Mattias Andersson, Joachim Giesen, Mark Pauly, Bettina Speckmann, Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces, Symposium on Point-Based Graphics 2004

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.

Bibtex: 

@inproceedings{agps-bknluss-04,
 author = {Mattias Andersson and  Joachim Giesen and Mark Pauly and Bettina Speckmann},
 title = {Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces},
 booktitle = {Symposium on Point-Based Graphics},
 year = {2004},
 }