Computing Volume Properties Using Low-Discrepancy Sequences

Abstract

This paper considers the use of low-discrepancy sequences for computing volume integrals in solid modelling. An introduction to low-discrepancy point sequences is presented which explains how they can be used to replace random points in Monte Carlo methods. The relative advantages of using low-discrepancy methods compared to random point sequences are discussed theoretically, and then practical results are given for a series of test objects which clearly demonstrate the superiority of the low-discrepancy method when used in a simple approach. Finally, the performance of such methods is assessed when used in conjunction with spatial subdivision in the svLis geometric modeller.