A new multiaffine approach to B-splines
type: Item
instance of: scholarly article
title: A new multiaffine approach to B-splines
zbMATH Open document ID: 0666.65011
DOI: 10.1016/0167-8396(89)90004-6
author: Hans-Peter Seidel
published in: Computer Aided Geometric Design
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 4090668
zbMATH Keywords: p-affine mappings
zbMATH Keywords: blossoming
zbMATH Keywords: B-splines
zbMATH Keywords: recurrence relations
zbMATH Keywords: algorithms
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: 0167-8396(89)90004-6
OpenAlex ID: W2058833320
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description: scientific article; zbMATH DE number 4090668