An exact solution for the roundness evaluation problems

Two theorems based on the minimax criterion are developed to solve the roundness evaluation problems. The Voronoi diagram is the basic component for this research. Using the Voronoi diagrams, the whole feasible plane is divided into a finite number of regions defined as the max regions. The first theorem shows that the exact minimum roundness can be obtained only at an X-type vertex on the max region. Theorem two indicates that the minimum roundness is determined by four critical measured points that lead to an efficient way to solve the minimax solution. (C) 1999 Elsevier Science Inc. All rights reserved.