Curve and Surface Generation and Refinement Based on a High Speed Derivative Algorithm

We propose an efficient algorithm for the refinement of curves and surfaces using simple knot B-splines. We develop a high speed algorithm for the computation of the rth derivative of an rth order spline and demonstrate that the inverse of this algorithm leads to an efficient refinement algorithm which is an order of magnitude faster than the well known Oslo algorithm. We show how the high speed derivative algorithm can also be used to directly generate spline curves and surfaces much more efficiently than linear combination algorithms and forward differencing.