一类特殊基函数构造的参数曲线  

A New Kind of Parametric Curves by Special Basis Function

作　　者：李敬改 陈秋阳 韩佳琦 黄奇立 朱春钢[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《计算机科学》2018年第3期46-50,共5页Computer Science

基　　金：国家级大学生创新创业训练计划资助项目(2016101410906);国家自然科学基金(11671068);中央高校基本科研业务费专项基金(DUT16LK38)资助

摘　　要：构造参数曲线曲面一直是计算机辅助几何设计研究的核心内容之一。以Bernstein基函数构造的Bézier曲线是参数曲线造型最基本的方法,B样条曲线和NURBS曲线都是在其基础上发展而来。利用给定的实数节点集,构造一类特殊的基函数,此类基函数是Bernstein基函数的推广。在此基础上,构造了一类新的参数曲线,称为T-Bézier曲线,T-Bézier曲线继承了有理Bézier曲线的若干性质;证明了当节点移动时极限曲线的几何性质,并通过实例进行了验证。The construction of parametric curves and surfaces is very important in computer aided geometric design.It's well known that Bézier curve,which is defined by Bernstein basis functions is a basic method in curve design,and the Bspline curve and NURBS curve are generalizations of the Bézier curve.This paper defined a new kind of basis functions by agiven real knot points set,which is a generalization of Bernstein basis functions,and defined a new parametric curve by these basis functions,called T-Bézier curve,which preserves some properties of Bézier curve.What's more,this paper presented the limit property of T-Bézier curve while some knots move and gave some examples to verify the properties of the curve.

关 键 词：参数曲线 基函数 有理BÉZIER曲线 计算机辅助几何设计 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]