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Obtuse triangle suppression in anisotropic meshes

Feng Sun 1 Yi-King Choi 2 Wenping Wang 1 Dong-Ming Yan 1, 3, 4 Yang Liu 3, 5 Bruno Lévy 3 
2 Computer Graphics Group [Hong Kong]
Department of Computer Science [Hong Kong]
3 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy
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Submitted on : Monday, December 10, 2012 - 3:17:53 PM
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Feng Sun, Yi-King Choi, Wenping Wang, Dong-Ming Yan, Yang Liu, et al.. Obtuse triangle suppression in anisotropic meshes. Computer Aided Geometric Design, Elsevier, 2011, 28 (9), pp.537-548. ⟨10.1016/j.cagd.2011.09.007⟩. ⟨hal-00763324⟩



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