Tensor product \(q\)-Bernstein polynomials

DOI10.1007/s10543-008-0192-xzbMath1169.65011OpenAlexW2060067266MaRDI QIDQ1014883

Halil Oruç, Çetin Dişibüyük

Publication date: 29 April 2009

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-008-0192-x

zbMATH Keywords

multivariate approximation\(q\)-Bernstein polynomialsde Casteljau algorithmtensor product \(q\)-Bernstein Bézier surfaces

Mathematics Subject Classification ID

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

Related Items (8)

Shape-preserving properties of a new family of generalized Bernstein operators ⋮ Generalized Bézier curves and surfaces based on Lupaş \(q\)-analogue of Bernstein operator ⋮ An evaluation algorithm for \(q\)-Bézier triangular patches formed by convex combinations ⋮ Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators ⋮ Bézier curves based on Lupaş \((p,q)\)-analogue of Bernstein functions in CAGD ⋮ Triangular surface patch based on bivariate Meyer-König-Zeller operator ⋮ Weighted Lupaş \(q\)-Bézier curves ⋮ Lupaş blending functions with shifted knots and \(q\)-Bézier curves

Cites Work

• A de Casteljau algorithm for generalized Bernstein polynomials
• Convergence of generalized Bernstein polynomials
• A generalization of rational Bernstein-Bézier curves
• \(q\)-Bernstein polynomials and their iterates.
• Interpolation and approximation by polynomials
• \(q\)-Bernstein polynomials and Bézier curves
• On the convergence and iterates of \(q\)-Bernstein polynomials
• Symmetric functions and the Vandermonde matrix
• Convexity and generalized Bernstein polynomials
• Generalized Bernstein polynomials
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