Degree reduction of B-spline curves Original Research Article

In this paper, we propose the generalized B divided difference, with which the (k−1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k−2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-spline curves are proposed using the constrained optimization methods.