A unified approach for circularity and spatial straightness evaluation using semi-definite programming

This paper demonstrates that a modern optimization method known as semi-definite programming (SDP) can serve as a unified tool for circularity and spatial straightness evaluation. Based on the minimum zone criterion (MZC), the problems of circularity and spatial straightness evaluation are formulated as differentiable constrained optimization problems firstly, and then reformulated as SDP problems. Within the SDP framework, both of the two aforementioned problems can be solved efficiently using recently developed interior-point algorithms, which are available in many efficient software packages. The effectiveness and efficiency of the novel approach are illustrated by examples and numerical simulations.