Hexahedral mesh generation via the dual

Abstract

Wereview the spatial twist continuum (STC), away of viewing the dual of a hexahedral (cubic) mesh as a simple non-degenerate arrangement of surfaces. Given a quadrilateral mesh of a closed surface, the STC gives insight into how the interior volume can be filled with hexahedra that respect the surface mesh. We review a hexahedral mesh generation heuristic called Whisker Weaving. Whisker Weaving incrementally builds the STC in an advancing front fashion. Although computational geometry has traditionally focussed on triangular and tetrahedral meshes, quadrilateral and hexahedral meshes are often considered to be more valuable for finite element analysis. The CUBIT environment being developed at Sandia National Laboratories is a suite of quadrilateral and hexahedral meshing tools. Whisker Weaving is one of these tools. CUBIT is used directly by practicing analysts, and is incorporated into a number of commercial mesh generation codes. 1 Spatial Twist Continuum We first describe the spatial twist continuum (STC) for a two-dimensional mesh and then generalize to three dimensions. It is possible to generalize to arbitrary dimensions. Consider the dual of a quadrilateral mesh. We use dual in the same sense as the Voronoi diagram is the dual of a Delaunay triangulation, except that here we concentrate on the graph properties of the dual and the geometric embedding is arbitrary. Each vertex of the dual has edge-degree four. As such, each vertex can be considered as the intersection of two curves as in Figure 1 left. Opposite edges at each vertex are identified as belonging to the same curve. In this way, the dual of the mesh can be considered as an arrangement of curves as in Figure 1 right. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association of Computing Machinery,To copy otherwise, or to republish, requires a fee and/or specific permission. 11th Computational Geometry, Vancouver, B.C. Canada @ 1995 ACM 0-89791 -724 -3/95/0006 ...$3.50 Figure