Perturbations for Delaunay and weighted Delaunay 3D Triangulations

Olivier Devillers 1 Monique Teillaud 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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Olivier Devillers, Monique Teillaud. Perturbations for Delaunay and weighted Delaunay 3D Triangulations. Computational Geometry, Elsevier, 2011, 44, pp.160--168. ⟨10.1016/j.comgeo.2010.09.010⟩. ⟨inria-00560388⟩

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