中文摘要：

对仅从剖分单元的形状和面积的变形研究,不能完全表达格网模型几何稳定性作了分析,并提出了从研究格网结点空间分布均匀性在多分辨率剖分过程中的变化出发,分析格网系统稳定性的研究思路,并选择能直接反映格网结点分布特性的四个统计量作为格网结点均匀性的评价指标。对几种离散格网系统的几何稳定性进行比较和评价,分析了不同格网生成方式对稳定性的影响,最后,在此研究基础之上,提出了进一步研究的工作方向。

英文摘要：

The geometrical stability of discrete grid systems couldn’t be represented completely only by studying the distortion characteristics such as area and shape of recursive partitions of the discrete grid systems. To study the spatial distributing homogenization of the grid nodes at each level of recursive subdivision is a new method to analyse the geometrical stability of discrete grid systems. Four statistical variables are selected to evaluate the homogenization of the grid nodes. The work of comparing the stability of several discrete grid systems is done and the factors which can influence the stability are also analysed. Finally,the direction of the study work in the future is identified.