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A weak definition of Delaunay triangulation

Vin de Silva
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Abstract

We show that the traditional criterion for a simplex to belong to the Delaunay triangulation of a point set is equivalent to a criterion which is a priori weaker. The argument is quite general; as well as the classical Euclidean case, it applies to hyperbolic and hemispherical geometries and to Edelsbrunner's weighted Delaunay triangulation. In spherical geometry, we establish a similar theorem under a genericity condition. The weak definition finds natural application in the problem of approximating a point-cloud data set with a simplical complex.

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Vin de Silva. 2003-10-16. A weak definition of Delaunay triangulation. https://arxiv.org/abs/cs/0310031

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