Robust and efficient delaunay triangulations of points on or close to a sphere

Authors:
Manuel Caroli;Pedro M. M. de Castro;Sébastien Loriot;Olivier Rouiller;Monique Teillaud;Camille Wormser
Affiliations:
INRIA Sophia Antipolis, Méditerranée, France;INRIA Sophia Antipolis, Méditerranée, France;INRIA Sophia Antipolis, Méditerranée, France;INRIA Sophia Antipolis, Méditerranée, France;INRIA Sophia Antipolis, Méditerranée, France;ETH Zürich, Switzerland
Venue:
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Year:
2010

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Abstract

We propose two ways to compute 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. We use the so-called space of circles as mathematical background for this work. We present a fully robust implementation built upon existing generic algorithms provided by the Cgal library. The efficiency of the implementation is established by benchmarks.