Quality Improvement and Boolean-Like Cutting Operations in Hexahedral Meshes.

In this paper, we propose a solution to improving the quality of hexahedral meshes derived from volumetric data using insights obtained from the structure of the dual of a hexahedral mesh. Our solution is to add a layer of hexes along the boundary, composed of well-shaped elements. The additional flexibility provided by this layer enables the optimization of the original poorly-shaped elements that are no longer on the boundary allowing for creation of a high-quality hexahedral mesh while maintaining a conformal mesh on both sides of the inserted layer. An extra benefit of our technique is being able to capture sharp features using a Boolean-like cutting operation and inserting multiple layers to maintain the high quality of the hexahedral mesh. 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.