Extremal Interpolation of Convex Scattered Data in R3 Using Tensor Product Bezier Surfaces

We consider the problem of extremal interpolation of convex scattered data in R-3 and propose a feasible solution. Using our previous work on edge convex minimum L-p-norm interpolation curve networks, 1 < p <= infinity, we construct a bivariate interpolant F with the following properties: (i) F is G(1)-continuous; (ii) F consists of tensor product Bezier surfaces (patches) of degree (n, n) where n is an element of N, n >= 4, is priorly chosen; (iii) The boundary curves of each patch are convex; (iv) Each B ezier patch satisfies the tetra-harmonic equation Delta F-4 = 0. Hence F is an extremum to the corresponding energy functional.