Spherical Harmonics Interpolatory Sampling

Abstract

If the data are localized, sampling problems on the sphere can be solved through application of methods designed for the two-dimensional Euclidean space. However, problems like the determination of an Earth’s Gravitational Model (EGM) involve essentially the entire surface of the sphere so that modeling of the data as arising in the two-space is no longer appropriate. Since there is no singularity-free mapping of the entire sphere to a bounded planar region, there is a need to develop coordinate-free approximation methods over the sphere itself.