Flatness tolerance evaluation: an approximate minimum zone solution

Abstract

This paper is concerned with the problem of flatness tolerance evaluation. First, we introduce the concepts of width and inner radius of point sets, and establish the equivalence between the width of a point set and the inner radius of the convex hull of the self-difference of the set. On this basis, we present an algorithm for calculating the exact minimum zone tolerance of flatness. Second, we prove that an approximation of the inner radius of a convex set can be obtained from the inner radius of the set in fixed direction. On this basis, we present an algorithm for calculating the ‘almost exact’ minimum zone solution. This algorithm is implemented by solving a single linear programming problem, of which the computational complexity is O( n). Numerical examples are given to validate the proposed algorithms.