Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions

DOI10.1016/j.cagd.2011.11.003zbMath1242.65037OpenAlexW1985635493MaRDI QIDQ419469

Rushan Ziatdinov, Norimasa Yoshida, Tae-Wan Kim

Publication date: 18 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2011.11.003

zbMATH Keywords

Gaussian quadraturegraphical examplesCornu spiralfair curveincomplete gamma functionslinear logarithmic curvature graphlog-aesthetic curvelog-aesthetic splinelogarithmic spiralsNielsen spiral

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Computer-aided design (modeling of curves and surfaces) (65D17) Numerical approximation and evaluation of special functions (33F05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (14)

Curvature sensitive analysis of axially compressed cylindrical tubes with corrugated surface using isogeometric analysis and experiment ⋮ Generation of log-aesthetic curves using adaptive Runge-Kutta methods ⋮ Geometric Hermite interpolation by logarithmic arc splines ⋮ Log-aesthetic curves as similarity geometric analogue of Euler's elasticae ⋮ Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin ⋮ Aesthetic Design with Log-Aesthetic Curves and Surfaces ⋮ Fairing of planar curves to log-aesthetic curves ⋮ Quintic polynomial approximation of log-aesthetic curves by curvature deviation ⋮ Log-aesthetic curves: similarity geometry, integrable discretization and variational principles ⋮ Family of superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function ⋮ Generalization of log-aesthetic curves via similarity geometry ⋮ Efficient intersection between splines of clothoids ⋮ Log-aesthetic curves for shape completion problem ⋮ Two-point \(G^1\) Hermite interpolation in biangular coordinates

Cites Work

• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• The use of Cornu spirals in drawing planar curves of controlled curvature
• Controlling the curvature of a quadratic Bézier curve
• A shape controled fitting method for Bézier curves
• Designing Bézier conic segments with monotone curvature
• Designing fair curves using monotone curvature pieces
• Class A Bézier curves
• Uniform Asymptotic Expansions of the Incomplete Gamma Functions and the Incomplete Beta Function
• Calculation of Gauss-Kronrod quadrature rules
• Logarithmic Curvature and Torsion Graphs
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