A multiresolution tensor spline method for fitting functions on the sphere

We present the details of a multiresolution method we proposed at the Taorm ina Wavelet Conference in 1993 ( see "L-spline wavelets" in Wavelets: Theor y, Algorithms, and Applications, C. Chui, L. Montefusco, and L. Puccio, eds ., Academic Press, New York, pp. 197-212) which is suitable for fitting fun ctions or data on the sphere. The method is based on tensor products of pol ynomial splines and trigonometric splines and can be adapted to produce sur faces that are either tangent plane continuous or almost tangent plane cont inuous. The result is a convenient compression algorithm for dealing with l arge amounts of data on the sphere. We give full details of a computer impl ementation that is highly efficient with respect to both storage and comput ational cost. We also demonstrate the performance of the method on several test examples.