一类T-Bézier曲线的α扩展

α extension of a class of the T-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,将一类T-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,the representation of the T-Bézier curve is extended.The generalized T-Bézier curve is denoted as α extension T-Bézier curve,whose shape-control capability is shown to be much better than that of T-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.