High accurate rational approximation of parametric curves
type: Item
instance of: scholarly article
title: High accurate rational approximation of parametric curves
zbMATH Open document ID: 0781.65008
DOI: 10.1016/0167-8396(93)90043-3
published in: Computer Aided Geometric Design
publication date: 1993-10-25T00:00:00Z
review text: The aim of this paper is to give a more precise definition of the notion of approximation order and then to prove that order eight can be attained by rational cubics instead of polynomial ones. This way a third order contact can be attained at both endpoints. It is shown that this rises the approximation order up to eight. A detailed analysis of the asymptotic behavior (as the segment's length tends to zero) is given. It leads to a purely geometric condition for the existence of that rational cubic approximant.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 431240
zbMATH Keywords: rational approximation
zbMATH Keywords: parametric curves
zbMATH Keywords: approximation order
zbMATH Keywords: order eight
zbMATH Keywords: rational cubics
zbMATH Keywords: third order contact
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: geometric condition
author: Wendelin L. F. Degen
reviewed by: R. S. Dahiya
MaRDI profile type: Publication
full work available at URL: 0167-8396(93)90043-3
OpenAlex ID: W2082405142
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description: scientific article; zbMATH DE number 431240