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Robust Three Dimensional Delaunay Refinement

Pav, Steven E. and Noel J. Walkington

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.145-156, September 19-22 2004


13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Steven E. Pav
University of California at San Diego, La Jolla, CA.

Noel J. Walkington
Carnegie Mellon University, Pittsburgh, PA.

The Delaunay Refinement Algorithm for quality meshing is extended to three dimensions. The algorithm accepts input with arbitrarily small angles, and outputs a Conforming Delaunay Tetrahedralization where most tetrahedra have radius-to-shortest-edge ratio smaller than some user chosen ยต > 2: Those tets with poor quality are in well defined locations: their circumcenters are describably near input segments. Moreover, the output mesh is well graded to the input: short mesh edges only appear around close features of the input. The algorithm has the added advantage of not requiring a priori knowledge of the "local feature size," and only requires searching locally in the mesh.

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