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An analysis of simplex shape measures for anisotropic meshes

机译：各向异性网格的单纯形量度分析

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This paper analyses and generalises several simplex shape measures documented in the literature and currently used for mesh adaptation and mesh optimisation. It first summarises important properties of simplices and their degeneration in Euclidean space. Different simplex shape measures are then defined and validated according to a validity criterion. The shape measures are generalised to Riemannian spaces in order to extend their use to anisotropic meshes. They are then analysed and compared using complementary approaches: a visualisation method helping to show their regularity, some theoretical relations establishing their equivalence, and a discussion on the evaluation of the global quality of a mesh. Conclusions are drawn on the choice of a simplex shape measure to guide mesh optimisation.
机译：本文分析并归纳了文献中记录的几种单形形状度量，这些度量目前用于网格自适应和网格优化。首先总结了单纯形的重要性质及其在欧几里得空间中的退化。然后根据有效性标准定义和验证不同的单纯形形状度量。形状度量被推广到黎曼空间，以便将其应用扩展到各向异性网格。然后使用补充方法对它们进行分析和比较：一种有助于显示其规则性的可视化方法，建立其等效性的一些理论关系以及关于网格整体质量评估的讨论。在选择单纯形形状度量以指导网格优化时得出结论。

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