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

作　　者：梁锡坤[1] 

机构地区：[1]杭州师范大学信息科学与工程学院,浙江杭州310018

出　　处：《计算机应用与软件》2009年第4期93-95,共3页Computer Applications and Software

基　　金：浙江省教育厅科研基金(20050718)

摘　　要：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.

关 键 词：参数变换 B样条函数类 BSC函数 曲线 重新参数化因子 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP391.72[自动化与计算机技术—计算机科学与技术]