Extremal Scattered Data Interpolation in R~3 Using Triangular Bezier Surfaces

摘要

We consider the problem of extremal scattered data interpolation in R~3. Using our previous work on minimum L_2-norm interpolation curve networks, we construct a bivariate interpolant F with the following properties: (ⅰ) F is G~1-continuous, (ⅱ) F consists of triangular Bezier surfaces, (ⅲ) each Bezier surface satisfies the tetra-harmonic equation Δ~AF = 0. Hence F is an extremum to the corresponding energy functional. We also discuss the case of convex scattered data in R~3.