Abstract: In order to construct B-spline curves with local shape control parameters，a class of polynomial basis functions with two local shape parameters λ_i，μ_i is presented in this paper.It is extensions of classical cubic uniform B-spline basis functions.Properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve is constructed with two local shape control parameters λ_i，μ_i accordingly.The curve not only inherits the outstanding properties of the cubic uniform B-spline curves，but also has a good performance on adjusting their local shapes by changing the two local shape control parameters.In particular，the G¹ continuuity and the shapes of other segments of the curve can remain unchangeably during the manipulation on the shape of each segment on the curve.Furthermore，its applications in curve design and interpolation are discussed and an extend application on surface design is also presented.Modeling examples show that the new curve is very valuable for the design of curves and surfaces.

Key words: cubic uniform B-spline, blending functions, local shape parameter, extension, curve design

摘要： 给出了一组含有2个形状参数λ_i，μ_i的三次多项式调配函数，它是三次均匀B样条基函数的扩展；分析了这组调配函数的性质，基于此组调配函数定义了一种带2个局部形状控制参数λ_i，μ_i的分段多项式样条曲线，它以三次均匀B样条曲线为特殊情形。新曲线不仅具有灵活的局部形状可调性和更强的描述能力，而且可以在不改变曲线G¹连续性和不影响曲线其他各段形状的同时，通过改变局部形状参数对曲线每段的形状进行多种方式的局部调整。最后讨论了新曲线在曲线造型中的应用，并给出了一个扩展曲面的定义。实例表明，新扩展曲线为曲线/曲面的设计提供了一种有效的新方法。

关键词: 三次均匀B样条, 调配函数, 局部形状参数, 扩展, 曲线设计