一种曲线拟合圆心坐标算法及精度分析

A curve fitting algorithm for the center coordinates and accuracy analysis

针对在工程应用中,经常需要根据某些圆形物体上的离散点求取其圆心坐标,而采用何种算法简单易行,其精度又与哪些因素有关的相关研究较少的问题,该文提出一种利用曲线拟合求取圆心坐标的简洁算法,并编程实现。然后采用模拟仿真结合统计分析的方法评估了该算法在不同条件下的拟合精度,得出测点误差越大,拟合精度越低;测点个数越多,分布越均匀,拟合精度越高;圆半径对拟合精度影响甚小等结论。在某工程项目中使用该算法得到的结果精度较高,验证了其有效可行,且与采用其他方法得到的坐标值较为接近,说明了该算法的可靠性高。

In engineering applications, the center coordinates often need getting from discrete points which distributed in some round object. But the researches about which kind of algorithm is simple and which factors are related with its accuracy is poor. Aiming at this problem, this article presents a simple curve fit algorithm for the center coordinates and programming. Then using statistical analysis and simula- tions to assess the accuracy of the algorithm in different conditions, drawing a conclusion： the bigger measuring point error, the lower accuracy; the more number of measuring points and the more evenly dis- tributed, the higher fitting precision; radius has little impact on fitting accuracy. In a project, the accura- cy of the result is high by using the algorithm, is verified its effectiveness. The results are closer to the co- ordinates by using other methods, which proves the high reliability of the algorithm.