Some remarks on \(V^ 2\)-splines
type: Item
instance of: scholarly article
title: Some remarks on \(V^ 2\)-splines
zbMATH Open document ID: 0598.41015
DOI: 10.1016/S0167-8396(85)80007-8
published in: Computer Aided Geometric Design
publication date: 1985-01-01T00:00:00Z
review text: Let X(t) be a plane curve. Differentiation with respect to arc length will be denoted by a prime ' while differentiation with respect to an arbitrary parameter will be denoted by a dot \({}^.\). It is shown that X(t) is visually \(C^ 2\) if and only if there is a function v(t) depending on the parameterization t(s) such that \(\ddot X(t+)-\ddot X(t- )=v(t)\dot X(t).\) This is applied to derive the defining equations of the interpolatory \(\nu\)-splines introduced by G. Nielson. Some piecewise polynomial alternatives to splines under tension, in: \textit{R. E. Barnhill} and \textit{R. F. Riesenfeld}, eds., ''Computer aided geometric design'' (1974; Zbl 0316.68006).
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 3964611
zbMATH Keywords: interpolatory \(\nu \) -splines
zbMATH Keywords: splines under tension
author: Gerald Farin
reviewed by: Franz-Jürgen Delvos
MaRDI profile type: Publication
cites work: Curvature continuous curves and surfaces
cites work: A survey of curve and surface methods in CAGD
cites work: Continuity conditions for spline curves
description: scientific article; zbMATH DE number 3964611