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arXiv · 1803.11436

Delaunay Triangulations of Points on Circles

Vincent Despré·Olivier Devillers·Hugo Parlier·Jean-Marc Schlenker
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Abstract

Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but since it is not a generic situation, this difficulty is usually handled by using a (symbolic or explicit) perturbation. As an alternative, we propose to define a canonical triangulation for a set of concyclic points by using a max-min angle characterization of Delaunay triangulations. This point of view leads to a well defined and unique triangulation as long as there are no symmetric quadruples of points. This unique triangulation can be computed in quasi-linear time by a very simple algorithm.

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Vincent Despré, Olivier Devillers, Hugo Parlier, Jean-Marc Schlenker. 2018-03-30. Delaunay Triangulations of Points on Circles. https://arxiv.org/abs/1803.11436

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