A new multiaffine approach to B-splines
The principle that polynomials of degree p and symmetric p-affine mappings are equivalent to each other is known as blossoming. \textit{L. Ramshaw} [Blossoming: A connect-the-dots approach to splines, Digital Systems Reserach Center, Palo Alto (1987); Bézier and B-splines as multiaffine maps, in Theoretical Foundations of Computer Graphics and CAD, Springer, New York, 757-776 (1987)] has recently introduced the principle for a study of Bézier and spline curves. This is motivated by the earlier works of \textit{P. de Casteljau} [Formes a poles (1986; Zbl 0655.41001)]. Unifying this approach and that given by \textit{C. de Boor} and \textit{K. Höllig} [see \textit{G. Farin} ed., Geometric Modelig Algorithms and New Trends, 21-27 (1987; Zbl 0636.53002)] the author directly applies the blossoming principle to the standard recurrence relations for B-splines. The basic algorithms for the theory of B-splines are derived with proofs that are shorter than the currently existing ones.
scientific article; zbMATH DE number 4090668