An efficient algorithm for generating B-spline interpolation curves and surfaces from B-spline approximations

A useful and simple algorithm is presented for interactively generating B-spline interpolation curves and surfaces from B-spline approximation solutions. The difference between the data points and the B-spline approximation is used to modify the control vertices in order to generate a succession of B-spline approximations which converge rapidly to the interpolation solution. The intermediate B-spline approximations can be viewed interactively and the most appropriate solution selected for a particular application.