Abstract:

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.

Key words:  radial basis function, scattered data, multiscale method