Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves

DOI10.1016/j.cagd.2014.02.002zbMath1293.65027OpenAlexW2070711497WikidataQ114202363 ScholiaQ114202363MaRDI QIDQ395899

Rida T. Farouki

Publication date: 7 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2014.02.002

zbMATH Keywords

complex polynomialsPythagorean-hodograph curves\(G^2\) continuitycurvature distributionrounded corners

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (10)

Classification of polynomial minimal surfaces ⋮ Interpolation of planar \(G^1\) data by Pythagorean-hodograph cubic biarcs with prescribed arc lengths ⋮ Algebraic and geometric characterizations of a class of algebraic-hyperbolic Pythagorean-hodograph curves ⋮ Geometric characteristics of planar quintic Pythagorean-hodograph curves ⋮ Rational swept surface constructions based on differential and integral sweep curve properties ⋮ High speed machining for linear paths blended with \(G3\) continuous Pythagorean-hodograph curves ⋮ Arc length preserving \(G^2\) Hermite interpolation of circular arcs ⋮ Unnamed Item ⋮ Identification of two classes of planar septic Pythagorean hodograph curves ⋮ Unnamed Item

Cites Work

• A generalisation of the Pythagorean hodograph quintic spiral
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• \(G^2\) curve design with a pair of pythagorean hodograph quintic spiral segments
• \(G^2\) cubic transition between two circles with shape control
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• G\(^{2}\) curves composed of planar cubic and Pythagorean hodograph quintic spirals
• The conformal map \(z\to z^ 2\) of the hodograph plane
• A planar cubic Bézier spiral
• Curve design with more general planar Pythagorean-hodograph quintic spiral segments
• FAIRING ARC SPLINE AND DESIGNING BY USING CUBIC BÉZIER SPIRAL SEGMENTS
• Cubic Spiral Transition Matching G2 Hermite End Conditions
• G²blends of linear segments with cubics and Pythagorean-hodograph quintics
• Clothoid Spline Transition Spirals
• Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve

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