散乱数据曲面拟合的局部加权最小二乘插值方法及权函数的选择讨论

The Topic on Choice of Weighted Functions and Local Weighted Least-mean Square Method for Surface Interpolation to Scattered Data

本文首先用局部加权最小二乘法将三维空间内任意散乱数据点集均匀,再估计出立方体网格点上的偏导数值及混合偏导数值,最后仅用网格点数据进行快速光滑插值加密计算,从而可得到任意点处的函数值。通过对已知函数的随机数据点集进行计算,取得了令人满意的效果。同时,在最小二乘逼近过程中,本文提供了一种权函数,并与其它二种权函数进行分析比较,给出了各种情况下的误差。

In this article,a uniform grid data is firstly sampled from the scattered data in 3D space by local weighted least square mean method, then partial and mixed partial derivative value on the volume grid node position is esfiraated, finally the grid data are interpolated to be a global functional by smoothing and densifieafion a prior. We reported some satisfactory case results at the end of this article. Also, in the process of least square mean fitting, a best weighted function was adopted after compared with other two traditional weighted functions. We also presented the error in the case of varied inputted parameters.