Spherical interpolation using the partition of unity method: an efficient and flexible algorithm

An efficient and flexible algorithm for the spherical interpolation of large scattered data sets is proposed. It is based on a partition of unity method on the sphere and uses spherical radial basis functions as local approximants. This technique exploits a suitable partition of the sphere into a number of spherical zones, the construction of a certain number of cells such that the sphere is contained in the union of the cells, with some mild overlap among the cells, and finally the employment of an optimized spherical zone searching procedure. Some numerical experiments show the good accuracy of the spherical partition of unity method and the high efficiency of the algorithm.