基于s-Power级数的对数螺线多项式逼近表示  

Polynomial approximation to logarithmic spiral via s-Power series

作　　者：张帆[1] 康宝生[1] 

机构地区：[1]西北大学信息科学与技术学院,陕西西安710127

出　　处：《西北大学学报（自然科学版）》2011年第1期33-37,共5页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学基金资助项目(FC06121)

摘　　要：目的为得到对数螺线的多项式逼近表示。方法利用s-Power级数,也就是泰勒两点展开的模式,得到它的多项式逼近表示。结果截断s-Power级数的前k项,就得到了k阶埃尔米特插值,也就是(2k+1)次的具有和给定区间对数螺线相同k阶端点导数的多项式曲线。通过分段拼接就得到了在拼接点具有Ck连续的Hermite B样条曲线。结论该方法计算简单,并且通过提高次数,可得到高精度逼近,是Christoph Baumgarten等人三次有理样条曲线逼近法的更合适的替代。Aim To obtain the polynomial approximation of logarithmic spiral.Methods Based on employing s-Power series,the two-point analogue of Taylor expansions,a polynomial approximation to logarithmic spiral is presented.Results Truncating at the kth term s-Power series results in the order-k Hermite interpolation,i.e.the degree-（2k＋1） polynomial curve that reproduces up to the kth derivative of the original curve at the endpoints of a given interval.By splicing these approximations,a Hermitian spline that exhibits Ck continuity at the joints is obtained.Conclusion The method proposed is simple in calculation and of high precision.It is a more suitable alternative than the rational cubic spline curves advocated by Christoph Baumgarten et al.[Computer-Aided Design 14（1997） 515].

关 键 词：对数螺线 埃尔米特逼近 s-Power级数 埃尔米特样条 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]