A linear algorithm of spatial straightness for five points

It is a non-linear problem to evaluate the minimum zone spatial (3-D) straightness. Because of the disadvantages of evaluating spatial straightness error with traditional method, such as difficulty in solving the non-linear equation, the evaluating precision is lower. This paper develops a solution that can transform the non-linear problem into a linear problem. The solution can obtain more exact results than traditional method using results of LSC as initial conditions. This methodology can also be applied to the problems of computing the minimum circumscribed cylinder and the maximum inscribed cylinder. The effectiveness and efficiency of the novel approach are illustrated by two examples.