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Robust and Efficient Delaunay triangulations of points on or close to a sphere

Manuel Caroli 1 Pedro Machado Manhães de Castro 1 Sebastien Loriot 2 Olivier Rouiller 1 Monique Teillaud 1 Camille Wormser 3
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 ABS - Algorithms, Biology, Structure
CRISAM - Inria Sophia Antipolis - Méditerranée
3 D-INFK - Department of Computer Science [ETH Zürich]
Abstract : We propose two approaches for computing the Delaunay triangulation of points on a sphere, or of rounded points close to a sphere, both based on the classic incremental algorithm initially designed for the plane. The space of circles gives the mathematical background for this work. We implemented the two approaches in a fully robust way, building upon existing generic algorithms provided by the cgal library. The effciency and scalability of the method is shown by benchmarks.
Keywords : Computational Geometry Delaunay Triangulation Voronoi Diagram Sphere Space of Circles Exact Geometric Computing CGAL
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https://hal.inria.fr/inria-00405478
Contributor : Manuel Caroli <>
Submitted on : Thursday, December 17, 2009 - 4:29:52 PM
Last modification on : Wednesday, October 30, 2019 - 7:36:17 PM
Long-term archiving on: : Saturday, November 26, 2016 - 3:20:55 PM

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Manuel Caroli, Pedro Machado Manhães de Castro, Sebastien Loriot, Olivier Rouiller, Monique Teillaud, et al.. Robust and Efficient Delaunay triangulations of points on or close to a sphere. [Research Report] RR-7004, INRIA. 2009. ⟨inria-00405478v4⟩

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