平面超椭圆曲线的二次NURBS逼近

基于超椭圆曲线的基本性质、方程及其图形表示,研究了超椭圆曲线指数s和欲逼近的二次NURBS曲线权重系数w之间的对应关系,给出了超椭圆曲线的一种高精确的二次NURBS逼近方法,避免了因超椭圆曲线取点误差而可能产生的对生成曲面的影响,也大大缩减了计算量。文中给出了超椭圆曲线的二次NURBS逼近效果图,探讨了将此方法用于飞机机身曲面外形设计的相关步骤。

Quadric NURBS Approximation of Planar Hyperelliptic Curve

Based on the geometric properties,curve equations and graphics of hyperelliptic curves,this paper analyzes the relation between the exponent of hyperelliptic curve and the weight coefficient of NURBS curve which approaches the hyperelliptic curve.An accurate approximation method for hyperelliptic curve with quadric NURBS curve is presented.Because of the inaccurate points from the hyperelliptic curve,the generated surface has errors.The method avoids these errors and reduces the computation time.Some cutlines are given to explain the good approximate impacts of quadric NURBS for the hyperelliptic curve.Additionally the correlative process of the airframe surface model built by the method is also discussed.