A B-spline curve extension algorithm

B-spline curve extension is an important operation in computer aided design systems. In this paper, we present a new extension algorithm for B-spline curves. The algorithm uses curve unclamping to generate a uniform B-spline curve segment from the original curve and gradually extends the segment to pass through every target point. Algorithms of uniform B-spline curves are used such that our algorithm has a low time cost and can easily handle arbitrary-order derivative constraints at the target points. Generalization for non-uniform rational B-spline curve extension is also discussed, and examples show the efficiency of our method.