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High Quality Compatible Triangulations

Surazhsky, Vitaly and Craig Gotsman

Proceedings, 11th International Meshing Roundtable, Springer-Verlag, pp.183-192, September 15-18 2002


11th International Meshing Roundtable
Ithaca, New York, USA.
September 15-18 2002
Center for Graphics and Geometric Computing
Dept. of Computer Science,
Technion Israel Institute of Technology, Haifa 32000, Israel

Compatible meshes are isomorphic meshing of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons with a very small number of Steiner (interior) vertices. Being close to optimal in terms of the number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e., do not have well-shaped triangles. We show how to increase the quality of these triangulations by adding Steiner vertices in a compatible manner, using several novel techniques for remeshing and mesh smoothing. The total scheme results in high-quality compatible meshes with a small number of triangles. These meshes may then be morphed to obtain the intermediate triangulated sections of a sweep, if needed.

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