Minimal range sampling algorithm for algebraic circle fitting and precision analysis

In the field of engineering surveying, it is necessary to measure discrete points on circular objects in order to obtain the coordinates of their centers. However, field measurements are often limited by environmental conditions, which result in uneven sampling of points and, consequently, deviations between the results of classical least-squares circle fitting algorithms and the actual situation. This paper improves upon the classical least-squares circle fitting algorithm by proposing an algebraic circle fitting algorithm. By combining simulation and statistical analysis, we analyze the fitting results under different distribution conditions for the collected data. Simulation results show that compared with the classical least squares circle fitting algorithm, the fitting accuracy (RMS) of the method in this paper is improved by 85.25% when sampling along small arcs. This indicates that the algorithm can perform local measurements in limited environments and accurately fit the circle center data, which will have good application prospects in fields such as engineering surveying.