三角Bézier曲线插值及其误差分析  

Trigonometric Polynomial Bézier Curve Interpolation and Its Error Analysis

作　　者：邱泽阳[1] 方永锋[1] 

机构地区：[1]兰州交通大学工业设计研究所,甘肃兰州730070

出　　处：《工程图学学报》2007年第2期104-108,共5页Journal of Engineering Graphics

基　　金：甘肃省自然科学基金资助项目(ZS031-A25-008-Z);兰州交通大学首批"青蓝"人才工程资助项目

摘　　要：Bézier曲线是计算机辅助几何设计中的一类重要曲线,以三次三角Bézier曲线为例,对三角Bézier曲线的性质进行了分析,并由此推出三次三角Bézier曲线比三次Bézier曲线更光滑。然后,由连续函数f在给定区间[a,b]上的分上上上a=t0<t 1<<tn?1<tn=b和函数值f(ti),导出了三次三角Bézier曲线插值算法,并对插值的整体误差和节点区间[1i,ti+1]内的误差进行了分析估计;最后给出的应用实例验证了上述结论。Bezier curve is an important one in CAGD. As an example to cubic trigonometric polynomial Bezier, the characters of trigonometric polynomial Bezier curve is analyzed, and deduced that cubic trigonometric polynomial Bezier curve is more smooth than cubic polynomial Bezier curve. Then the algorithm for cubic Trigonometric Bezier curve interpolation is deduced from continuous function f defined in area [a,b] with partitions △ ： a = t0 〈 t1 〈… 〈 tn-1 〈 tn = b and their values f（ti） （i = 0, 1, ..., n）. Meanwhile the holistic error for the interpolation and the error in partition [ti, ti＋1 ] are analyzed. At last, the examples is given to verity the conclusions are correct.

关 键 词：计算机应用 曲线插值 三角多项式 BEZIER曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] O241.3[自动化与计算机技术—计算机科学与技术]