Family of superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function

DOI10.1016/j.cagd.2012.03.006zbMath1250.65029OpenAlexW2049644343MaRDI QIDQ450242

Rushan Ziatdinov

Publication date: 13 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2012.03.006

zbMATH Keywords

numerical examplesGauss hypergeometric functionsurface of revolutiongraphical examplesspiralfair curvelog-aesthetic curvemonotone curvatureGauss-Kronrod integration methodsuperspiralsuperspiraloid

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (5)

Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin ⋮ Attractive Plane Curves in Differential Geometry ⋮ Generalization of log-aesthetic curves via similarity geometry ⋮ A sufficient condition for 3D typical curves ⋮ Two-point \(G^1\) Hermite interpolation in biangular coordinates

Cites Work

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• Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions
• Applying inversion to construct planar, rational spirals that satisfy two-point \(G^{2}\) Hermite data
• Two-point \(G^{2}\) Hermite interpolation with spirals by inversion of hyperbola
• Fair cubic transition between two circles with one circle inside or tangent to the other
• General properties of spiral plane curves
• \(G^2\) cubic transition between two circles with shape control
• The use of Cornu spirals in drawing planar curves of controlled curvature
• Planar \(G^2\) transition between two circles with a fair cubic Bézier curve.
• Planar \(G^{2}\) transition curves composed of cubic Bézier spiral segments
• Designing Bézier conic segments with monotone curvature
• Designing fair curves using monotone curvature pieces
• Class A Bézier curves
• The G and H Functions as Symmetrical Fourier Kernels
• Hypergeometric Functions, My Love
• Calculation of Gauss-Kronrod quadrature rules
• Completely monotonic functions
• G 2 Planar Cubic Transition Between Two Circles
• Logarithmic Curvature and Torsion Graphs
• Curvature Monotony Condition for Rational Quadratic B-spline Curves
• The analytic continuation of the Gaussian hypergeometric function \(_2F_1(a,b;c;z)\) for arbitrary parameters
• Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve

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