Two blossoming proofs of the Lane-Riesenfeld algorithm (Q884714)

The original proof of the Lane-Riesenfeld algorithm for knot insertion into uniform B-spline curves is based on the continuous convolution formula for the uniform B-spline basis functions. In the case of quadratic B-splines, a straightforward proof of this algorithm was given by \textit{R. Goldman} [Pyramid algorithms: A dynamic programming approach to curves and surfaces for geometric modeling. San Diego: Morgan Kaufmann Publishers/Academic Press (2002)] using the blossoming technique. The present paper provides two new blossoming proofs of the Lane-Riesenfeld algorithm for uniform B-splines of arbitrary degree. The authors point out that it is an open problem to find a blossoming proof of the extension of the Lane-Riesenfeld algorithm to knots in geometric progression.