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Incrementally Constructing and Updating Constrained Delaunay Tetrahedralizations with Finite Precision Coordinates

Si, Hang and Jonathan Richard Shewchuk

21st International Meshing Roundtable, Springer-Verlag, pp.173-190, October 7-10 2012

IMR
PROCEEDINGS

21st International Meshing Roundtable
San Jose, CA
October 7-10,2012

Weierstrass Institute for Applied Analysis and Stochastics (WIAS), MohrenstraBe 39, 10117, Berlin, Germany
Email: si@wias-berlin.de

Summary
Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when nite-precision coordinates yield vertices on a line that are not perfectly collinear and polygonal facets that are not perfectly at. We experimentally compare two recent algorithms for inserting a polygonal facet into a CDT: a bistellar ip algorithm of Shewchuk (Proc. 19th Annual Symposium on Computational Geometry, June 2003) and a cavity retriangulation algorithm of Si and Gartner (Proc. Fourteenth International Meshing Roundtable, September 2005). We modify these algorithms to succeed in practice for polygons whose vertices deviate from exact coplanarity.

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