Finding the exact volume of a polyhedron

Abstract

This paper addresses the design and development of a computer program for finding the exact volume of a multi-dimensional polyhedron that is enclosed by a set of linear inequalities. The program is designed to calculate the volume of a polyhedron of any dimensions defined by a set of linear inequalities. The speed of the program depends on the number of inequalities and the number of variables. The program has been tested against several two- and three-dimensional polygons in which the volume can be calculated by formulae. The results of the tests show that the accuracy of the program is at least up to 10-6 and it can calculate the volume of a three-dimensional polygon defined by a few hundred inequalities in just a few minutes. However, as the number of variables increases, the computation time increases exponentially. The program can be used in some science and engineering application such as finding the probability of an event, the volume of a crystal in a wafer fabrication industry, and other applications in the manufacturing industry. © 2003 Elsevier Science Ltd. All rights reserved.