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Perturbing Slivers in 3D Delaunay Meshes

Tournois, Jane, Rahul Srinivasan, and Pierre Alliez

Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.157-173, October 25-28 2009


18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009

INRIA Sophia Antipolis - MĀ„editerranĀ„ee, France

Isotropic tetrahedron meshes generated by Delaunay refinement algorithms are known to contain a majority of well-shaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicity. The solution which explicitly perturbs the slivers through random vertex relocation and Delaunay connectivity update is very effective but slow. In this paper we present a perturbation algorithm which favors deterministic over random perturbation. The added value is an improved efficiency and effectiveness. Our experimental study applies the proposed algorithm to meshes obtained by Delaunay refinement as well as to carefully optimized meshes.

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