Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces

Andersson, Mattias; Giesen, Joachim; Pauly, Mark; Speckmann, Bettina

Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces

Files

167-171.pdf (647.05 KB)

Date

2004

Authors

Andersson, Mattias
Giesen, Joachim
Pauly, Mark
Speckmann, Bettina

Publisher

The Eurographics Association

Abstract

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view.

        @inproceedings{:10.2312/SPBG/SPBG04/167-171
,
booktitle = {SPBG'04 Symposium on Point - Based Graphics 2004
},
editor = {Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon Rusinkiewicz
},
title = {{Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces
}},
author = {Andersson, Mattias and 
Giesen, Joachim and 
Pauly, Mark and 
Speckmann, Bettina
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {3-905673-09-6
},
DOI = {/10.2312/SPBG/SPBG04/167-171
}
}