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Sliver-suppressing tetrahedral mesh optimization with gradient-based shape matching energy. (English) Zbl 1366.65043
Summary: In this paper, a novel shape matching energy is proposed to suppress slivers for tetrahedral mesh generation. Given a volumetric domain with a user-specified template (regular) simplex, the tetrahedral meshing problem is transformed into a shape matching formulation with a gradient-based energy, i.e., the gradient of linear shape function. It effectively inhibits small heights and suppresses all the badly-shaped tetrahedrons in tetrahedral meshes. The proposed approach iteratively optimizes vertex positions and mesh connectivity, and makes the simplices in the computed mesh as close as possible to the template simplex. We compare our results qualitatively and quantitatively with the state-of-the-art algorithm in tetrahedral meshing on extensive models using the standard measurement criteria.

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
Software:
CGALmesh; Netgen
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