基于MATLAB单双圆弧混合逼近曲线的算法及实现

Algorithm and Realization of Single and Double Arc Mixed Approximating Curve in MATLAB

讨论了单圆弧和双圆弧逼近的特点,结合两者的优点,用优化三点圆弧以允差逼近曲线和单双圆弧混合逼近的算法,理论上使得曲线有拐点和极值点时整个逼近圆弧的光滑连接,并保证了圆弧逼近的段数达到最少。基于Matlab采用比例法、一维搜索和优化相结合的方法进行程序的编制求解节点,算法简单,可靠,程序运行快速高效。为数控加工复杂的曲线和CAD系统提供了参考。

This paper discusses the features of single and double arc approximating, and combines the merits of two kinds of fitting. By the algorithm of approximating curve in optimizing three - point arc and mixing single and double arc in permission tolerance, smooth link of whole approximating arc with inflexion points and extreme value points is attained in theory, and the minimal number of arc approximating segments is ensured. Joining optimization with scale and linear search, the nodes are solved by programming in MATLAB software, the algorithm is more simple and reliable, thus the program runs more rapidly and efficiently. This algorithm provides reference for processing complex curve in numerical control and CAD system.