【摘要】 论文利用曲线摄动的思想给出了用区间Bzier曲线逼近有理曲线的一种方法 .由于采用恰当的范数 ,该方法可以对摄动曲线赋予较多的限制 .实例表明 ,论文中的方法要优于传统的Hermite插值方法及文献 [3]中提出的杂交曲线逼近算法 .更多还原

【Abstract】 In this paper, by using the perturbation theory, A new approach is presented to approximate rational curves with the interval Bz 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 Bzier 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 Bzier 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 Bzier 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.更多还原