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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.
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Submitted on : Wednesday, May 24, 2006 - 6:10:34 PM
Last modification on : Friday, February 4, 2022 - 3:16:43 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:52:12 PM


  • 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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