A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere

We present the details of a multi-resolution method which we proposed in Taormina in 1993 (see [6]) which is suitable for fitting functions or data on the sphere. The method is based on tensor products of polynomial splines and trigonometric splines, and produces surfaces which are tangent plane continuous. The result is a convenient compression algorithm for dealing with large amounts of data on the sphere. We give full details of a computer implementation which is highly efficient with respect to both storage and computational cost. We also demonstrate the performance of the method on two typical test examples.