Geometric Hermite interpolation with Tschirnhausen cubics
type: Item
instance of: scholarly article
title: Geometric Hermite interpolation with Tschirnhausen cubics
zbMATH Open document ID: 0880.65003
DOI: 10.1016/S0377-0427(97)00066-6
author: D. S. Meek
author: D. J. Walton
published in: Journal of Computational and Applied Mathematics
publication date: 1998-01-22T00:00:00Z
review text: The authors consider the following Hermite interpolation problem: Given two distinct points in the plane, find a function that passes through these points and matches the (unit) tangent vectors there. The uniquely determined Tschirnhausen cubic that solves this Hermite problem is given explicitly. This solution is used to create a \(G^1\)-spline by pasting together segments of Tschirnhausen cubics. Moreover it is shown that if the Hermite data come from a sufficiently smooth function, then the approximation order of the Tschirnhausen cubic is four. The results are illustrated by a numerical example.
reviewed by: Guido Walz
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1043289
zbMATH Keywords: approximation error
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: Tschirnhausen cubic
zbMATH Keywords: numerical example
MaRDI profile type: Publication
cites work: High accuracy geometric Hermite interpolation
cites work: Q3995065
cites work: The conformal map \(z\to z^ 2\) of the hodograph plane
cites work: Q4881343
cites work: On \(G^ 2\) continuous interpolatory composite quadratic Bézier curves
cites work: Rational Approximations for the Fresnel Integrals
cites work: Q4278198
cites work: Approximation of discrete data by \(G^ 1\) arc splines
cites work: Approximating smooth planar curves by arc splines
cites work: Hermite interpolation with Tschirnhausen cubic spirals
cites work: Interpolation with piecewise quadratic visually \(C^ 2\) Bézier polynomials
cites work: A geometric characterization of parametric cubic curves
Wikidata QID: Q126804670
description: scientific article; zbMATH DE number 1043289