A planar cubic Bézier spiral

DOI10.1016/0377-0427(95)00246-4zbMath0857.65019OpenAlexW2038854446MaRDI QIDQ1923625

D. J. Walton, D. S. Meek

Publication date: 20 February 1997

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

Full work available at URL: https://doi.org/10.1016/0377-0427(95)00246-4

zbMATH Keywords

Bézier curvesclothoid curvesCAD methodscircular involutescontinuous curvature transitionplanar cubic Bézier spiralspiral arc

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Curves in Euclidean and related spaces (53A04) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (24)

Smooth path planning via cubic GHT-Bézier spiral curves based on shortest distance, bending energy and curvature variation energy ⋮ Fair cubic transition between two circles with one circle inside or tangent to the other ⋮ Interpolation with cubic spirals ⋮ Planar interpolation with a pair of rational spirals ⋮ G\(^{2}\) curves composed of planar cubic and Pythagorean hodograph quintic spirals ⋮ Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves ⋮ Spiral transitions ⋮ Curves used in highway design and Bezier curves ⋮ A further generalisation of the planar cubic Bézier spiral ⋮ Planar \(G^{2}\) transition curves composed of cubic Bézier spiral segments ⋮ Curve design with more general planar Pythagorean-hodograph quintic spiral segments ⋮ \(G^2\) cubic transition between two circles with shape control ⋮ A New Planar Bezier-Like Spiral Defined by Exponential Functions And Transition Curves ⋮ Geometric constraints on quadratic Bézier curves using minimal length and energy ⋮ 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 ⋮ A sufficient condition for 3D typical curves ⋮ Transition between concentric or tangent circles with a single segment of \(G^2\) PH quintic curve ⋮ Approximation of a planar cubic Bézier spiral by circular arcs ⋮ A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter ⋮ G²curve design with planar quadratic rational Bézier spiral segments ⋮ Trigonometric B

Cites Work

• Shape determination of planar uniform cubic B-spline segments
• Offset curves of clothoidal splines
• The use of Cornu spirals in drawing planar curves of controlled curvature
• A geometric characterization of parametric cubic curves
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