Dimension elevation for Chebyshevian splines
type: Item
instance of: scholarly article
title: Dimension elevation for Chebyshevian splines
zbMATH Open document ID: 1216.65016
author: Marie-Laurence Mazure
published in: Numerical Algorithms
publication date: 2011-01-28T00:00:00Z
review text: The author deals with the dimension elevation problem for Chebyshevian splines which consists in increasing the knot multiplicity -- a Chebyshevian version of the classical degree elevation process for a polynomial spline. The increasing of the degree for a polynomial spline is motivated by gaining more flexibility possibilities for parametric curves by adding \(q+1\) degrees of freedom, \(q\) being the number of joints. The problem of how to obtain the new poles from the initial ones has been solved. In case of Chebyshevian splines, the author describes the original spline space based on a given extended Chebyshevian space as embedded in a larger one (dimension of the new extended Chebyshevian space is increased by one). Starting from this point, the author proposes some methods to compute new poles of any spline in the original spline space in terms of its initial poles.
reviewed by: Nicoleta Breaz
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 5842759
zbMATH Keywords: degree elevation
zbMATH Keywords: extended Chebyshev space
zbMATH Keywords: Chebyshevian splines
zbMATH Keywords: dimension elevation
zbMATH Keywords: blossoms
zbMATH Keywords: knot multiplicities
zbMATH Keywords: parametric curves
zbMATH Keywords: poles
MaRDI profile type: Publication
full work available at URL: s11075-010-9369-x
OpenAlex ID: W2056703476
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DOI: 10.1007/S11075-010-9369-X
description: scientific article; zbMATH DE number 5842759