Optimal parametric interpolants of circular arcs

DOI10.1016/j.cagd.2020.101891zbMath1505.65099arXiv1911.05425OpenAlexW3102227034MaRDI QIDQ2187379

Aleš Vavpetič

Publication date: 2 June 2020

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

Full work available at URL: https://arxiv.org/abs/1911.05425

zbMATH Keywords

circular arcoptimal interpolationBézier curvegeometric interpolationparametric polynomial

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Numerical interpolation (65D05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (7)

Construction of \(G^2\) planar Hermite interpolants with prescribed arc lengths ⋮ Geometric approximation of the sphere by triangular polynomial spline patches ⋮ Optimal approximation of spherical squares by tensor product quadratic Bézier patches ⋮ Arc length preserving \(G^2\) Hermite interpolation of circular arcs ⋮ Editorial. From theoretical to applied geometry -- recent developments ⋮ Parameterization for polynomial curve approximation via residual deep neural networks ⋮ On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance

Cites Work

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• The best \(G^{1}\) cubic and \(G^{2}\) quartic Bézier approximations of circular arcs
• On parametric polynomial circle approximation
• Chebyshev approximation of plane curves by splines
• Approximation of circular arcs by Bézier curves
• Uniform approximation of a circle by a parametric polynomial curve
• Interpolation of circular arcs by parametric polynomials of maximal geometric smoothness
• A general framework for the optimal approximation of circular arcs by parametric polynomial curves

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