The Iteration Method for Sample-based Polynomial Approximation of Rational B-spline Curves

摘要

A method to approximate rational B-spline curves with B-spline curve sequences is presented. Firstly, data points are obtained by evenly sampled from the given rational B-spline curve. Then an initial B-spline approximation curve is generated simultaneously by using these points as initial control points. Secondly, these control points are adjusted gradually by the scheme of progressive iterative approximation. Weighted and local progressive iterative approximations are also used to accelerate speed or obtain more flexibility. At last, numerical examples exhibit convergence rates with different error algorithms and show that L_1-error criterion is better than L_2-error and L_∞-error criterions.