An Effective Condition for Sampling Surfaces with Guarantees

Boissonnat, J. D.; Oudot, S.

An Effective Condition for Sampling Surfaces with Guarantees

Files

101-112_boissonnat.pdf (2.58 MB)

Date

2004

Authors

Boissonnat, J. D.
Oudot, S.

Publisher

The Eurographics Association

Abstract

The notion of e-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 e-sample of a smooth surface S for a suf ciently small e, 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 e-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 e-sample. We show that the set of loose e-samples contains and is asymptotically identical to the set of e-samples. The main advantage of loose e-samples over e-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.

        @inproceedings{10.2312:sm.20041381
,
booktitle = {Solid Modeling
},
editor = {Gershon Elber and Nicholas Patrikalakis and Pere Brunet
},
title = {{An Effective Condition for Sampling Surfaces with Guarantees
}},
author = {Boissonnat, J. D. and 
Oudot, S.
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7783
},
ISBN = {3-905673-55-X
},
DOI = {10.2312/sm.20041381
}
}