Sample-based polynomial approximation of rational Bézier curves

We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The L_p-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the L_p-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L₁-error criterion are better than those obtained using the L₂-error and L_∞-error criteria.