三次均匀B样条曲线的扩展  

An Extension of the Cubic Uniform B-Spline Curve

作　　者：韩旭里[1] 刘圣军[1] 

机构地区：[1]中南大学应用数学与应用软件系,长沙410083

出　　处：《计算机辅助设计与图形学学报》2003年第5期576-578,共3页Journal of Computer-Aided Design & Computer Graphics

基　　金：湖南省自然科学基金 (0 1JJY2 0 95 );教育部回国人员科研基金 (教外司 [2 0 0 1] 498号 )

摘　　要：给出四次多项式调配函数 ,它是三次B样条函数的扩展 基于给出的调配函数 ,建立一种带形状参数的分段多项式曲线的生成方法 通过改变形状参数的取值 ,可以调整曲线接近其控制多边形的程度 ;可以调整曲线从三次均匀B样条曲线的两侧逼近三次均匀B样条曲线 选取不同的形状参数值 ,可以得到不同位置的C2 连续的曲线 ,且所给曲线与三次均匀B样条曲线有相同的端点性质A class of polynomial blending functions of degree 4 is presented Based on the blending functions, we get a method of generating piecewise polynomial curves with a shape parameter By changing the value of the shape parameter, we can adjust the approaching degree of the curves to their control polygon and manipulate the curves to approximate the cubic uniform B spline curves from their both sides For the given value of the shape parameter, the generated curves can be C 2 continuous and have the same terminal properties as the cubic uniform B spline curves Some computing examples of the curve design are given

关 键 词：CAGD 计算机辅助设计 三次均匀B样条曲线 基函数 形状参数 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]