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Complexity of the Delaunay triangulation of points on surfaces: the smooth case (2003)
| Venue: | In Annual Symposium on Computational Geometry |
| Citations: | 53 - 15 self |
BibTeX
@INPROCEEDINGS{Attali03complexityof,
author = {Dominique Attali and Jean-daniel Boissonnat and Andre ́ Lieutier},
title = {Complexity of the Delaunay triangulation of points on surfaces: the smooth case},
booktitle = {In Annual Symposium on Computational Geometry},
year = {2003},
pages = {201--210}
}
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Abstract
It is well known that the complexity of the Delaunay trian-gulation of N points in 3, i.e. the number of its faces, can be (N2). The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms rst construct the Delau-nay triangulation of a set of points measured on a surface. In this paper, we bound the complexity of the Delaunay triangulation of points distributed on generic smooth sur-faces of 3. Under a mild uniform sampling condition, we show that the complexity of the 3D Delaunay triangulation of the points is O(N log N). Categories and Subject Descriptors F.2.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity|Geometrical problems and com-
