Bounds on the k-neighborhood for locally uniformly sampled surfaces

Authors:
Mattias Andersson;Joachim Giesen;Mark Pauly;Bettina Speckmann
Affiliations:
Department of Computer Science, Lund Institute of Technology, Lund, Sweden;Department of Computer Science, ETH Zurich, Zurich, Switzerland;Computer Science Department, Stanford University, Stanford, CA;Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, The Netherlands
Venue:
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Year:
2004

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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.