G\(^{2}\) curves composed of planar cubic and Pythagorean hodograph quintic spirals

DOI10.1016/S0167-8396(97)00028-9zbMath0905.68147OpenAlexW2015649089WikidataQ114121811 ScholiaQ114121811MaRDI QIDQ1128902

D. J. Walton, D. S. Meek

Publication date: 13 August 1998

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

Full work available at URL: https://doi.org/10.1016/s0167-8396(97)00028-9

zbMATH Keywords

fair curvescubic spiralspythagorean hodograph quintic spirals

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (15)

Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths ⋮ Identification and ``reverse engineering of Pythagorean-hodograph curves ⋮ Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves ⋮ Spiral transitions ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ Planar \(G^{2}\) transition curves composed of cubic Bézier spiral segments ⋮ Curve design with more general planar Pythagorean-hodograph quintic spiral segments ⋮ Hermite interpolation by Pythagorean hodograph curves of degree seven ⋮ Note on planar Pythagorean hodograph curves of Tschirnhaus type ⋮ A generalisation of the Pythagorean hodograph quintic spiral ⋮ Curvature extrema of planar parametric polynomial cubic curves ⋮ Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve ⋮ \(G^2\) curve design with a pair of pythagorean hodograph quintic spiral segments ⋮ Euclidean and Minkowski Pythagorean hodograph curves over planar cubics ⋮ G²curve design with planar quadratic rational Bézier spiral segments

Cites Work

• The conformal map \(z\to z^ 2\) of the hodograph plane
• A planar cubic Bézier spiral
• Hermite Interpolation by Pythagorean Hodograph Quintics
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