二次均匀B样条曲线的新扩展及应用

New extensions of quadratic uniform B-spline curve and its applications

文章给出含2个参数λi、μi的三次和四次多项式调配基函数,并将其推广到高次形,它们都是二次B样条基函数的推广;基于给出的调配函数,建立带双参数的分段多项式曲线,讨论了基函数的性质和参数的几何意义;最后给出实例,表明新推广的曲线为曲线设计提供了一种有效的方法。

A class of polynomial basis functions of degree 3 and degree 4 with two parameters λi,μi are presented in this paper,which are the extensions of the uniform quadratic B-spline basis functions and can be extended to the case of degree n.Based on these blending functions,a method of generating piecewise polynomial curves with two parameters is given.The properties of the basis functions and the geometric meaning of the parameters are discussed.The examples of the curve design given in this paper show that these new curves provide a very effective method for curve design.