An effective determination of the minimum circumscribed circle and maximum inscribed circle using the subzone division approach

Abstract

Abstract Aiming to develop a more effective circularity evaluation method that satisfies the definition of a particular reference circle criterion, this paper proposes a strategy to determine the minimum circumscribed circle (MCC) and maximum inscribed circle (MIC) using the subzone division approach. The whole circumference zone space that encloses all the sampling data points is divided into different subzones to determine the target candidate feature points, which are used for constructing the MCC or MIC. The first feature point of the MCC/MIC is evaluated according to the farthest/nearest distance from the center of the least squares circle (LSC) within the whole circumference subzone. Subzone with a 120° central angle is designated in the direction of the first feature point that is mapped about the center of the LSC. The second candidate feature point is constrained and determined within this subzone. The third subzone, which contains the third feature point, is formed in the direction of the first and second feature points that are mapped about the center of the LSC. The mathematical model of the MCC or MIC is then constructed using these three feature points. Experimental examples (using five different datasets) and a comparison with previous studies demonstrate that the proposed method yields the exact solution for the MIC and MCC in only 1–2 iterations.