三次Bézier曲线的新扩展及其应用  

New extension of cubic Bézier curve and its applications

作　　者：秦新强[1] 胡钢[1] 张素霞[1] 

机构地区：[1]西安理工大学理学院应用数学系,西安710054

出　　处：《计算机工程与应用》2008年第2期112-115,共4页Computer Engineering and Applications

基　　金：国家自然科学基金( the National Natural Science Foundation of China under Grant No.60672135);陕西省自然科学基金( the Natural Science Foundation of Shaanxi Province of China under Grant No.2005F44) 。

摘　　要：给出了两组分别含有2个和3个形状控制参数的三次和四次多项式基函数,它们都是三次Bernstein基函数的扩展;分析了这两组基函数的性质,基于此两组基定义了两种分别带形状参数α,γ和α,β,γ的多项式曲线,它们都以三次Bézier曲线为特殊情形。两种新曲线不仅具有三次Bézier曲线的特性,而且具有灵活的形状可调性和更好的逼近性。最后讨论了两种扩展曲线的拼接条件及它们在曲线曲面造型中的应用,并给出了两个扩展曲面的定义。实例表明,定义的两种新扩展曲线为曲线/曲面的设计提供了两种有效的新方法。In order to construct Bezier curves with shape control parameters,two classes of polynomial basis functions of 3th and 4th degree are presented in this paper.They are both extensions of cubic Bernstein basis functions.Properties of the proposed basis functions are analyzed and the corresponding polynomial curves with shape control parameters α,γ and α,β,γ are constructed accordingly.The constructed curves not only inherit the outstanding properties of the cubic Bezier curve,but also are adjustable in shape and fit close to the control polygon.In addition,the continuity condition and some applications in curve and surface design about the new curves are discussed,and two definition of Extension-surface are also presented.Some examples illustrate the new curves are very valuable for the design of curves and surfaces.

关 键 词：BÉZIER曲线 曲线设计 形状参数 扩展 拼接 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]