A two-point \(G^1\) Hermite interpolating family of spirals
type: Item
instance of: scholarly article
title: A two-point \(G^1\) Hermite interpolating family of spirals
zbMATH Open document ID: 1156.65016
author: D. S. Meek
author: D. J. Walton
published in: Journal of Computational and Applied Mathematics
publication date: 2008-11-20T00:00:00Z
review text: A one-parameter family of spirals that can match planar, two-point \(G^1\) Hermite data, called \(i\)-spiral [cf. \textit{H. Pottmann}, Comput. Aided Geom. Des. 12, No.~2, 175--192 (1995; Zbl 0872.65011)] is presented. These spirals can be used as an alternative to the biarc, which is also a one- parameter family of curves that can match two-point \(G^1\) Hermite data. It is also shown that there is a unique \(G^1\) Hermite interpolating spiral that passes through a given point in an allowable region. Some examples of use of these spirals are also given. The \(i\)-spiral has been used by \textit{T. N. T. Goodman} et al. [a paper submitted to Comput. Aided Geom. Des.] for \(G^2\) Hermite interpolation.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5370021
zbMATH Keywords: family of spirals
zbMATH Keywords: two-point Hermite interpolation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2007.12.027
OpenAlex ID: W1999421029
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DOI: 10.1016/J.CAM.2007.12.027
description: scientific article; zbMATH DE number 5370021