Accurate evaluation algorithm for bivariate polynomial in Bernstein–Bézier form

In this paper it is presented a compensated de Casteljau algorithm to accurately evaluate a bivariate polynomial in Bernstein–Bézier form. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. A forward error and a running error analysis are performed. Finally, some numerical experiments illustrate the accuracy of the proposed algorithm in ill-conditioned problems.