形状可调Bézier曲线的构造方法  

The Construction Method of Shape Adjustable Bézier Curve

作　　者：严兰兰 韩旭里[2] 黄涛[1] Yan Lanlan;Han Xuli;Huang Tao(College of Science, East China University of Technology, Nanchang 330013, China;School of Mathematics and Statistics, Central South University, Changsha 410083, China)

机构地区：[1]东华理工大学理学院,江西南昌330013 [2]中南大学数学与统计学院,湖南长沙410083

出　　处：《湖南科技大学学报（自然科学版）》2018年第2期110-117,共8页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：国家自然科学基金资助项目(11261003;11761008);江西省自然科学基金资助项目(20161BAB211028);江西省教育厅科技项目(GJJ160558)

摘　　要：针对Bézier曲线相对于控制顶点形状固定的不足,各种含参数的、性质类似于Bernstein基函数的调配函数纷纷被提出,但这些调配函数是如何推导出来的却无从知晓.本文借助经典Bernstein基函数的升阶公式,基于由可调控制顶点定义可调曲线的思想来定义形状可调Bézier曲线,详细展示了调配函数的构造过程,现有文献中的很多调配函数都可用该方法得到.按本文方法定义可调Bézier曲线,其形状参数的几何意义直观明了.本文不仅揭示了可调Bézier曲线形状可调的本质,而且给出了构造含参数的多项式调配函数的通用方法.Aiming at the drawback that the shape of Bezier curve was fixed with respect to the control points, various blending functions with parameter and with similar properties to the Bemstein basis functions were presented. But there was no way to know how do theses blending functions were derived. With the help of the degree elevation formula of the classical Bernstein basis function and based on the idea that the adjustable curve was defined by the adjustable control points, the shape adjustable B6zier curve is defined. The construction process of the blending function was demonstrated in detail. Many blending functions in the existing literatures can be obtained by this method. To define the adjustable B6zier curve according to the method given here, the geometric meaning of the shape parameter is straightforward. Not only the nature of shape adjustable of the Bezier curve is revealed, but also the general method of constructing polynomial blending functions with parameter is given.

关 键 词：曲线表示方法 BÉZIER曲线 形状参数 调配函数 

分 类 号：G633.66[文化科学—教育学]