In this paper, by using the perturbation theory, A new approach is presented to approximate rational curves with the interval Bz ier curves. First of all the coefficients of a rational curve are perturbed und er the Bernstein bases so as to get a polynomial curve, and such that the perturbed rat ional curve is minimized in the L 2 norm. Then by solving the maximal cont rol points, a perturbed rational curve is obtained which is contained inside an interval Bzier curve. Because the L 2 norm... In this paper, by using the perturbation theory, A new approach is presented to approximate rational curves with the interval Bz ier curves. First of all the coefficients of a rational curve are perturbed und er the Bernstein bases so as to get a polynomial curve, and such that the perturbed rat ional curve is minimized in the L 2 norm. Then by solving the maximal cont rol points, a perturbed rational curve is obtained which is contained inside an interval Bzier curve. Because the L 2 norm is used, the method shown in t his paper allows more restriction to the perturbed rational curve, su ch as smoothness restriction. Therefore the interval Bzier curve and its conta ining approximation curve can be used to interpolate the rat ional curve at the two end points. Such interpolation can be kept in a certain order of smoothness. By the application of the well known subdivision approach to this method, in a continuous piecewise polynomial can be obtained which appro xim ates the rational curve with certain global continuation, and a piecewise interv al Bzier curve which also approximates the rational curve with certain globa l continuation and interpolates the rational curve at the end points. Finally, s ome examples are given to show that the the met hod used to approximate the rational curve is generally better than Hermite inte rpolation and hybrid curve approximation. |