Advanced Automatic Hexahedral Mesh Generation from Surface Quad Meshes

A purely topological approach for the generation of hexahedral meshes from quadrilateral surface meshes of genus zero has been proposed by M. Müller-Hannemann: in a first stage, the input surface mesh is reduced to a single hexahedron by successively eliminating loops from the dual graph of the quad mesh; in the second stage, the hexahedral mesh is constructed by extruding a layer of hexahedra for each dual loop from the first stage in reverse elimination order. In this paper, we introduce several techniques to extend the scope of target shapes of the approach and significantly improve the quality of the generated hexahedral meshes. While the original method can only handle "almost convex" objects and requires mesh surgery and remeshing in case of concave geometry, we propose a method to overcome this issue by introducing the notion of concave dual loops. Furthermore, we analyze and improve the heuristic to determine the elimination order for the dual loops such that the inordinate introduction of interior singular edges, i.e. edges of degree other than four in the hexahedral mesh, can be avoided in many cases.