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ISSN: 1077-2626
Tengfei Jiang , Zhejiang University, Hangzhou
Jin Huang , Zhejiang University, Hangzhou
Yuanzhen Wang , Michigan State University, East Lansing
Yiying Tong , Michigan State University, East Lansing
Hujun Bao , Zhejiang University, Hangzhou
We present an automatic hexahedralization tool, based on a systematic treatment that removes some of the singularities that would lead to degenerate volumetric arameterization. Such singularities could be abundant in automatically generated frame fields guiding the interior and boundary layouts of the hexahedra in an all hexahedral mesh. We first give the mathematical definitions of the inadmissible singularities prevalent in frame fields, including newly introduced surface singularity types. We then give a practical framework for adjusting singularity graphs by automatically modifying the rotational transition of frames between charts (cells of a tetrahedral mesh for the volume) to resolve the issues detected in the internal and boundary singularity graph. After applying an additional re-smoothing of the frame field with the modified transition conditions, we cut the volume into a topologically trivial domain, with the original topology encoded by the self-intersections of the boundary of the domain, and solve a mixed integer problem on this domain for a global parameterization. Finally, a properly connected hexahedral mesh is constructed from the integer isosurfaces of (u, v, w) in the parameterization. We demonstrate the applicability of the method on complex shapes, and discuss its limitations.
Image edge detection, Mesh generation, Compounds, Topology, Shape, Convergence, Vectors, volumetric parameterization, automatic hexahedral meshing, frame field, field singularity

Y. Tong, Y. Wang, J. Huang, T. Jiang and H. Bao, "Frame Field Singularity Correction for Automatic Hexahedralization," in IEEE Transactions on Visualization & Computer Graphics.
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