Planar cubic \(G^{1}\) interpolatory splines with small strain energy
type: Item
instance of: scholarly article
title: Planar cubic \(G^{1}\) interpolatory splines with small strain energy
zbMATH Open document ID: 1214.65005
author: Gašper Jaklič
author: Emil Žagar
published in: Journal of Computational and Applied Mathematics
publication date: 2011-03-09T00:00:00Z
review text: A classical problem of the construction of a cubic \(G^1\) continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. The tangent directions are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally. The spline is regular, cusp-, loop- and fold-free. Numerical examples demonstrate effectiveness of the considered method.
reviewed by: Mykhaylo Pahirya
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5863174
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: spline curve
zbMATH Keywords: minimization
zbMATH Keywords: strain energy
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2010.11.025
OpenAlex ID: W2147107998
cites work: A practical guide to splines.
cites work: Q3364412
cites work: Choosing nodes in parametric curve interpolation
cites work: High accuracy geometric Hermite interpolation
cites work: High order approximation method for curves
cites work: Geometric Hermite interpolation with maximal order and smoothness
cites work: A general framework for high-accuracy parametric interpolation
cites work: On Geometric Interpolation by Polynomial Curves
cites work: On geometric interpolation by planar parametric polynomial curves
cites work: Geometric interpolation by planar cubic \(G^{1}\) splines
cites work: On geometric interpolation of circle-like curves
cites work: Shape-Preserving Interpolation by Parametrically Defined Curves
cites work: Shape preserving C2 cubic spline interpolation
cites work: Convexity-preserving interpolatory parametric splines of non-uniform polynomial degree
cites work: Piecewise \(C^ 1\)-shape-preserving Hermite interpolation
cites work: Shape-preserving interpolants with high smoothness
cites work: A general scheme for shape preserving planar interpolating curves
cites work: On the deviation of a parametric cubic spline interpolant from its data polygon
cites work: Note on curve and surface energies
cites work: Geometric Hermite curves with minimum strain energy
DOI: 10.1016/J.CAM.2010.11.025
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description: scientific article; zbMATH DE number 5863174