Accurate evaluation of Bézier curves and surfaces and the Bernstein-Fourier algorithm

The Bernstein–Fourier algorithm for the evaluation of polynomial curves is extended for the evaluation of polynomial tensor product surfaces. Under a natural hypothesis, accurate evaluation of Bézier curves and surfaces through several algorithms is discussed. Numerical experiments comparing the accuracy of the corresponding Horner, de Casteljau, VS and Bernstein–Fourier algorithms are presented.