An Implementation Method

Figure 1: High quality all-hex meshes generated by our method. Comparisons with CubeCover [Nieser et al. 2011] and volumetric PolyCube [Gregson et al. 2011] demonstrate that the hex meshes by our method are superior in mesh quality (the minimal scaled Jacobian of hexes is shown in the figure, bigger is better) and singularity placement (see the zoom-in views for comparison). Decomposing a volume into high-quality hexahedral cells is a chal-lenging task in geometric modeling and computational geometry. Inspired by the use of cross field in quad meshing and the CubeCover approach in hex meshing, we present a complete all-hex meshing framework based on singularity-restricted field that is essential to induce a valid all-hex structure. Given a volume represented by a tetrahedral mesh, we first compute a boundary-aligned 3D frame field inside it, then convert the frame field to be singularity-restricted by our effective topological operations. In our all-hex meshing framework, we apply the CubeCover method to achieve the volume parametrization. For reducing degenerate elements appearing in the volume parametrization, we also propose novel tetrahedral split operations to preprocess singularity-restricted frame fields. Experi-mental results show that our algorithm generates high-quality all-hex meshes from a variety of 3D volumes robustly and efficiently