三次Bézier曲线的α扩展

α Extension of the Cubic Bézier Curve

利用一个对称的调配函数,结合NURBS曲线中权的思想,在曲线控制顶点处引进调配参数,将三次Bézier曲线进行扩展,得到的新曲线比原来的曲线有更强的描述能力,并且包含了原曲线形式。讨论了扩展曲线的基表示及曲线的性质,调配参数可以用来控制曲线的局部形状,特别适用于自由曲线曲面的设计,在CAD/CAM中具有很好的应用前景。

By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the cubic Bézier curve.The generalized cubic Bézier curve is denoted as α Extension cubic Bézier curve,whose shape-control capability is shown to be much better than that of Bézier curve.The representation and properties of the extension curve is studied.The curve is easy and intuitive to reshape by varying the parameters;so it is useful in some applications of CAD/CAM .