A Hierarchical Approach to 3D Scattered Data Interpolation with Radial Basis Functions

Based on globally supported radial basis functions, this paper presents a hierarchical approach to 3D scattered data interpolation. Given a scattered data set distributed along a surface, we first obtain a sparse approximation of the scattered data set by filtering the scattered data with two different steps, and identify the characteristic points by the measurements of bounding cube and the distance between the points and the interpolating surface. Then using multi-level hierarchy of point sets, the accuracy of interpolating surface can be gradually improved. On the basis of effective selection of the off-surface normal points, the number of constraint conditions is reduced, and trivial solutions of the interpolating equations can be avoided. Above all, we can identify the characteristic points in the model with less data points, and obtain interpolating surface with higher fitting accuracy by solving equations with lower order. The numerical experiments show that the method is more efficient and easy to implement.