基于径向基函数的3D散乱数据插值多尺度方法

A Multi-scale Approach to 3D Scattered Data Interpolation Based on Radial Basis Function

提出一种新的用径向基函数插值3D散乱数据的多尺度方法.对于给定分布在曲面上的散乱数据点,首先通过空间划分形成一个粗糙到完美的分层点集;对于给定的控制误差,先在粗糙层对点集进行插值,再对每个分层上的点集进行插值,将其作为对前一层得到的插值函数的弥补.数值试验结果表明,该方法可以利用较少的采样点达到较高的逼近精度,并且算法比较容易实现.

We proposed a hierarchical approach to 3D scattered data interpolation based on radial basis function. Given a scattered point distributed along a surface, we first used spatial down sampling to construct a coarse-to-fine hierarchy of point sets. Given a controlled error, then we interpolated the sets starting from the coarsest level. We interpolated a point set of the hierarchy, as an offsetting of the interpolating function computed at the previous level. According to our numerical experiments, our algorithm can attain to a higher approximation precision only using a less number of points, and the implementation of algorithm is very easily.