有理曲线的区间Bzier曲线的逼近  

Interval Bzier Curves Approximation of Rational Curves

作　　者：陈效群[1] 娄文平[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《中国科学技术大学学报》2001年第4期379-385,406,共8页JUSTC

基　　金：国家自然科学基金 (199710 87);中国科学技术大学数学机械化 (G19980 30 6 0 0 );教委博士点基金资助项目

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 .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.

关 键 词：有理曲线 区间Bézier曲线 多项式曲线 杂交曲线 逼近 HERMITE插值 CAD 

分 类 号：O18[理学—数学] TP391.72[理学—基础数学]