Transition between concentric or tangent circles with a single segment of \(G^2\) PH quintic curve

DOI10.1016/j.cagd.2007.10.006zbMath1172.65313OpenAlexW2042109120MaRDI QIDQ735470

Manabu Sakai, Zulfiqar Habib

Publication date: 22 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.2007.10.006

zbMATH Keywords

computer graphicsquinticrobot path planninghighway designingPythagorean hodograph

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Computer science aspects of computer-aided design (68U07)

Related Items (10)

Shape-preserving curve interpolation ⋮ Fair cubic transition between two circles with one circle inside or tangent to the other ⋮ A note on Pythagorean hodograph quartic spiral ⋮ Spiral transitions ⋮ Positivity-preserving scattered data interpolation scheme using the side-vertex method ⋮ \(G^3\) quintic polynomial approximation for generalised Cornu spiral segments ⋮ Pythagorean hodograph spline spirals that match \(G^3\) Hermite data from circles ⋮ Algebraic-trigonometric Pythagorean-hodograph curves and their use for Hermite interpolation ⋮ \(G^2\) cubic transition between two circles with shape control ⋮ 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
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• \(G^2\) curve design with a pair of pythagorean hodograph quintic spiral segments
• The use of Cornu spirals in drawing planar curves of controlled curvature
• Inflection points and singularities on planar rational cubic curve segments
• Planar \(G^2\) transition between two circles with a fair cubic Bézier curve.
• Planar \(G^{2}\) transition curves composed of cubic Bézier spiral segments
• A planar cubic Bézier spiral
• Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve

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