基于径向基函数的3D散乱数据插值多尺度方法

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.

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

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...