Blossoming and knot insertion algorithms for B-spline curves (Q750080)

Blossoming means replacing a degree n polynomial in one variable by an equivalent symmetric polynomial in n variables where each new variable appears only to the first power. In this paper the blossoming technique is used to provide elementary derivations of knot insertion algorithms for B-spline curves. The author presents a new more efficient version of the Oslo knot insertion algorithm [see \textit{E. Cohen}, \textit{T. Lyche} and \textit{R. Riesenfeld}, Computer Graphics and Image Processing 14(2), 87-111 (1980)]. It is shown that this version is as fast and requires exactly the same number of computations as Boehm's knot insertion algorithm.