THE MAP AND BLEND SCATTERED DATA INTERPOLANT ON A SPHERE

The map and blend technique constructs a function defined over the sphere that interpolates to a discrete sample of measurements at arbitrary locations on the sphere. This technique consists of two different mappings of the sphere to planar domains, solving two corresponding scattered data interpolation problems on the planar domains, and then the interpolant on the sphere is formed by blending these two planar interpolants. If the user has software for solving the scattered data interpolation problem on a planar domain, only a small programming effort is needed to implement the map and blend interpolant on the sphere. Although any interpolant to scattered data on a planar domain can be used in our general technique, we use the multiquadric radial basis method.