中文摘要：

利用代数和三角多项式加权的方法,构造了一种二次混合样条曲线,这种曲线具有二次非均匀B样条曲线相似的性质.这里的权系数也是形状参数,称之为权参数,取值范围从[0,1]扩大到[-3.659 79,5.278 98].权参数的不同取值可以整体或局部地调整曲线的形状,并且权参数能像开关那样,使得曲线的各段非常方便灵活地在代数多项式、三角多项式之间转换.不需要用重节点或解方程组方法,而只要令某个或某些权参数取-3.659 79,曲线就能接插值于控制点或控制边.

英文摘要：

A method for generating quadratic blending spline curve with weighted algebraic and trigonometric polynomial was presented.The method possesses many important properties similar to those of quadratic non-uniform B-splines.Here weight coefficients are also shape parameters,which are called weight parameters.The interval of weight parameter values can be extended to [-3.659 79,5.278 98].Taking different values of the weight parameters,one can not only totally or locally adjust the shape of the curves but also change the type of some segments of a curve among trigonometric or algebraic polynomial.Without using multiple knots or solving the system of equations and letting one or some weight parameters be-3.659 79,the curve can interpolate certain control points or control polygon edge directly.