中文摘要：

文章给出了一组由3个含参数的4次多项式构成的基函数,在此基础上递推定义了由任意n＋1（n≥3）个含参数的代数三角混合函数构成的函数组,称之为n阶λ-Bernstein基,它具有Bernstein基函数的非负性、规范性、对称性等性质。由之定义的λ-Bézier曲线除了具备Bézier曲线的基本性质以外,还具有2个突出的优点：其形状可以在不改变控制顶点的情况下自由调整;当相邻λ-Bézier曲线的控制顶点满足普通Bézier曲线的G1光滑拼接条件时,曲线在公共连接点处可达G2光滑拼接。运用张量积方法定义的λ-Bézier曲面同样具有很多良好的性质。

英文摘要：

A group of basis function consisting of three quartic polynomials with parameter is given. Then based on it, a set of basis function which is composed of n＋1 （n≥3） algebraic trigonometric blending functions with parameter, to be called λ-Bernstein bases＇ of order n, is defined recursively. They have many basic properties of Bernstein basis functions, such as non-negativity, normalization, symmetry, etc. The λ-Bezier curves defined by them possess the basic properties of Bezier curve. Furthermore, the new curves have two distinct advantages. Firstly, their shape can be adjusted freely without changing the control points. Secondly, when the control points of two adjacent λ-Bezier curves satisfy the G1 continuity conditions of Bezier curve, they can achieve G2 continuity. By using the tensor product method, λ-Bezier surfaces can be defined, which also show many good properties.