Anisotropic Delaunay Meshes of Surfaces

Jean-Daniel Boissonnat 1 Kan-Le Shi 2 Jane Tournois 3 Mariette Yvinec 1, *
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown to be well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface repre- sentation. Given a surface S endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields.
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Jean-Daniel Boissonnat, Kan-Le Shi, Jane Tournois, Mariette Yvinec. Anisotropic Delaunay Meshes of Surfaces. [Research Report] RR-8400, INRIA. 2013, pp.24. ⟨hal-00907088⟩

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