Qualitative symbolic perturbation: two applications of a new geometry-based perturbation framework

Devillers, Olivier; Karavelas, Menelaos I.; Teillaud, Monique

doi:10.20382/jocg.v8i1a11

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Corollary 2 a Set Of Points In The Euclidean Plane With Dist...1

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2018

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“…The usual and generic way to address degeneracies is the use of symbolic perturbations [2,5,6,8] that perturb the input point set by an infinitesimal quantity in a way that is guaranteed to remove degeneracies. This approach has been used for Delaunay triangulation and allows to draw diagonals in a set of concyclic points in a consistent but not really meaningful manner [1,3].…”

Section: Corollary 2 a Set Of Points In The Euclidean Plane With Dist...mentioning

confidence: 99%

Delaunay Triangulations of Points on Circles

Despré¹,

Devillers²,

Parlier³

et al. 2018

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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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