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

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