带多形状参数的三角多项式均匀B样条曲线曲面  

Trigonometric Polynomial Uniform B-spline Curves and Surfaces with Multiple Shape Parameters

作　　者：尹池江[1] 檀结庆[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2011年第7期1131-1138,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60773043;61070227);教育部博士点基金(20070359014);教育部科学技术研究重大项目(309017)

摘　　要：由于在进行几何外形设计时对曲线曲面的局部调控能力要求越来越高,为了给设计者们提供更丰富的方法,利用分段积分的思想构造了一类带多个形状参数的三角多项式均匀B样条曲线曲面,并讨论了这类曲线曲面所具有的重要性质.通过改变形状参数的取值来整体或局部调控曲线曲面形状,随着曲线阶数的升高扩展形状参数的取值范围;通过公式推导给出了曲线精确表示直线、椭圆、抛物线、螺旋线的表达式.最后给出了曲线的几何造型实例,体现了该类曲线在CAGD中的应用价值.In geometric modelling,the demand of local control ability of curves and surfaces is increasing.To provide more alternative approaches for designers,based on the piecewise integral,a class of trigonometric polynomial uniform B-spline curves and surfaces with multiple shape parameters is presented and the important properties of these curves and surfaces are discussed.The shape of such curves and surfaces can be adjusted totally or locally by changing the values of the shape parameters,and feasible range of the shape parameter values can be extended with the elevation of the order.The accurate expressions of straight lines,ellipses,parabolas and spirals are worked out by means of the presented trigonometric polynomial uniform B-spline curves,and some geometrical modelling examples of the curves are given to show that this kind of curves are of significant practical applications in computer aided geometric design.

关 键 词：形状参数 调配函数 三角多项式 均匀B样条 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]