Quality Improvement and Feature Capture in Hexahedral Meshes
Jason F. Shepherd, Claurissa J. Tuttle, Yongjie Jessica Zhang · 2006
Building high-quality quadrilateral/hexahedral meshes directly from volumetric data is hard. Existing algorithms for generating meshes from volumetric data are based on primal and dual isocontouring algorithms, and current research focuses on improving the quality of such meshes. Most techniques are based on isocontouring techniques, and work by generating a grid of hexahedra on the interior/exterior of an isosurface, and then adjusting the elements that lie on the boundary of the grid to fit the surface. As a result of the element adjustment, many of these elements lose their convexity, as measured by the scaled Jacobian metric. Recovering the convexity of these elements is difficult since the position of boundary vertices is restricted to the domain of the isosurface. In this paper, we propose a solution to this problem using insights obtained from the structure of the dual of a hexahedral mesh. Our solution is to add a sheet of hexes along the boundary, composed of well-shaped elements. The additional degrees of freedom provided by this sheet enables the optimization of the original poorly-shaped elements that are no longer on the boundary allowing for the creation of a high-quality mesh. An extra benefit of our technique is being able to capture sharp features, which is done by inserting multiple sheets. Our experimental results demonstrate the successful removal of all bad elements (i.e. those elements of the mesh that have a scaled Jacobian measure of less than 0.2) in a number of complex examples.