Two-point methods for evaluation of the minimum zone circle

Xiuming Li; Xuedi Hao; Guangjie Wang; Yuanzhuo Tang; Xudong Li

doi:10.1063/5.0234792

Two-point methods for evaluation of the minimum zone circle

Rev Sci Instrum. 2024 Dec 1;95(12):125104. doi: 10.1063/5.0234792.

Authors

Xiuming Li^{1

2}, Xuedi Hao¹, Guangjie Wang¹, Yuanzhuo Tang³, Xudong Li⁴

Affiliations

¹ School of Mechanical and Electronic Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China.
² Key Laboratory of Intelligent Mining and Robotics, Ministry of Emergency Management, Beijing 100083, China.
³ Flying College, Beihang University, Beijing 100191, China.
⁴ Shenzhen Experimental School, Shenzhen 518055, China.

PMID: 39625357
DOI: 10.1063/5.0234792

Abstract

According to the cross-distribution of four control points of the minimum zone circle, the four-point conditions that two control points on the circumscribed circle and two control points on the inscribed circle meet are proposed. Based on these conditions, a two-point method is proposed, which is suitable not only for the determination of two control points on the circumscribed circle but also for the determination of two control points on the inscribed circle. In the iterative process, redundant data points can be simply determined by using dichotomy in order to improve computational efficiency. Several examples have been carried out to validate the validity of the algorithm proposed.