【摘要】 <正>1引言曲线曲面造型技术在航空航天和船舶制造业有着非常重要的作用,但圆锥曲线中常见的圆、椭圆及双曲线却无法用多项式函数精确表示,因此人们广泛研究圆锥曲线的多项式逼近问题.作为最常用的圆锥曲线,圆弧的Bézier逼近方法一直是人们研究和关注的重点.自上世纪90年代初,Dokken^[1]研究圆弧的曲率连续三次Bézier逼近方法,此后二十多年来,人们主要围绕逼近误差的分析、逼近曲线的次数以及类型等方面进行广泛研究,取得丰富的研究成果^[2-5].作为圆的更一般情形,椭圆与圆具有很多类似之处,其逼近方法也存在更多还原

【Abstract】 In CAD system, Bézier curve could not accurately represent the ellipse.A high-precision approximation method of ellipse by the cubic Bézier function is proposed in this paper. Firstly, the positional parameter is determined by minimizing the maximum of the error function, and the explicit coordinates of all of the control vertexes of approximation curve are given. Thus cubic B é zier approximation of a quarter elliptical arc is constructed. Then cubic Bézier spline approximation of full ellipse is obtained using the symmetry of ellipse. The cubic Bézier spline approximation satisfy C1 continuity as a whole. Compared with the conventional method, the error obtained is smaller and the calculation is easier.Numerical example shows that the method is simple and effective.更多还原