Investigations of a Functional Version of a Blending Surface Scheme for Regular Data Interpolation

This paper describes an implementation and tests of a blending scheme for regularly sampled data interpolation, and in particular studies the order of approximation for the method. This particular implementation is a special case of an earlier scheme by Fang for fitting a parametric surface to interpolate the vertices of a closed polyhedron with n-sided faces, where a surface patch is constructed for each face of the polyhedron, and neighbouring faces can meet with a user specified order of continuity. The specialization described in this paper considers functions of the form z=f(x,y) with the patches meeting with C2 continuity. This restriction allows for investigation of order of approximation, and it is shown that the functional version of Fang's scheme has polynomial precision.