基于渐进迭代逼近的等距曲线改进算法

An Improved Algorithm for Offset Curves Based on the Progressive-iteration Approximation

提出一种基于渐进迭代逼近的等距曲线改进算法.该改进算法利用曲线段的高控制采样误差,在充分反映基曲线的形状特征的前提下尽可能地减少采样点数量.在采样点中选取等距曲线上的特征点作为主控制点,利用渐进迭代逼近方法插值所选取的主控制点,迭代过程中综合考虑法矢和参数化一致性两个因素以更好地控制等距逼近曲线的形状.最后,同样利用曲线段的高控制逼近误差,以避免误差过估,对得到的逼近等距曲线的B样条曲线实现更精确的全局误差控制.给出一些实例来验证该改进算法在采样点数量、所需控制顶点个数、迭代次数、误差控制、等距逼近曲线的形状控制等方面实现了性能的提高.

It proposes an improved algorithm for offset curve based on the progressive-iteration approximation. The improved algorithm controls the sampling error using the high of curve section. It could reduce the number of sample point as possible at the premise of reflecting the shape feature of the progenitor curve. Then the improved algorithm selects the characteristic points on the offset curve as the dominant points and interpolates the dominant points by using the progressive-iteration approximation, while taking into account of consistency of the normal vector and parameterization to control the shape of offset approximating curve better. Lastly, the algorithm controls the approximation error using the high of curve section to avoid overestimation the error. The B-spline curve approximating offset curve can achieve global error control. Some experimental results demonstrated the proposed algorithm can improve the performance in terms of controlling the number of sampling point, the number of control point, iteration times, error control, shape-control of offset curve.