Approximating conic sections by constrained Bézier curves of arbitrary degree

DOI10.1016/J.CAM.2012.01.017zbMath1241.65027OpenAlexW2083656934MaRDI QIDQ413722

Qian-Qian Hu

Publication date: 7 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.cam.2012.01.017

zbMATH Keywords

algorithmnumerical examplesapproximationleast squares methodBézier curvesconic sectionsarbitrary degreeBernstein basis functionscurve subdivision schemeeigenvalues of recurrence equationsmethod of undetermined coefficients

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (7)

Constrained polynomial approximation of quadric surfaces ⋮ Optimal parameter values for approximating conic sections by the quartic Bézier curves ⋮ \(G^1\) approximation of conic sections by quartic Bézier curves ⋮ Approximation of conic section by quartic Bézier curve with endpoints continuity condition ⋮ The representation of circular arc by using rational cubic Timmer curve ⋮ Explicit \(G^1\) approximation of conic sections using Bézier curves of arbitrary degree ⋮ Approximating of conic sections by DP curves with endpoint interpolation

Cites Work

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• The rational cubic Bézier representation of conics
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• Approximation of circular arcs by Bézier curves
• An \(O(h^{2n})\) Hermite approximation for conic sections
• A rational quartic Bézier representation for conics
• \(G^3\) approximation of conic sections by quintic polynomial curves
• High order approximation of rational curves by polynomial curves

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