Shape-preserving approximation of spatial data
type: Item
instance of: scholarly article
title: Shape-preserving approximation of spatial data
zbMATH Open document ID: 1045.65010
DOI: 10.1023/A:1025803122254
author: Francesca Pelosi
author: Paolo Costantini
published in: Advances in Computational Mathematics
publication date: 2004-03-15T00:00:00Z
review text: The authors combine the approach of \textit{P. Costantini} and \textit{F. Pelosi} [Numer. Algorithms 27, 237--264 (2001; Zbl 1079.65018)] with the results of \textit{P. Costantini} and \textit{C. Manni} [Adv. Comput. Math. 18, No. 1, 41--63 (2003; Zbl 1018.65017)] and obtain \(C^3\) shape-preserving splines, approximating an ordered set of spatial data. First, the shape of the data is defined and a precise formulation of the shape constraints is provided. Next, the B-splines like basis are computed. These approximating splines satisfy boundary conditions. The precise statement of the best approximation problem and the analysis of asymptotic properties of the splines are also provided. Algorithms for global and semilocal shape-preserving approximation are presented. Finally, some graphical examples are presented.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 2057581
zbMATH Keywords: shape preserving interpolation
zbMATH Keywords: parametric curves
zbMATH Keywords: splines
zbMATH Keywords: graphical examples
zbMATH Keywords: best approximation
zbMATH Keywords: tension property
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: a:1025803122254
OpenAlex ID: W126449241
description: scientific article; zbMATH DE number 2057581