Hexahedral mesh generation via constrained quadrilateralization

Decomposing a volume into high-quality hexahedral cells is a challenging task in finite element simulations and computer graphics. Inspired by the use of a spatial twist continuum and frame field in previous hexahedral mesh generation methods, we present a method of hexahedral mesh generation via constrained quadrilateralization that combines a spatial twist continuum and frame fields. Given a volume represented by a tetrahedral mesh, surface quadrilateral mesh and frame field, we first extend the loop of the surface of a solid to a layer of hexahedral elements, then divide the solid into two smaller sub-solids by the layer, and finally handle them recursively until all of the sub-solids are empty. In our hexahedral mesh generation framework, we apply constrained quadrilateralization to extend the loop to a layer of hexahedral elements. The "divide-and-conquer" strategy used in this method is suitable for parallelization. This method can potentially lead to easier and more robust implementations that are more parallelizable and less dependent on heavy numerical libraries. The testing results show that the quality of the meshes generated by this method is similar to those produced by current state-of-the-art mesh generation methods.