Evaluation algorithm and knot insertion algorithm for B-spline surfaces

A new representation to B-splines and the concept of generalized B-spline are introduced in this paper by considering the null space of a second order constant coefficient differential operator and the unique solution to an initial-value problem.The evaluation algorithm and knot insertion algorithm for generalized B-splines are also presented,and it is extended to surfaces by taking polynomial spline surface for example.The numerical examples showed that the algorithms are valid to both curves and surfaces.