Topology and Geometry of Hexahedral Complex: Combined Approach for Hexahedral Meshing

Abstract

In present paper a new approach for hexahedral mesh generation is suggested. The process of hexahedral mesh generation for an arbitrary volume is an open subject. Two main stages exist: determining topological connectivity of the mesh and its geometrical embedding. There are many interesting solutions proposed in various methods, which mostly rely on topological validity of the mesh. Nevertheless, the final quality of the mesh strongly depends on the step of mesh embedding, which has direct connection with geometry of the mesh and shapes of the elements. In order to generate hexahedral meshes topologically valid and geometrically qualitative, we propose a new guide for hexahedral meshing that combines both geometrical and topological aspects of hexahedral complex, which is to be generated. This guide includes topological construction of the spine of three-manifold and encoding with a matrix of incidence based on curvature information.