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Meshing Volumes Bounded by Smooth Surfaces

Oudot, Steve, Laurent Rineau, and Mariette Yvinec

Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.203-220, September 11-14 2005


14th International Meshing Roundtable
San Diego, CA, USA
September 11-14, 2005

Steve Oudot and Mariette Yvinec
INRIA, BP 93 06902 Sophia Antipolis, France

Laurent Rineau
ENS, 45 rue díUlm, 75005 Paris, France

This paper introduces a three-dimensional mesh generation algorithm for domains bounded by smooth surfaces. The algorithm combines a Delaunay-based surface mesher with a Ruppert-like volume mesher, to get a greedy algorithm that samples the interior and the boundary of the domain at once. 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 noticeable 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 segment intersects the boundary. This makes the algorithm generic enough to be applied to a wide variety of objects, ranging from domains defined by implicit surfaces to domains defined by level-sets in 3D grey-scaled images or by point-set surfaces.

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