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We present a unified approach to and a generalization of almost all known recursion schemes concerning B-spline functions. This includes formulas for the computation of a B-spline's values, its derivatives (ordinary and partial), and for a knot insertion method for B-spline curves. Furthermore, our generalization allows us to derive also some new relations for these purposes.

A unified approach to B-spline recursions and knot insertion, with application to new recursion formulas