q-Bernstein polynomials and Bézier curves

@inproceedings{Oru2003qBernsteinPA,
  title={q-Bernstein polynomials and B{\'e}zier curves},
  author={Halil Oruç and George M. Phillips},
  year={2003}
}
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… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 18 references

The Theory of Partitions

G. E. Andrews
1998
View 8 Excerpts
Highly Influenced

On the Convergence and Iterates of q-Bernstein Polynomials

Journal of Approximation Theory • 2002
View 1 Excerpt

Convexity and generalized Bernstein polynomials

T.N.T. Goodman, H. Oruç, G. M. Phillips
Proc. Edin. Math. Soc • 1999
View 2 Excerpts

Bernstein polynomials based on the q-integers

G. M. Phillips
Ann. Numer. Math • 1997
View 1 Excerpt

A de Casteljau algorithm for generalized Bernstein polynomials

G. M. Phillips
1996

A de Casteljau algorithm for generalized Bernstein polynomials, BIT

G. M. Phillips
1996
View 1 Excerpt

Total positivity and shape of curves, in: Total Positivity and its Applications (M

T.N.T. Goodman
Gasca and C. A. Micchelli ed.), (Kluwer Academic Publishers, Dordrecht, • 1996
View 2 Excerpts

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