On the randomized construction of the Delaunay tree

Jean-Daniel Boissonnat 1 Monique Teillaud 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The Delaunay is a hierarchical data structure that has been introduced. The Delaunay tree is defined from the Delaunay triangulation and, roughly speaking, represents a triangulation as a hierarchy of balls. It allows us to incrementally construct the Delaunay triangulation of a finite set of n points in any dimension. In this paper, we prove that a randomized construction of the Delaunay tree (and thus, of the Delaunay triangulation) ca be done in 0(n log n) expected time in the plane and in [??] expected time in d-dimensional space. These results are optimal for fixed d. The algorithm is extremely simple and experimental results are given.
Type de document :
[Research Report] RR-1140, INRIA. 1989
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Soumis le : mercredi 24 mai 2006 - 18:10:34
Dernière modification le : samedi 27 janvier 2018 - 01:31:05
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:52:12



  • HAL Id : inria-00075419, version 1



Jean-Daniel Boissonnat, Monique Teillaud. On the randomized construction of the Delaunay tree. [Research Report] RR-1140, INRIA. 1989. 〈inria-00075419〉



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