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High quality compatible triangulations

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Abstract

Compatible meshes are isomorphic meshings 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, sometimes requiring extra (Steiner) vertices. Experimental results show that for typical real-life inputs, the number of Steiner vertices introduced is very small. However, having a small number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e. they 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 remeshing and mesh smoothing techniques. 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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Acknowledgements

The work was carried out while the authors were at Technion—Israel Institute of Technology. Thanks to Tatiana Surazhsky and Michael Floater for their contribution to the area-based remeshing method, to Alla Sheffer for helpful discussions on sweeps and to Gill Barequet for helpful discussions on the implementation of minimum-link path algorithms. This work was partially supported by the Technion Computer Science Software Technology Laboratory (STL) and the Technion Fund for Promotion of Research.

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Authors and Affiliations

  1. Department of Informatics, Oslo University, Oslo, Norway

    V. Surazhsky

  2. Center for Graphics and Geometric Computing, Department of Computer Science, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    C. Gotsman

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  1. V. Surazhsky
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  2. C. Gotsman
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Correspondence to V. Surazhsky.

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Surazhsky, V., Gotsman, C. High quality compatible triangulations. Engineering with Computers 20, 147–156 (2004). https://doi.org/10.1007/s00366-004-0282-6

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