Topological and geometrical properties of hexahedral meshes

摘要

Over the years, there have been a number of practical studies with working definitions of 'mesh' as related to computational simulation, however, there are only a few theoretical papers with formal definitions of mesh. Algebraic topology papers are available that define tetrahedral meshes in terms of simplices. Algebraic topology and polytope theory has also been utilized to define hexahedral meshes. Additional literature is also available describing particular properties of the dual of a mesh. In this paper, we give several formal definitions in relation to hexahedral meshes and the dual of hexahedral meshes. Our main goal is to provide useful, understandable and minimal definitions specifically for computer scientists or mathematicians working in hexahedral meshing. We also extend these definitions to some useful classifications of hexahedral meshes, including definitions for 'fundamental' hexahedral meshes and 'minimal' hexahedral meshes.