一类特殊基函数构造的参数曲线

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 B-spline curve and NURBS curve are generalizations of the Bézier curve.This paper defined a new kind of basis functions by a given 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 pa-per presented the limit property of T-Bézier curve while some knots move and gave some examples to verify the proper-ties of the curve.