Surface fitting to random data via constrained shaping

Given a random data set that covers a surface patch, a method is presented to fit a B-spline surface to the data. The surface fit can be an interpolating or an approximating surface, depending on the number of points involved. The general technique is to apply a base surface and to modify this surface, via constrained shaping, to achieve interpolation or approximation to a given tolerance. The base surface is either a bilinearly or a bicubically blended Coons patch, defined by the boundaries and any number of cross-derivatives. With appropriately chosen cross-derivatives, a smooth surface patch complex can be computed in which the individual patches interpolate and/or approximate, depending on the number of internal random points.