An exact minimum zone solution for three-dimensional straightness evaluation problems

A mathematical model giving the exact solution for three-dimensional (3-D) straightness evaluation based on the minimum zone criterion is presented in this paper. This model builds upon the convex hull of the measured point set to show that the 3-D straightness is determined simply by some measured points on the vertices of the convex hull. The axis of the critical cylinder giving the minimum objective value is proved to be parallel to one of the edges of the convex hull. This model is effective and easy for implementation.