一类可调控的三次多项式曲线

为拓展Bézier曲线的表示方法,本文首先给出了一组带有两个形状参数的三次调配函数,是二次Bernstein基函数的一种扩展。然后,基于该调配函数生成了一类可调控的三次多项式曲线,并讨论了该曲线与二次Bézier曲线及三次Bézier曲线之间的关系。事实表明,该曲线是二次Bézier曲线的一种扩展,不仅具有二次Bézier曲线的诸多特性,而且由于带有两个形状参数,使得曲线具有更强的表现能力,在控制顶点不变时,可通过修改两个形状参数对曲线进行局部或全局调节。为方便自由曲线的设计,还讨论了两段曲线的拼接条件,给出了该曲线在曲线设计中的实例应用。

A Class of Modifiable Cubic Polynomial Curve

For extending the representation of the Bézier curve, a class of cubic polynomial basis functions with two shape parameters is presented in this paper firstly, which is an extension of the quadratic Bernstein basis. Then, a modifiable cubic polynomial curve is presented based on the basis functions, and the relation between the curve and the classical Bézier curves is discussed. The curve is an extension of the quadratic Bézier curve, which inherits most properties of the quadratic Bézier curve, and its shape can be local or globally modified by changing the values of the two shape parameters when the control points are not changed. For designing free curves, the continuity condition of the two-piece curves is discussed. Finally, some application examples of the curve in the curve design are presented.