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Random sampling of a cylinder yields a not so nasty Delaunay triangulation

Olivier Devillers 1 Xavier Goaoc 2
1 GEOMETRICA - Geometric computing
INRIA Futurs, CRISAM - Inria Sophia Antipolis - Méditerranée
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that the expected size of the 3D Delaunay triangulation of n points evenly distributed on a cylinder is Theta(n log n). This shows that the n sqrt(n) behavior of the cylinder-example of Erickson is pathological.
Mots-clés : Delaunay triangulation random distribution random sample surface reconstruction
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Submitted on : Monday, October 22, 2007 - 11:16:02 AM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Friday, November 25, 2016 - 6:53:47 PM

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Olivier Devillers, Xavier Goaoc. Random sampling of a cylinder yields a not so nasty Delaunay triangulation. [Research Report] RR-6323, INRIA. 2007, pp.10. ⟨inria-00179313v2⟩

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