An interpolating 6-point \(C^2\) non-stationary subdivision scheme
type: Item
instance of: scholarly article
title: An interpolating 6-point \(C^2\) non-stationary subdivision scheme
zbMATH Open document ID: 1171.65010
author: Sunita Daniel
author: P. Shunmugaraj
published in: Journal of Computational and Applied Mathematics
publication date: 2009-06-25T00:00:00Z
review text: An interpolating 6-point \(C^2\) non-stationary scheme for generating smooth curves and surfaces from discrete sets of control points is investigated. The considered interpolating scheme is a particular member of a family of approximating subdivision schemes that generate piecewise exponential polynomials and can be converted into interpolating schemes. The presented scheme is able to reproduce important trigonometric and transcendental curves, in particular circle, ellipse and cardioid. The outstanding properties of the considered scheme are demonstrated and a wide comparison with some known interpolating schemes is presented. Many examples of smooth curves generated by different interpolating schemes are shown, too. The conclusion from this paper can be used in computer graphics and geometric modelling of both, curves and surfaces, therefore the schemes for generating curves can be considered as the basic tools for the design of schemes for generating surfaces.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5570565
zbMATH Keywords: Interpolation
zbMATH Keywords: \(C^2\) continuity
zbMATH Keywords: subdivision
zbMATH Keywords: non-stationary subdivision
zbMATH Keywords: convergence
zbMATH Keywords: curves
zbMATH Keywords: surfaces
zbMATH Keywords: computer graphics
zbMATH Keywords: geometric modelling
MaRDI profile type: Publication
full work available at URL: j.cam.2008.11.006
OpenAlex ID: W183873540
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DOI: 10.1016/J.CAM.2008.11.006
description: scientific article; zbMATH DE number 5570565