带双参数六次Said-Ball曲线的扩展

Extension of Six Times Said-Ball Curves with Two Parameters

为了满足曲线的设计要求,针对六次Said-Ball曲线不能调整曲线形状的不足,一个含有双形状参数的六次多项式基函数被给出,探讨了所构造的基函数的性质。基于该基函数定义了带有双形状参数的六次Said-Ball扩展曲线,分析了2段扩展曲线连续拼接应满足的条件。在给定控制多边形的情况下,通过改变形状参数值,可以调整曲线形状,增强了曲线的表达能力,弥补了六次Said-Ball曲线不能调整曲线形状的不足。该方法是不仅实用而且有效,在计算机辅助几何设计中可以得到广泛地应用。

The six Said-Ball curves have a deficiency that their shapes cannot be adjusted. In order to meet the design requirements of the curves,a six order polynomial basis function with double shape parameters is constructed,and the properties of the basis functions are discussed. Based on the basis function,the six Said-Ball expansion curves with two shape parameters are defined; the conditions for continuous splicing of two section extension curves are analyzed. For a given control polygon,the shape of the curves can be adjusted by changing the shape parameter values,which enhances the expression ability of the curves so that the deficiency of the six Said-Ball curves is made up. The method is practical and effective,and can be widely used in computer aided geometric design.