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A new multiaffine approach to B-splines. (English) Zbl 0666.65011
The principle that polynomials of degree p and symmetric p-affine mappings are equivalent to each other is known as blossoming. 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 P. de Casteljau [Formes a poles (1986; Zbl 0655.41001)]. Unifying this approach and that given by C. de Boor and K. Höllig [see 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.
Reviewer: H.P.Dikshit

MSC:
65D07 Numerical computation using splines
41A15 Spline approximation
65D15 Algorithms for approximation of functions
65D05 Numerical interpolation
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