16th International Meshing Roundtable
Seattle, Washington, U.S.A.
October 14-17, 2007
University of California at Berkeley
We present a tetrahedral mesh improvement schedule that usually creates
meshes whose worst tetrahedra have a level of quality substantially better than
those produced by any previous method for tetrahedral mesh generation or "mesh
clean-up." Our goal is to aggressively optimize the worst tetrahedra, with speed a
secondary consideration. Mesh optimization methods often get stuck in bad local optima
(poor-quality meshes) because their repertoire of mesh transformations is weak.
We employ a broader palette of operations than any previous mesh improvement
software. Alongside the best traditional topological and smoothing operations, we
introduce a topological transformation that inserts a new vertex (sometimes deleting
others at the same time). We describe a schedule for applying and composing these
operations that rarely gets stuck in a bad optimum. We demonstrate that all three
techniques-smoothing, vertex insertion, and traditional transformations-are substantially
more effective than any two alone. Our implementation usually improves
meshes so that all dihedral angles are between 31 degrees and 149 degrees, or (with a different
objective function) between 23 degrees and 136 degrees.
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