带两个形状参数的五次Bézier曲线的扩展

Extension of the Quintic Bézier Curve with Two Shape Parameters

给出了一组含有两个形状参数α,β的六次多项式基函数,是五次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线具有五次Bézier曲线的性质,改变参数α,β的取值,曲线具有更灵活的形状可调性,而且能向上或从两侧逼近控制多边形.另外,经典的五次Bézier曲线和有关文献中带一个形状参数的曲线均是该文所定义曲线的特例.实例表明,定义的曲线为曲线/曲面的设计提供了一种有效的方法.

A class of 6-degree polynomial basis functions containing two shape control parameters α,β is presented.It is the extention of quintic Berstein basis functions.Properties of this new basis are analyzed and a polynomial curve with two shape parameters is defined based on it.The curve inherits the outstanding properties of the quintic Bézier curve,its shape can adjusted flexibility through changing the value of α,β and approach to the given polygon up or from both sides.The classical quintic Bézier curve and the curves with a parameter in related literatures are especial examples of this paper.Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.