Approximating Rational Bézier Curve with Polynomial Curve Using Re-parameterization

The problem of approximating rational curves by polynomial curves is studied in this paper. A simple method of approximation, which uses the control points of the degree-elevated curve to approximate the original rational curve, is introduced at first. Meanwhile as to achieve better efficiency, the idea of re-parameterization of rational Bézier curves is presented. The re-parameterization makes uniform the weights of the rational Bézier curve as accordant as possible, and then approximation can achieve better efficiency. In this way, one gets better approximating result with less error, and meanwhile the same approximating degree is preserved. The algorithm is easy to carry out and can be widely applied in areas such as numerical controlling manufacturing, design in robotics, computer graphics and so on.