三次Bézier曲线的两种新扩展

Two New Extensions of Cubic Bézier Curve

给出了两种带两个形状参数的三次基函数,两种基函数不是通过提高次数引入形状参数,而是直接在三次Bernstein基函数引入两个形状参数,是三次Bernstein基函数的新扩展。基于此两种基函数定义了两种扩展的三次Bézier曲线,扩展曲线不仅具有三次Bézier曲线的类似性质,而且具有更好的形状可调性。实例表明,新扩展曲线为曲线的设计提供了两种新方法。

Two cubic basis functions with two shape parameters are presented,and they are not constructed by increas-ing the degree of basis functions, but directly in the cubic Bernstein basis functions into two shape parameters. They are both extensions of cubic Bernstein basis functions. The corresponding polynomial curves are constructed accordingly. The constructed curves not only inherit the outstanding properties of cubic Bézier curve, but also are adjustable in shape. Some examples illustrate the new curves are very valuable for curves design.