一种基于模糊相似度的球面格网几何变形评价指标

An Geometry Deformation Evaluation Index of the Spherical Discrete Grid Based on the Fuzzy Similarity

全球离散格网模型的不确定性,包括格网单元的几何变形及空间分布问题,是制约其广泛应用的主要因素之一。该文从三角形相似的角度出发,构造了球面三角格网的模糊相似度评价指标,以此对球面四元三角格网模型的几何变形特征及其收敛性进行分析评价,并给出了格网单元变形在八面体单元和全球区域的位置分布规律。最后,与传统评价指标进行对比实验,结果表明:该指标不但能够反映剖分模型的几何变形分布,而且还具有两大优势:1)能够同时反映剖分单元的几何形状和面积变形,可作为格网形状和面积变形的综合评价指标;2)该指标是相对于不同递归层次上理想剖分单元的绝对变形量,相比其他统计量,更便于表达不同层次间的格网几何变形。

The uncertainty problem of discrete global grid models,including geometry deformation and spatial distribution,has been one of the restricting factors in its broad applications.In this paper,a fuzzy similarity evaluation index which based on the principle of similar triangles is constructed,and the geometry deformation characteristics and the convergence property of QTM（Quaternary Triangular Mesh）grid are analyzed using the above index.Meanwhile,the location distribution rules of the grid deformation on the octahedral unit and sphere are also presented.Finally,the contrast experiment with the traditional evaluation index（such as the compactness index）is given.The results show that the index not only can reflect the geometry deformation distribution of subdivision models,but also has two advantages just as follows.Firstly,it can reflect both the shape and area deformation of subdivision units,so it can be used as a synthesized evaluable index for the grid′s shape and size.Secondly,the index is an absolute deformation relative to the ideal subdivision units in different recursion levels,and compared with other statistics,it is easier to express the grid geometry deformation in different levels.