A quick algorithm for evaluation of minimum zone circles from polar coordinate data

It is very important to select the initial four candidate points of the minimum zone circles to improve the computational efficiency. According to the radius of the measured points, three models of error evaluation are proposed and corresponding algorithms are given for evaluating the minimum zone circles based on the lower envelope lines, four-point intersection principle, and bisection method. The points constructing the lower envelope lines can be used for the evaluation of the maximum inscribed circle. Several examples have been carried out to validate the validity of the proposed algorithm.It is very important to select the initial four candidate points of the minimum zone circles to improve the computational efficiency. According to the radius of the measured points, three models of error evaluation are proposed and corresponding algorithms are given for evaluating the minimum zone circles based on the lower envelope lines, four-point intersection principle, and bisection method. The points constructing the lower envelope lines can be used for the evaluation of the maximum inscribed circle. Several examples have been carried out to validate the validity of the proposed algorithm.