An Interior Surface Generation Method for All-Hexahedral Meshing

Abstract

This paper describes an interior surface generation method and a strategy for all-hexahedral mesh generation. It is well known that a solid homeomorphic to a ball with even number of quadrilaterals bounding the surface should be able to be partitioned into a compatible hex mesh, where each associated hex element corresponds to the intersection point of three interior surfaces. However, no practical interior surface generation method has been revealed yet for generating hexahedral meshes of quadrilateral- bounded volumes. We have deduced that a simple interior surface with at most one pair of self-intersecting points can be generated as an orientable regular homotopy, or more definitively a sweep, if the self-intersecting point types are identical, while the surface can be generated as a non-orientable one (i.e. a Möbius band) if the self-intersecting point types are distinct. A complex interior surface can be composed of simple interior surfaces generated sequentially from adjacent circuits, i.e. non-self-intersecting partial dual cycles partitioned at a self-intersecting point. We demonstrate an arrangement of interior surfaces for Schneiders’ open problem, and show that for our interior surface arrangement Schneiders’ pyramid can be filled with 146 hexahedral elements. We also discuss a possible strategy for practical hexahedral mesh generation.

The submitted manuscript has been co-authored by a contractor of the United States Government under contract. Accordingly the United States Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for United States Government purposes.