四次NURBS表示对称圆弧曲线的实用方法

Some Practical Approaches of Representing Symmetric Clrcular Arcs With Biquadratic Nurbs

研究了用四次NURBS表示标准解析形状中最简单也最有代表性的圆锥曲线———对称圆弧的问题,给出了一种实用的四次NURBS表示对称圆弧曲线的方法,该方法用5个控制顶点的NURBS曲线来表示一象限的对称圆弧,使参数u=1/2的值为圆弧的中心点,同时满足控制顶点和权因子在圆弧中心点处是对称的.该方法给出的控制顶点和权因子的计算结果,符合对圆弧NURBS表示的要求,不必进行推导计算,便于工程应用中推广使用.

This paper mainly studies how to use biquadratic NURBS to represent symmetric circular arcs, the simplest and the most representative conic curve and gives a practical approach of representing symmetric circular arcs with biquadratic NURBS, in which a quadrant of symmetric circular arcs are represented by a segment of NURBS curve determined by five control points, the of value is made as the circular arcs central point, and at the same time the demand is met that the control points and weights are symmetry in the circular arcs central point. The calculated results of control points and weights given by the method meets the demands of circular arcs NURBS representation and need no calculating. The method is convenient to be generalized in engineering application .