五次Bézier曲线的三种不同扩展

三组含有参数λ的六次多项式基函数是五次Bernstein基函数的扩展;基于此三组基分别定义了带有形状参数的三类多项式曲线;三类曲线不仅具有五次Bézier曲线的特性,而且具有形状的可调性和更好的逼近性;在一组基的基础上利用的de Casteljau算法,得到n+1次n+1个带有参数λ的的基函数,并定义了相应的n+1次曲线。应用实例表明,本文定义的曲线应用于曲线曲面的设计十分有效。

Three Different Extensions of Quintic B(e)zier Curve

Three classes of polynomial basis functions of 6th degree with shape control parameter λ are presented.They are extensions of quintic Bernstein basis functions.Properties of these three bases are analyzed and the corresponding polynomial curves with a shape parameterare λ are defined accordingly.These curves not only inherit the outstanding properties of quintic Bézier curve,but also are adjustable in shape and fit close to the control polygon.And a class of polynomial function of(n+1)th degree that containing an parameter is obtained by using de Casteljau algorithm Some examples illustrate the method of constructing curve is very useful for curve and surface design.