High Quality Compatible Triangulations

Proceedings, 11th International Meshing Roundtable, Sandia National Laboratories, pp.183-192, September 15-18 2002

MESHING
RESEARCH
CORNER

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
{vitus|gotsman}@cs.technion.ac.il

Abstract
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 trian-gulations of planar polygons with a very small number of Steiner (interior) vertices. Being close to optimal in terms of the num-ber 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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