A generalisation of the Pythagorean hodograph quintic spiral

DOI10.1016/j.cam.2004.02.008zbMath1070.65012OpenAlexW2093822692WikidataQ114202166 ScholiaQ114202166MaRDI QIDQ704192

D. S. Meek, D. J. Walton

Publication date: 13 January 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.02.008

zbMATH Keywords

computer graphicsCADBézier curvespiralcomputer applicationsCAGDclothoidPythagorean hodograph quintic

Mathematics Subject Classification ID

Computer science aspects of computer-aided design (68U07) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (16)

A note on Pythagorean hodograph quartic spiral ⋮ Generating planar spiral by geometry driven subdivision scheme ⋮ Rational swept surface constructions based on differential and integral sweep curve properties ⋮ Approximation of logarithmic spirals ⋮ Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves ⋮ Planar quintic \(G^2\) Hermite interpolation with minimum strain energy ⋮ An involute spiral that matches \(G^{2}\) Hermite data in the plane ⋮ On control polygons of quartic Pythagorean-hodograph curves ⋮ Incenter subdivision scheme for curve interpolation ⋮ Matching admissible \(G^2\) Hermite data by a biarc-based subdivision scheme ⋮ \(G^2\) curve design with a pair of pythagorean hodograph quintic spiral segments ⋮ Transition between concentric or tangent circles with a single segment of \(G^2\) PH quintic curve ⋮ G²blends of linear segments with cubics and Pythagorean-hodograph quintics ⋮ Algorithm 952 ⋮ A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter ⋮ $C^2$ Hermite interpolation by Pythagorean Hodograph space curves

Cites Work

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• High accuracy geometric Hermite interpolation
• The use of Cornu spirals in drawing planar curves of controlled curvature
• G\(^{2}\) curves composed of planar cubic and Pythagorean hodograph quintic spirals
• A shape controled fitting method for Bézier curves
• A planar cubic Bézier spiral
• Hermite Interpolation by Pythagorean Hodograph Quintics

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