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Meshing Volumes with Curved Boundaries

Steve Oudot 1, * Laurent Rineau 2 Mariette Yvinec 1
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : This paper introduces a three-dimensional mesh generation al- gorithm for domains whose boundaries are curved surfaces, possibly with sharp features. The algorithm combines a Delaunay-based surface mesher with a Ruppert-like volume mesher, resulting in a greedy scheme to sample the interior and the boundary of the domain simultaneously. The algorithm constructs provably-good meshes, it gives control on the size of the mesh elements through a user-defined sizing field, and it guarantees the accuracy of the approximation of the domain boundary. A notable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line seg- ment intersects the boundary. This makes the algorithm generic enough to be applied to domains with a wide variety of boundary types, such as im- plicit surfaces, polyhedra, level-sets in 3D gray-scaled images, or point-set surfaces.
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https://hal.inria.fr/hal-00880334
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Steve Oudot, Laurent Rineau, Mariette Yvinec. Meshing Volumes with Curved Boundaries. Engineering with Computers, Springer Verlag, 2010, pp.265-279. ⟨hal-00880334⟩

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