Interpolatory blending net subdivision schemes of Dubuc-Deslauriers type
type: Item
instance of: scholarly article
title: Interpolatory blending net subdivision schemes of Dubuc-Deslauriers type
zbMATH Open document ID: 1280.65023
author: Lucia Romani
author: Costanza Conti
author: Nira Dyn
published in: Computer Aided Geometric Design
publication date: 2012-12-04T00:00:00Z
review text: The authors present a general construction of families of interpolatory net subdivision schemes generating limit bivariate functions by repeated refinements of nets of univariate functions. In this construction, the refined nets are obtained by sampling on refined grids Gordon blending interpolation to the coarser nets. For a given scheme, the blending function in the Gordon interpolants is the same at all refinement levels, and has properties which relates it to a corresponding Dubuc-Deslauriers interpolatory scheme [\textit{G. Deslauriers} and \textit{S. Dubuc}, Constructive Approximation 5, No. 1, 49--68 (1989; Zbl 0659.65004)] refining points. The main results in this paper show that these schemes converge to limit functions having the same integer smoothness as the limits of the corresponding Dubuc-Deslauriers schemes using the properties of the blending functions together with the general analysis tools by \textit{C. Conti} and \textit{N. Dyn} [J. Comput. Appl. Math. 236, No. 4, 461--475 (2011; Zbl 1235.65020)]. These results are proved for net subdivision schemes corresponding to the first 84 members of the Dubuc-Deslauriers family, and conjectured for the rest. A concrete example of a family of piecewise polynomial blending functions is considered, together with the corresponding family of net subdivision schemes.
reviewed by: Wang-Q Lim
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 6112271
zbMATH Keywords: interpolatory net subdivision
zbMATH Keywords: Dubuc-Deslauriers interpolatory subdivision
zbMATH Keywords: blending
zbMATH Keywords: proximity
zbMATH Keywords: controllability
zbMATH Keywords: convergence
zbMATH Keywords: smoothness
zbMATH Keywords: Z-splines
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cagd.2012.08.001
OpenAlex ID: W2045600219
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DOI: 10.1016/J.CAGD.2012.08.001
description: scientific article; zbMATH DE number 6112271