【作者】 王园园；

【导师】 王晶昕；

【作者基本信息】 辽宁师范大学 ， 基础数学， 2009， 硕士

【摘要】 在样条函数的逼近领域及应用领域中,在原来设计样条函数的基础上做必要的修正以求达到更好的逼近效果是非常重要的的课题,在这方面已经有很多的方法,而运用调节参数就是一个主要的方法.本文在对[15, 16, 17, 18, 19, 20, 21, 22, 23]的工作的充分分析的基础上,重新给出了两类带多调节参数的参数曲线的构造方法,包括:1.用变换矩阵给出带多调节参数的Be′zier曲线扩展,并具体分析了其性质,根据几何性质将其进行了分类.本文在第二章给出了带两个调节参数的二阶Be′zier曲线的扩展:在第三章给出了带n个调节参数的n阶Be′zier曲线的扩展:2.运用前面的思路给出带多个调节参数的均匀B样条曲线的构造方法,并体分析了其性质.在第四章首先给出了带多个调节参数的三阶B样条曲线扩展,其表示为:继带多个调节参数的三阶B样条曲线后,本文在第四章构造了带多个调节参数的n阶B样条曲线,其表示为:在本文中给出的这两类曲线引入了多个调节参数,这使得参数成为局部参数,它既能整体调控曲线的形状,又能局部调控.而且有别于其它参数曲线,它是在基函数不变即仍然使用Be′zier和B样条基的前提下,通过通过使用参数调节控制点来调节曲线形状.由于函数基是不变的,因此减弱了对参数的范围限制,使参数的取值有任意性,增加增加了带参数的曲线的自由度,因此能很好的调节曲线.更多还原

【Abstract】 In the field of B-spline function approximation theory and application,in orderto arriving at better effect ,modulating basis functions is an important way,and therehave been many methods abort that,using shape modification parameters is one ofthese.In this paper,at the base of the job of [15, 16, 17, 18, 19, 20, 21, 22, 23], we constructand research two kinds of curves with multiple modification parameters are listed asfollows:1. Given an extension of Be′zier curve with multiple modification parameters,andprofoundly research the properties of it.Further more ,we class it with its Geo-metric characters.In the second chapter,we are given a kind of an extension of order two Be′zierIn the third chapter,we are given a kind of an extension of n order Be′zier curvewith n modification parameters:2. Given an extension of uniform B-spline curve with multiple modification param-eters,and profoundly research the properties of it.In the forth chapter,we are given a kind of an extension of three order B-splinecurve with multiple modification parameters:curve with two modification parameters: After the extension of three order B-spline curve with multiple modification pa-rameters,we give n order uniform B-spline curve with multiple modification pa-rameters:In the paper we Take different values of modification parameters make the pa-rameters become of local parameters,so we can globally or locally adjust the curveshape.Not liking other kinds of parameters curves,the two kinds of curves given inthis paper are given modification parameters at the base of without changing basisfunctions of the original Be′zier and uniform B-spline basis functions,therefore reduc-ing limits of parameters value. Because of values of these parameters can been chosenat random,we can adjust Be′zier curve with parameters much more liberty,can adjustthe shape of curves effectively.更多还原