四面体模型质量度量准则及其之间的关系

Relationship between quality measures criterion of tetrahedral mesh

四面体模型质量度量准则是评价网格模型质量的标准,但长期以来,对四面体单元质量的度量和评价并没有公认的标准。因此,本文对常用的四面体网格模型质量度量准则进行总结,并从理论上证明了各质量度量准则之间的关系,同时通过实验分析各质量度量准则之间的这种关系是否成立。分析认为在优化四面体模型时,不能仅仅采用某一种度量标准来评价网格的质量,应根据不同的四面体类型,采用不同的准则或将几种准则联合起来对四面体模型质量进行度量。

The quality measures criterion of tetrahedral model have been used to assess applicability. However,it lacks a recognized standard for such measures. This paper reviews the existing quality measures criterion in tetrahedral mesh generation and presents a rigorous proving of the relationship among various measures. The derived relationship among quality measures is experimented numerically. It concludes that in the optimization of a tetrahedral model,a single evaluation is not sufficient to ensure the quality. Instead,a hybrid （combined with multiple measures） method may be used to evaluate the quali- ty of tetrahedral mesh model.