基于直曲线判断的曲线拟合研究

Research on Curve Fitting Based on Straight Curve Judgment

针对数控加工中任意形状的轮廓拟合速度慢、精度低等问题,提出一种基于直曲线判断的非均匀有理B样条曲线自适应逼近方法。该方法首先得到直线和曲线的过渡点,并按离散点顺序判断出直线或曲线。若是直线,采用最小二乘法拟合该直线;若是曲线,采用曲率与斜率相结合的方法求出曲率极大值点,作为关键点插值非均匀有理B样条曲线,利用德布尔递推公式反求出控制点,生成初始插值曲线。然后求出所有原始离散点与初始插值曲线上对应点的误差,若最大误差不满足给定要求,则在最大误差处自适应增加一个关键点形成新的插值曲线,反复迭代直到最大误差满足给定误差条件。相比传统算法,该方法能够更好地凸显整体轮廓的主要特征。实验证明该方法不仅可以得到最少的控制点数目,还具有速度快、逼近精度高等特点。

Aiming at the problem of slow speed and low precision of arbi trary shape in NC maching,a non-uniform rational B-spline curve adaptive approximation method based on straight curve judgement is proposed. The method first obtains the transition point of the straight line and the curve？ and in accordance with the order of discrete points to determine the straight line or curve. In the case of a straight line,the straight line is fitted by the least squares method. If the curve , u s in g th e c om b in a t io n o f c u r v a tu re and slope method to find the curvature of the maximum point？ as a key point interpolation non-uniform rational B-spline curve. Using the De Boer recursion formula to find out the control points,generating the initial interpolation curve. And then find out error between all the original discrete points and the corresponding points on the initial interpolation curve. If the maximum error does not meet the given requirthe maximum error in the adaptive increase of a key to form a new interpolation curve.until the maximum error satisfies the given error conditions. Compare with the traditional algorithm,the method can meet the specified accuracy requirements faster. Experiments show that the method can not only get the minimum number of control points , b u t also has th e c h a ra c te r is t ic s o f fa s t speed a n d h ig hprecision.