带形状参数的二次混合函数均匀B-样条

Quadratic mixed functional uniform B splines with shape parameters

文章利用控制多边形的方法,提出了3类带形状参数的二次混合函数均匀B样条,它们都具有二次多项式均匀B样条的基本性质;适当选取形状参数的值,不仅能整体或局部调控曲线形状,而且能使之直接插值某些控制点;此外,还可以使得同一曲线的某些子段在多项式、三角和双曲函数类中任取两类直接互相转换。

The technique of control polygons is used, and three types of quadratic mixed functional B spline curves with shape parameters are presented in this paper. These curves possess many important properties of quadratic B splines. By taking proper values of the parameters, one can not only totally or locally adjust the shape of the curves, but can interpolate directly some control points as well. Moreover, different segments of the same curve can change from one type to another type among polynomial, trigonometric or hyperbolic functions.