Nonlinear subdivision schemes on irregular meshes
type: Item
instance of: scholarly article
title: Nonlinear subdivision schemes on irregular meshes
zbMATH Open document ID: 1247.65018
author: Andreas Weinmann
published in: Constructive Approximation
publication date: 2010-06-09T00:00:00Z
review text: The convergence and the \(C^{1}\) smoothness of nonlinear subdivision rules for irregular meshes are studied. First of all, a class of nonlinear schemes \(T\) related to a class of linear schemes is defined by identifying a proximity condition. The case when the existence of such a proximity condition implies the convergence of the nonlinear scheme for dense enough input data is emphasized. The \(C^{1}\) smoothness of the nonlinear limit function in the vicinity of an extraordinary point over \textit{U. Reif}'s [Comput. Aided Geom. Des. 12, No.~2, 153--174 (1995; Zbl 0872.65007)] characteristic parametrization is obtained. The manner in which subdivision in the geometric setting can be used to generate manifold-valued smooth functions on smooth 2D manifolds comes as an application.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 53A99
Mathematics Subject Classification ID: 58C07
zbMATH DE Number: 5719083
zbMATH Keywords: nonlinear subdivision
zbMATH Keywords: extraordinary point
zbMATH Keywords: irregular mesh
MaRDI profile type: Publication
full work available at URL: s00365-009-9063-1
OpenAlex ID: W2017499683
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DOI: 10.1007/S00365-009-9063-1
description: scientific article; zbMATH DE number 5719083