三次参数曲线的区间扩展

Interval extension of the cubic parametric curves

为了在传统三次参数曲线中引入形状参数,通过将三次Ferguson曲线、三次Bézier曲线、三次均匀B样条曲线等传统三次参数曲线的定义区间由固定区间[0,1]扩展为动态区间[0,α],构造了3种带参数α的三次参数曲线,分别称之为三次α-Ferguson曲线、三次α-Bézier曲线以及三次均匀α-B样条曲线.所构造的α-曲线是原三次参数曲线的同次扩展,不仅方程结构简单,继承了原曲线的性质,而且可通过修改参数α的值实现对曲线形状的调整,是一种简单有效的形状可调参数曲线构造方法.

In order to introduce the shape parameter into the traditional cubic parametric curves,definition interval of cubic Ferguson curve,cubic Bézier curve and cubic uniform B-spline curve is extended from a fixed interval[0,1]to a dynamic interval[0,α].Then three cubic parametric curves with parameterαare constructed,which are named cubicα-Ferguson curve,cubicα-Bézier curve and cubic uniformα-B-spline curve,respectively.The proposed threeα-curves are extensions of the corresponding cubic parametric curves.They not only have simple structure,inherit the properties of the corresponding cubic parametric curves,but also can be adjusted by altering the value of parameterα.Therefore,the proposed method is a simple and effective method for constructing shape-adjustable parametric curves.