Technical Section: Quality encoding for tetrahedral mesh optimization

Authors:
Kai Xu;Zhi-Quan Cheng;Yanzhen Wang;Yueshan Xiong;Hao Zhang
Affiliations:
School of Computer Science, National University of Defense Technology, China and School of Computing Science, Simon Fraser University, Canada;School of Computer Science, National University of Defense Technology, China;School of Computer Science, National University of Defense Technology, China;School of Computer Science, National University of Defense Technology, China;School of Computing Science, Simon Fraser University, Canada
Venue:
Computers and Graphics
Year:
2009

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Abstract

We define quality differential coordinates (QDC) for per-vertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation of different choices of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra. We develop an algorithm for tetrahedral mesh optimization through energy minimization driven by QDC. The variational problem is solved efficiently and robustly using gradient flow based on a stable semi-implicit integration scheme. To ensure quality boundary of the resulting tetrahedral mesh, we propose a harmonic-guided optimization scheme which leads to consistent handling of both the interior and boundary tetrahedra.