Modified form of binary and ternary 3-point subdivision schemes
type: Item
instance of: scholarly article
title: Modified form of binary and ternary 3-point subdivision schemes
zbMATH Open document ID: 1198.65042
author: Shahid S. Siddiqi
author: Kashif Rehan
published in: Applied Mathematics and Computation
publication date: 2010-05-11T00:00:00Z
review text: A modification of both a binary 3-point approximating subdivision scheme and a ternary 3-point approximating subdivision scheme is presented. The modification lies in an introduction of a tension parameter which generates a family of \(C^1\) limiting curves in case of the binary 3-point scheme and \(C^1\) and \(C^2\) limiting curves in case of the ternary 3-point scheme. After the introduction, the analysis of the modified binary and ternary 3-point approximating subdivision scheme is presented. Then, many examples of subdivision results for both open and closed curves are given to show the usefulness of the suggested modification and the role of the introduced tension parameter. The obtained results can be used in many areas of computer aided geometric design when generating smooth shapes of curves or surfaces through subdivision techniques.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 5707077
zbMATH Keywords: subdivision scheme
zbMATH Keywords: subdivision curve
zbMATH Keywords: subdivision surface
zbMATH Keywords: smoothness
zbMATH Keywords: binary 3-point scheme
zbMATH Keywords: ternary 3-point scheme
zbMATH Keywords: computer aided geometric design
MaRDI profile type: Publication
full work available at URL: j.amc.2010.01.115
OpenAlex ID: W2074932484
cites work: An interpolating 4-point \(C^{2}\) ternary non-stationary subdivision scheme with tension control
cites work: Sur une courbe plane
cites work: Symmetric iterative interpolation processes
cites work: Q5702287
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DOI: 10.1016/J.AMC.2010.01.115
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description: scientific article; zbMATH DE number 5707077