Fitting scattered data on sphere-like surfaces using spherical splines

Spaces of polynomial splines defined on planar triangulations are very useful tools for fitting scattered data in the plane. Recently, [4, 5], using homogeneous polynomials, we have developed analogous spline spaces defined on triangulations on the sphere and on sphere-like surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and fitting methods. Here we examine some of the more interesting ones is detail. For interpolation, we discuss macro-element methods and minimal energy splines, and for fitting, we consider discrete least squares and penalized least squares.