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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