Shape-preserving \(C^1\) Hermite interpolants generated by a Gori-Pitolli subdivision scheme
type: Item
instance of: scholarly article
title: Shape-preserving \(C^1\) Hermite interpolants generated by a Gori-Pitolli subdivision scheme
zbMATH Open document ID: 1153.65013
author: Francesca Pelosi
author: P. Sablonnière
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-22T00:00:00Z
review text: The paper starts by recalling some basic properties of Gori-Pitolli (GP) B-splines (Section 2) and cubic GP B-splines (Section 3) [\textit{L. Gori} and \textit{F. Pitolli}, Rend. Mat. Appl., VII. Ser. 20, No.1--4, 305--322 (2000; Zbl 0989.65153); together with \textit{E. Santi}, Numer. Algorithms 28, No.1--4, 199--213 (2001; Zbl 0993.65157)]. Next (Section 4), the local Bernstein-Bezier representation of cubic GP B-splines is constructed. Section 5 is devoted to the description of the main properties of quadratic GP splines and polynomials, while in Section 6, the family of Hermite subdivision schemes depending on a parameter is described. This family contains as a particular case the cubic Hermite interpolants. Next, a monotone Hermite problem and a convex Hermite interpolation problem are studied. The authors purpose is to give algorithms for the construction of monotone interpolants to arbitrary nondecreasing data and also for the construction of convex interpolants to arbitrary convex data. These algorithms are illustrated by some examples.
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5315429
zbMATH Keywords: Refinable function
zbMATH Keywords: Interpolation
zbMATH Keywords: Shape preservation
zbMATH Keywords: Corner cuting
reviewed by: Dan Bărbosu
describes a project that uses: pchip
MaRDI profile type: Publication
full work available at URL: j.cam.2007.09.013
OpenAlex ID: W1964300072
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DOI: 10.1016/J.CAM.2007.09.013
description: scientific article; zbMATH DE number 5315429