On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus

DOI10.1016/j.cagd.2014.02.010zbMath1310.65021OpenAlexW4253389742MaRDI QIDQ2513781

Rudolf Winkel

Publication date: 29 January 2015

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2014.02.010

zbMATH Keywords

interpolationumbral calculusgeneralized de Casteljau algorithmefficient evaluationgeneralized Bernstein polynomial

Mathematics Subject Classification ID

Computer science aspects of computer-aided design (68U07) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (4)

Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curves ⋮ On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus. II: De Casteljau algorithm ⋮ On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus. III: Blossoming ⋮ On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

Cites Work

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• Computing with barycentric polynomials
• The umbral calculus
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• Polya’s Urn Model and Computer Aided Geometric Design
• Interpolation and approximation of curves and surfaces using Pólya polynomials
• On the optimal stability of the Bernstein basis
• The History of Blissard's Symbolic Method, with a Sketch of its Inventor's Life
• Generalized Bernstein polynomials and Bézier curves: an application of umbral calculus to computer aided geometric design

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