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Anisotropic Delaunay meshes of surfaces.

Abstract : Anisotropic simplicial meshes are triangulations with elements elongatedalong prescribed directions. Anisotropic meshes have been shown tobe well suited for interpolation of functions or solving PDEs. They can alsosignificantly enhance the accuracy of a surface representation. Given a surfaceS endowed with a metric tensor field, we propose a new approach togenerate an anisotropic mesh that approximates S with elements shapedaccording to the metric field. The algorithm relies on the well-establishedconcepts of restricted Delaunay triangulation and Delaunay refinement andcomes with theoretical guarantees. The star of each vertex in the outputmesh is Delaunay for the metric attached to this vertex and the facets havegood aspect ratio with respect to this metric. The algorithm is easy to implement.It can mesh various types of surfaces like implicit surfaces, polyhedraor isosurfaces in 3D images. It can handle complicated geometries andtopologies, and very anisotropic metric fields.
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Submitted on : Thursday, December 19, 2013 - 4:51:15 AM
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  • HAL Id : hal-00920678, version 1



Jean-Daniel Boissonnat, Kan-Le Shi, Jane Tournois, Mariette Yvinec. Anisotropic Delaunay meshes of surfaces.. ACM Transactions on Graphics, Association for Computing Machinery, 2014. ⟨hal-00920678⟩



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