Constrained C/sup 1/ piecewise bicubic Bezier surface interpolation

The construction of a C/sup 1/ piecewise bicubic Bezier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.