Evaluation of the derivative of a polynomial in Bernstein form

摘要

In geometric modelling and computer-aided design a polynomial is usually represented in Bernstein form. Forward error analysis for the computation of the derivative of a polynomial in Bernstein form is performed. The corresponding running error is also analyzed. We have compared our results with those corresponding to a polynomial represented in power basis and using Legendre and Chebyshev forms. Since the conversions between the Bernstein and the power bases and between Bernstein and Chebyshev polynomials were already studied in the literature, for the sake of completeness the conversion between Bernstein and Chebyshev polynomials of the first kind is analyzed in an appendix.