Approximating the helix with rational cubic Bézier curves
type: Item
instance of: scholarly article
title: Approximating the helix with rational cubic Bézier curves
zbMATH Open document ID: 0836.65016
DOI: 10.1016/0010-4485(95)99795-A
author: Imre Juhász
published in: CAD. Computer-Aided Design
publication date: 1995-11-20T00:00:00Z
review text: Helices, being given by transcendental functions, cannot be used directly in CAD programs based on rational surfaces. The author shows explicitly how to construct a cubic rational approximation to an arc of helix such that either given tangent directions are observed at the endpoints or, more importantly, that rotated copies of such arcs can be composed to yield a \(G^2\) (geometrically second order smooth) curve. He carefully discusses the error and produces charts for the selection of the optimal angle (giving minimal error) for a given parameter of the helix.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 818586
zbMATH Keywords: rational cubic Bézier curves
zbMATH Keywords: rational surfaces
zbMATH Keywords: cubic rational approximation
zbMATH Keywords: helix
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: 0010-4485(95)99795-a
OpenAlex ID: W2089573510
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description: scientific article; zbMATH DE number 818586