B样条类曲线及其在曲线参数化中的应用

BASIC SPLINE CLASS CURVES AND ITS APPLICATION IN PARAMETRIZATION OF CURVES

从B样条基函数出发,通过参数变换,导出B样条函数类的概念,讨论了它们的性质。给出B样条类曲线和附加权因子的B样条类曲线的理论,研究了它们与B样条曲线的关系。提出B样条曲线重新参数化因子的概念,探讨通过基函数的重新参数化实现B样条曲线的重新参数化的方法。结果表明,该方法具有较好的通用性以及计算简单、便于操作等特点。

Proceeding from the expression of basic spline basis functions, the concept of basic spline function class is deduced from parameter transformation, their properties are discussed in details. As a member of basic spline basis function class, BSC （ Basic Spline Class ） functions are defined and the theory of BSC curves and BSC curves with weighted factors are systematically founded. Then, the relation between BSC curves and basic spline curves is studied. Finally, the notion of reparametrization factor of B-spline curves is given and a new way of reparametrization of basic spline curves realized through the reparametrization of basis function is investigated. In dealing with the reparametrization of basic spline curves, it can be concluded that a new useful method with many advantages, such as good in universality and simple computation as well as convenient in operation, is obtained.