Intrinsic parametrization for approximation
type: Item
instance of: scholarly article
title: Intrinsic parametrization for approximation
zbMATH Open document ID: 0644.65011
DOI: 10.1016/0167-8396(88)90017-9
author: J. Hoschek
published in: Computer Aided Geometric Design
publication date: 1988-01-01T00:00:00Z
review text: Let \(P_ i\) \((i=1(1)n)\) be n given points. If this set of points is parametrized by a parameter \(t_ i\), the approximation curve \[ Y(t)=\sum^{n}_{i=0}b_ if_ i(t)\quad (t\in I,\quad I=[a,b])\quad (n+1<N) \] with prescribed basis functions \(f_ i\) is called optimal if the shortest distances between the points \(P_ i\) and the approximation curve Y(t) is minimized. An iterative Newton-like approach of intrinsic parametrization for the optimal approximation is proposed. The method is extended to optimal approximation surface of a given set of points \(P_{ik}\) parametrized by parameter values \((u_ i,v_ k)\).
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 4050843
zbMATH Keywords: curve approximation
zbMATH Keywords: Newton-like methods
zbMATH Keywords: approximation curve
zbMATH Keywords: intrinsic parametrization
zbMATH Keywords: optimal approximation surface
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
full work available at URL: 0167-8396(88)90017-9
OpenAlex ID: W2005907009
cites work: On the Influence of Parametrization in Parametric Interpolation
cites work: Approximate conversion of spline curves
cites work: A spline approximation of offset curves
description: scientific article; zbMATH DE number 4050843