
J.D. Boissonnat, S. Y. Oudot. An effective condition for sampling surfaces with guarantees. Proc. 9th ACM Sympos. on Solid Modeling and Applications, pp. 101112, 2004.
Abstract:
The notion of rsample, 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
rsample 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
rsample, 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 rsample.
We show that the set of loose rsamples contains and is
asymptotically identical to the set of rsamples. The main
advantage of loose rsamples over rsamples 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{boecssg04,
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 = {101112},
year = {2004}
}

