三次Ball曲线的两种新扩展

Two New Extensions of Cubic Ball Curve

给出了次数分别为3和4的含参数的多项式基,它们都是三次Ball曲线基函数的扩展。基于这两组基函数定义了两类带形状参数的多项式曲线,新曲线不仅具有三次Ball曲线的特征,而且具有形状可调性和比三次Ball曲线更好的逼近性。通过分析新曲线与Bézier曲线之间的关系,得出了形状参数的几何意义,并给出了新曲线的几何作图法。

Two classes of polynomial basis of 3th and 4th degree are presented.They are extensions of cubic Ball basis.Based on these two bases,two polynomial curves with shape parameters are defined.They not only inherit the outstanding properties of the cubic Ball curve,but also are adjustable in shape and fit closer to the control polygon than the cubic Ball curve.The geometrical meaning of shape parameters is discovered by analyzing the connection of the new curves and the Bézier curve.Meanwhile,the geometrical drawing method of the extension curves is given out.