四点细分法极限曲线与控制多边形的距离估计

Estimating the Distance between the Limit Curves of Four-point Subdivision Scheme and Its Control Polygon

四点插值细分法已广泛应用于几何造型及其相关领域。通过估计若干次细分后的点与控制多边形之间距离及细分后控制多边形的边长,推导了四点插值细分法的极限曲线与其初始控制多边形之间的距离上界。理论分析和计算实例表明,该距离上界优于已有的距离上界。

The four-point subdivision scheme is wildly used in geometric modeling and related fields. By estimating the distance between the points and the control polygon and the length of the edges of control polygon after some subdivision steps, we get some bounds of the distance between the limit curves of four-point subdivision scheme and its control polygon. Theoretical analysis and calculation examples show that our distance bound is better than existing one.