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J.-D. Boissonnat, S. Y. Oudot. An effective condition for sampling surfaces with guarantees. Proc. 9th ACM Sympos. on Solid Modeling and Applications, pp. 101-112, 2004.
Abstract:
The notion of r-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
r-sample of a smooth surface S for a sufficiently small
r, 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
r-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 r-sample.
We show that the set of loose r-samples contains and is
asymptotically identical to the set of r-samples. The main
advantage of loose r-samples over r-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.
Bibtex:
@inproceedings{bo-ecssg-04,
author = {J.-D. Boissonnat and S. Y. Oudot},
title = {An effective condition for sampling surfaces with guarantees},
booktitle = {Proc. 9th ACM Sympos. on Solid Modeling and Spplications},
pages = {101--112},
year = {2004}
}
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