二次均匀B样条曲线的扩展

Extension of the uniform quadratic B-spline curves

该文给出三次和四次多项式调配函数,并将之推广得到高次调配函数,它们是二次B样条函数的进一步扩展。基于给出的调配函数,可建立一种带形状参数的分段多项式曲线;调整形状参数可使三次多项式曲线在二次均匀B样条曲线两侧摆动,而四次多项式曲线在三次多项式曲线两侧摆动;最后给出实例,分别利用它们构造出带局部调节参数的G1和G2连续的曲线。

A class of polynomial functions of degree 3 and degree 4 are presented in this paper, which can be extended to the case of degree n. They are extension of the uniform quadratic B-spline basis functions. Based on the functions, a method of generating piecewise polynomial curves with a shape parameter is given. By changing the values of the shape parameters of polynomial functions of degree 3,a cluster of cubic curves containing uniform quadratic B-spline curves can be obtained, and changing the values of the shape parameters of polynomial functions of degree 4 results in the cluster of curves of degree 4 which includes the cubic B-spline curve as its special case. Two examples of the curve design are given at the end, and the generated curves with local shape parameters can beG^1andG^2continuous separately.