Smoothness driven frame field generation for hexahedral meshing

For many years, providing an algorithm to generate hexahedral meshes that fulfill minimal geometric criteria (boundary-alignment, minimum of singularity vertices) and that is not limited to a category of geometries has been an open issue. In the past couple of years, techniques using 3D frame fields have emerged to design such meshes (Huang et al., 2011; Li et al., 2012). Those methods are based on a two-step process where a 3D frame field is built by assigning a frame to each cell of a tetrahedral mesh, then a parametrization algorithm is applied to generate a hexahedral mesh. In this work, we propose a novel algorithm to generate block-structured hexahedral meshes for any CAD domain Ω. This work differs from previous ones in many points: (1) the proposed approach does not need to start from a pre-meshed quad boundary; (2) The frame field initialization does not put singularity lines around the medial object of Ω; (3) Conceptually, frames are assigned to the vertices and not to the cells of the tetrahedral mesh; (4) The parametrization process is replaced by a constructive algorithm that generates a block structure, which partitions Ω in meshable regions.