Planar \(G^2\) transition between two circles with a fair cubic Bézier curve.
type: Item
instance of: scholarly article
title: Planar \(G^2\) transition between two circles with a fair cubic Bézier curve.
zbMATH Open document ID: 1038.68579
DOI: 10.1016/S0010-4485(99)00073-1
author: D. J. Walton
author: D. S. Meek
published in: CAD. Computer-Aided Design
publication date: 1999-01-01T00:00:00Z
review text: Consumer products such as ping-pong paddles, can be designed by blending circles. To be visually pleasing it is desirable that the blend be curvature continuous without extraneous curvature extrema. Transition curves of gradually increasing or decreasing curvature between circles also play an important role in the design of highways and railways. Recently planar cubic and Pythagorean hodograph quintic spiral segments were developed and it was demonstrated how these segments can be composed pairwise to form transition curves that are suitable for \(G^2\) blending. It is now shown that a single cubic curve can be used for blending or as a transition curve with the guarantee of curvature continuity and fairness. Use of a single curve rather than two segments has the benefit that designers and implementers have fewer entities to be concerned with.
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 1964466
zbMATH Keywords: \(G^2\) transition
zbMATH Keywords: Blending
zbMATH Keywords: Fair
zbMATH Keywords: Cubic
zbMATH Keywords: Bézier
MaRDI profile type: Publication
full work available at URL: s0010-4485(99)00073-1
OpenAlex ID: W2001817216
description: scientific article; zbMATH DE number 1964466