Degree raising for splines
type: Item
instance of: scholarly article
title: Degree raising for splines
zbMATH Open document ID: 0621.41009
DOI: 10.1016/0021-9045(86)90059-6
author: Tom Lyche
author: Elaine Cohen
author: Larry L. Schumaker
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The authors study the problem of converting an mth order B-spline expansion into an equivalent \((m+1)th\) order B-spline expansion. Let a spline \(s=\sum^{n}_{i=1}c_ iN^ m_ i\) be given, where \(\{N^ m_ i\}^ n_ 1\) are normalized B-splines of order m associated with a knot sequence \(\tau_ 1,...,\tau_ k\) of multiplicities \(m_ 1,...,m_ k\). It is shown that s can be represented in the form \(s=\sum^{\tilde n}_{j=1}\tilde c_ j\tilde N_ j^{m+1}\), where \(\{\tilde N_ j^{m+1}\}_ 1^{\tilde n}\) are normalized B-splines of order \(m+1\) associated with the knot sequence \(\tau_ 1,...,\tau_ k\) of multiplicities \(m_ 1+1,...,m_ k+1\). Moreover, formulae for computing the coefficients \(\tilde c_ 1,...,\tilde c_{\tilde n}\) are derived. By using discrete B-splines a recursion relation is established which plays an important role in computing these coefficients. It is pointed out that these results can be used in computer-aided design to obtain flexibility in manipulating the shape of a given spline curve by degree raising.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 4006894
zbMATH Keywords: B-spline expansion
zbMATH Keywords: computer-aided design
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90059-6
OpenAlex ID: W1965691524
cites work: Q4112369
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description: scientific article; zbMATH DE number 4006894