Constructing Cubic Splines on the Sphere

Abstract

A method to approximate functions defined on a sphere using Tensor Product cubic B-splines is presented here. The method is based on decomposing the sphere into six identical patches obtained by radially projecting the six faces of a circumscribed cube onto the spherical surface. The theory of univariate splines has been generalized in different forms to functions of several variables. Among these extensions the tensor product splines are the easiest to handle. Although the tensor product splines are restricted to rectangular domains rendering their applicability limited they are extremely efficient compared to other surface approximation techniques which are far more complicated and hence computationally less attractive.