q-Bernstein polynomials and Bézier curves

Authors:
Halil Oruç;George M. Phillips
Affiliations:
Department of Mathematics, Dokuz Eylül University, Fen Edebiyat Fakültesi, Tinaztepe Kampüsü 35160 Buca, Izmir, Turkey;Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 4
Cited 10

On the numerical condition of polynomials in Berstein form

Computer Aided Geometric Design
Fundamentals of computer aided geometric design

Fundamentals of computer aided geometric design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code

Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
On the convergence and iterates of q-Bernstein polynomials

Journal of Approximation Theory

Symmetric functions and the Vandermonde matrix

Journal of Computational and Applied Mathematics
Dual generalized Bernstein basis

Journal of Approximation Theory
A novel generalization of Bézier curve and surface

Journal of Computational and Applied Mathematics
Direct and converse results for multivariate generalized Bernstein polynomials

Journal of Computational and Applied Mathematics
Tensor Product q -Bernstein Bézier Patches

Numerical Analysis and Its Applications
Dual generalized Bernstein basis

Journal of Approximation Theory
Shape design component of a strain-stress analysis system

ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume II
On a new approach to obtain spline Bézier curves

ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume II
Local path fitting: A new approach to variational integrators

Journal of Computational and Applied Mathematics
Generalized Bézier curves and surfaces based on Lupaş q-analogue of Bernstein operator

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

We define q-Bernstein polynomials, which generalize the classical Bernstein polynomials, and show that the difference of two consecutive q-Bernstein polynomials of a function f can be expressed in terms of second-order divided differences of f. It is also shown that the approximation to a convex function by its q-Bernstein polynomials is one sided.A parametric curve is represented using a generalized Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We study the nature of degree elevation and degree reduction for this basis and show that degree elevation is variation diminishing, as for the classical Bernstein basis.