权函数支持域尺寸和场节点间距对移动最小二乘法拟合精度的影响

移动最小二乘法作为一种拟合插值方法,当其基函数采用非正交基时,移动最小二乘法中采样点支持域尺寸、节点间距大小将影响到力矩矩阵的可逆性.力矩矩阵可逆是移动最小二乘法拟合成功的必要条件.因此如何合理地选取节点间距及采样点支持域尺寸以确保力矩矩阵可逆,成为移动最小二乘法应用过程中的一个重要环节.其值的选取也是移动最小二乘法主要误差来源之一.理论上,至今仍无法推导出采样点支持域尺寸及节点间距最优取值.实践中,可通过拟合实验寻找支持域尺寸、节点间距的变化规律,给出具有建议性的取值范围.本文在节点均匀分布的情况下,对其变化规律进行研究并提出了可以保证插值精度的支持域尺寸、节点间距的建议取值.

Influence of Support Region of Weight Function and Node Spacing on the Fitting Precision of MLS

As a fitting and interpolation method, moving least-square method （MLS） has many advantages such as local surface fitting method and high-precision, and has been widely used. When basis function uses the non-orthogonal bases, the size of support region of the sample points of MLS, and the size of the node spacing of MLS will affect the reciprocity of matrix moment. This reciprocity is a necessary condition for the successful fitting. How to reasonably select the node spacing and the size of support region of the sample points to ensure the reciprocity of matrix moment has become an important part in the application process of fitting and interpolation of MLS. The selection of their values is one of the chief sources of error of MLS. Unfortunately, the support region of the sample points and the optimal value of the node spacing have not been deduced in theory. In practice, it is possible to find the transformation rule by fitting experiment and propose the suggested values. The transformation rule is about the size of support region of the sample points and the node spacing. Under the condition of a uniform distribution, and according to the study of the change rule, the suggested values which can ensure the accuracy of the interpolation are proposed in this paper.