Two essential properties of \((q, h)\)-Bernstein-Bézier curves

DOI10.1016/j.apnum.2015.04.005zbMath1321.65023OpenAlexW268631799MaRDI QIDQ492925

Ronald N. Goldman, Plamen C. Simeonov

Publication date: 21 August 2015

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2015.04.005

zbMATH Keywords

algorithmconvergencevariation diminishing propertydegree elevationcontrol polygon\((q, h)\)-Bernstein basis\((q, h)\)-Bézier curveBernstein-Bézier curvesDescartes' law of signs

Mathematics Subject Classification ID

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

Related Items (8)

Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights ⋮ Polynomial degree reduction in the discrete \(L_2\)-norm equals best Euclidean approximation of \(h\)-Bézier coefficients ⋮ On the accuracy of de Casteljau-type algorithms and Bernstein representations ⋮ An evaluation algorithm for \(q\)-Bézier triangular patches formed by convex combinations ⋮ Best polynomial degree reduction on \(q\)-lattices with applications to \(q\)-orthogonal polynomials ⋮ Quantum Lorentz degrees of polynomials and a Pólya theorem for polynomials positive on \(q\)-lattices ⋮ A polynomial blossom for the Askey-Wilson operator ⋮ Quantum Bernstein bases and quantum Bézier curves

Cites Work

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• \(h\)-blossoming: A new approach to algorithms and identities for \(h\)-Bernstein bases and \(h\)-Bézier curves
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• Shape parameter deletion for Pólya curves
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• \(q\)-Bernstein polynomials and Bézier curves
• Shape preserving representations and optimality of the Bernstein basis
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• Approximation properties for generalized \(q\)-Bernstein polynomials
• Polya’s Urn Model and Computer Aided Geometric Design
• A generalization of the Bernstein polynomials
• A survey of results on the q-Bernstein polynomials
• Generalized Bernstein polynomials
• Quantum calculus

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