基于代数和三角多项式加权的二次混合样条曲线  

Quadratic blending spline curves based on weighted algebraic and trigonometric polynomials

作　　者：谢进[1,2] 檀结庆[2] 李声锋[2,3] 

机构地区：[1]合肥学院数理系,安徽合肥230601 [2]合肥工业大学计算机与信息学院,安徽合肥230009 [3]蚌埠学院数理系,安徽蚌埠233000

出　　处：《中国科学技术大学学报》2011年第6期512-518,共7页JUSTC

基　　金：国家自然科学基金(61070227);教育部科学技术研究重大项目(309017);教育部博士点基金(20070359014);安徽省教育厅教研重点项目(20100935);合肥学院科研重点项目(11KY02ZD)资助

摘　　要：利用代数和三角多项式加权的方法,构造了一种二次混合样条曲线,这种曲线具有二次非均匀B样条曲线相似的性质.这里的权系数也是形状参数,称之为权参数,取值范围从[0,1]扩大到[-3.659 79,5.278 98].权参数的不同取值可以整体或局部地调整曲线的形状,并且权参数能像开关那样,使得曲线的各段非常方便灵活地在代数多项式、三角多项式之间转换.不需要用重节点或解方程组方法,而只要令某个或某些权参数取-3.659 79,曲线就能接插值于控制点或控制边.A method for generating quadratic blending spline curve with weighted algebraic and trigonometric polynomial was presented.The method possesses many important properties similar to those of quadratic non-uniform B-splines.Here weight coefficients are also shape parameters,which are called weight parameters.The interval of weight parameter values can be extended to [-3.659 79,5.278 98].Taking different values of the weight parameters,one can not only totally or locally adjust the shape of the curves but also change the type of some segments of a curve among trigonometric or algebraic polynomial.Without using multiple knots or solving the system of equations and letting one or some weight parameters be-3.659 79,the curve can interpolate certain control points or control polygon edge directly.

关 键 词：代数三角多项式 权参数 整体与局部调控 插值 混合曲线段 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]