literature [1 references]  Display  Hide  Download

Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 5:49:50 PM
Last modification on : Friday, February 4, 2022 - 3:16:22 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:21:46 PM


  • 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⟩



Record views


Files downloads