Rapid precise detection on arc with discrete points arbitrarily distributed based on the coordinates

Arc detection is difficulty for the processing, assembly and testing of industrial production because of limitations of the detection method, algorithm and the instrument. The least-squares algorithm usually is used to fit data in circle detection. The application of the conventional least-squares algorithm is limited, its roundness error is bigger, and precision is lower. For detecting arc with data points of non-uniform distribution, obtained least-squares algorithm (Equation 1-4), for the arc with discrete points non-uniformly distributed, fitted data based on least-square definition. Developed an analysis algorithm for assessing the minimum region roundness error (Equation 5), center and radius can be accurately solved, without iteration, without truncation error. Used the discrete data instances to verify different roundness error evaluation methods (Table 1), roundness errors of uniformly distributed arc with 7 points are 0.73mm, 0.6mm, 0. 8mm and 0.8mm, and roundness errors of non-uniformly distributed arc with 7 points are 0.69mm,0.61mm,1.32mm and 0.72mm. Leading the relative error rate of roundness error ∮k, can analyse the roundness error, the machining accuracy, processing method and micro ratio etc.. The relative error rate are ∮k1=0.0676, ∮k2= 0.0489, ∮k3=0.0829, ∮k4=0.0481 and ∮k1=0.0550,∮k2= 0.0495,∮k3=0.1514,∮k4=0.0494 respectively The improved least-squares algorithm and the minimum area algorithm are suitable for distributed data of all kinds situations, particularly suitable for the realization of machine vision inspection system, fast speed and high precision.