New accurate algorithms of circularity evaluation

Abstract

The minimum circumscribed circle (MCC), maximum inscribed circle (MIC), and minimum zone circle (MZC) methods for circularity evaluation are difficult to execute due to the lack of specific rules in mathematics, especially the MZC. New accurate algorithms have been proposed to realize the MIC, MCC and MZC evaluation methods. First, the diameter criterion and acute triangle criterion of control points defining the MIC or MCC are presented. The definition of the crossing sector structure is introduced in the minimum zone criterion and transformed into an angular relationship of control points, making it easy to identify the MZC. Then the key points of the algorithms are presented in details including the initial circle or the initial region, centre moving direction, minimum step size and updating rules of control points. Flow charts are provided to make the algorithm producible. Finally, four cases are selected to demonstrate the advantages of the algorithms. The results show that the proposed MZC algorithm is more general than that in the published reference. Compared to the traditional ergodic searching algorithms, the efficiency of the new algorithm for the MIC, the MCC and the MZC evaluations of circularity can be improved by 100% when the point set increases to 100 and above.

An Efficient Improved Harris Hawks Optimizer and Its Application to Form Deviation-Zone Evaluation

“…A minimum-zone fitting function was created to enhance the roundness error evaluation. Zhuo et al [24] introduced the definition of the crossing sector structure based on the minimum-zone criterion and transformed it into an angular relationship of control points, making it easy to identify the MZC. For straightness error, Li et al [25] proposed a simple bidirectional algorithm based on a four-point model for the calculation of the minimum-zone straightness error from planar coordinate data.…”