Planar-faced two-refinement method improves quality of hexahedral meshes
Planar-faced and high-Jacobian two-refinement hexahedral templates
GraphicsComputational Geometry
Summary
Creating high-quality 3D grids made of cube-like shapes (hexahedra) is hard but important for simulations. The authors found a new way to refine these grids more efficiently, using fewer extra cubes while ensuring all cube faces are flat. Their method balances the need for quality with fewer added elements and produces grids that fit well into advanced mesh tools. It compares favorably to older methods by having better shape quality and similar accuracy.
What this means in practice
- •For simulation engineers: Generate conforming hex meshes with flat-faced elements that improve simulation quality and integrate with guaranteed quality mesh reconstruction.
- •For computer graphics developers: Produce cleaner hexahedral meshes for 3D modeling or animation pipelines requiring high mesh quality and fewer elements.
Authors
Hua Tong, Yongjie Jessica Zhang
Abstract
Automatically generating high-quality conforming hexahedral (hex) meshes from general input boundaries remains a challenging problem, despite the numerical advantages hex elements offer in simulation. Grid-based adaptive refinement, followed by hanging-node removal, is the most robust fully automatic choice. Among two-refinement methods, primal templates have better mesh quality than dual templates but depend on a strong balancing condition that over-refines the grid; neither family guarantees planar quadrilateral (quad) faces. This paper generalizes recent primal three-refinement templates to a two-refinement scheme under a moderate balancing condition, a relaxation of the strong one. 32 special and five fundamental patterns resolve all 144 symmetry-reduced configurations, followed by either a fast greedy algorithm or an integer linear programming (ILP) algorithm that trades extra runtime for a further reduction in element count. The scheme is the first two-refinement method in which all hexes have planar faces, and its meshes feed directly into a recent quality-guaranteed hex mesh reconstruction algorithm. At comparable element counts, it attains a similar Hausdorff ratio (HR) and a higher minimum scaled Jacobian (min SJ) than its three-refinement counterpart.