q-Bernstein polynomials and Bézier curves

  title={q-Bernstein polynomials and B{\'e}zier curves},
  author={Halil Oruç and George M. Phillips},
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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