带形状参数的Bézier曲线  

Bézier curves with shape parameters

作　　者：严兰兰[1] 梁炯丰[2] 黄涛[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000 [2]东华理工大学土木与环境工程学院,江西抚州344000

出　　处：《合肥工业大学学报（自然科学版）》2009年第11期1783-1788,共6页Journal of Hefei University of Technology：Natural Science

基　　金：东华理工大学校长基金资助项目(DHXK0808);东华理工大学校长基金资助项目(DHXK0828)

摘　　要：文章首先将二次Bernstein基函数进行扩展,定义了带2个形状参数的四次多项式基函数,它以二次Bernstein基和三次-λB基为特例;再利用de Casteljau算法进行递推,得到了一般n次Bernstein基函数的扩展,它由n+1个带形状参数的n+2次多项式组成;基于这组基函数定义了带2个形状参数的多项式曲线,它以一般n次Bézier曲线和n+1次-λBézier曲线为特例;分析了这组基以及由其定义的曲线的性质,给出了形状参数的几何意义和曲线的几何作图法。A class of polynomial functions of 4th-degree with two parameters is presented,which is the extension of quadratic Bernstein and cubic λ-B basis functions. Then using the de Casteljau arithmetic,the generalized basis function of degree n＋2 with two shape parameters is obtained. Based on this, a new type of curve with two shape parameters is defined. The new curve contains generalized Bezier curves and λ-Beizier curves. The properties of the new basis and the new curve are analyzed： Meanwhile, the geometry meaning of the shape parameters and the geometric drawing method of the new curve are given.

关 键 词：计算机辅助几何设计 曲线设计 BÉZIER曲线 形状参数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]