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Aggressive tetrahedral mesh improvement. (English) Zbl 1238.65011
Brewer, Michael L. (ed.) et al., Proceedings of the 16th international meshing roundtable, Seattle, WA, USA, October 14–17, 2007. Berlin: Springer (ISBN 978-3-540-75102-1/hbk). 3-21 (2008).
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 \(31^\circ\) and \(149^\circ\), or (with a different objective function) between \(23^\circ\) and \(136^\circ\).
For the entire collection see [Zbl 1122.65002].

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
52A37 Other problems of combinatorial convexity
52B11 \(n\)-dimensional polytopes
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)