拟三次Bézier曲线

Cubic Quasi-Bézier Curve

给出了一组含有2个参数的多项式基函数，它是三次Bernstein基函数的扩展；基于该组基定义了带形状参数的多项式曲线，称之为拟三次Bezier（Q-Bezier）曲线。Q-Bezier曲线不仅具有三次Bezier曲线的特征，而且在控制多边形保持不变的条件下，具有形状可调性和对控制多边形更好的逼近性。形状参数具有明显的几何意义：控制曲线端点的性质。最后，给出了一些图形实例。

A class of polynomial basic function with two adjustable shape parameters is presented. It is an extension to classical cubic Bernstein basis function. A polynomial curve, called cubic Quasi- Bezier （Q-Bezier） curve with two shape parameters is defined based on it. The curve inherits the most properties of cubic Bezier curve and the shape of Q-Bezier curve can be adjusted by alerting the two shape parameters when the control polygon is maintained. The Q-Bezier curve can be more approximated to the control polygon. It is visible that the properties of end-point on Q-Bezier curve can be controlled by the two shape parameters. Finally, some examples are given by figures.