Given a complex of vertices, constraining segments, and planar straight-line constraining facets in E3, with no input angle less than 90'. an algorithm presented herein can generate a conforming mesh of Delaunay tetrahedra whose circumradius-to-shortest edge ratios are no greater than two. The sizes of the tetrahedra can provably gr
Summary. 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• and 149• , or (with a different objective function) between 23• and 136• .
We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteed-quality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of anisotropic Voronoi diagrams of arbitrary dimensionality-most notably circumstances in which a site can see its entire Voronoi cell. In two dimensions, the anisotropic Voronoi diagram dualizes to a triangulation under these same circumstances. We use these properties to develop an algorithm for anisotropic triangular mesh generation in which no triangle has an angle smaller than 20 • , as measured from the skewed perspective of any point in the triangle.
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