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Journal Articles Computational Geometry Year : 2011

Perturbations for Delaunay and weighted Delaunay 3D Triangulations

Olivier Devillers
Monique Teillaud

Abstract

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code; It is implemented in CGAL, and guarantees that both vertex insertion and vertex removal are fully robust.
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inria-00560388 , version 1 (28-01-2011)

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Olivier Devillers, Monique Teillaud. Perturbations for Delaunay and weighted Delaunay 3D Triangulations. Computational Geometry, 2011, 44, pp.160--168. ⟨10.1016/j.comgeo.2010.09.010⟩. ⟨inria-00560388⟩
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