\(G^2\) curve design with a pair of pythagorean hodograph quintic spiral segments

DOI10.1016/j.cagd.2007.03.003zbMath1171.65357OpenAlexW2092078117WikidataQ114202405 ScholiaQ114202405MaRDI QIDQ733418

D. J. Walton, D. S. Meek

Publication date: 16 October 2009

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2007.03.003

zbMATH Keywords

Bézier curvespiralpythagorean 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 (19)

Smooth path planning via cubic GHT-Bézier spiral curves based on shortest distance, bending energy and curvature variation energy ⋮ Generating planar spiral by geometry driven subdivision scheme ⋮ Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves ⋮ Classification of planar Pythagorean hodograph curves ⋮ Spiral transitions ⋮ An involute spiral that matches \(G^{2}\) Hermite data in the plane ⋮ A further generalisation of the planar cubic Bézier spiral ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves ⋮ \(G^3\) quintic polynomial approximation for generalised Cornu spiral segments ⋮ Incenter subdivision scheme for curve interpolation ⋮ Matching admissible \(G^2\) Hermite data by a biarc-based subdivision scheme ⋮ Curve design with more general planar Pythagorean-hodograph quintic spiral segments ⋮ Pythagorean hodograph spline spirals that match \(G^3\) Hermite data from circles ⋮ \( G^2 \slash C^1\) Hermite interpolation by planar PH B-spline curves with shape parameter ⋮ Unnamed Item ⋮ Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves ⋮ Transition between concentric or tangent circles with a single segment of \(G^2\) PH quintic curve ⋮ Fairing an arc spline and designing with G ² PH quintic spiral transitions

Cites Work

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• A generalisation of the Pythagorean hodograph quintic spiral
• \(G^2\) Pythagorean hodograph quintic transition between two circles with shape control
• G\(^{2}\) curves composed of planar cubic and Pythagorean hodograph quintic spirals
• Planar \(G^2\) transition between two circles with a fair cubic Bézier curve.
• A planar cubic Bézier spiral
• Shape-preserving interpolation by G1 and G2 PH quintic splines
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve
• Planar \(G^2\) Hermite interpolation with some fair, \(C\)-shaped curves

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