Computation of intersection volume using discrete quadrature algorithm

Abstract

Quasi Monte Carlo algorithm is one of the most famous particle method, which is used to solve intersection volume computation problem. Inspired by the quasi Monte Carlo algorithm, a discrete quadrature algorithm is proposed to calculate the intersection volume. First, the three dimensional entity with unknown function is divided into a series of random sequences points using the quasi Monte Carlo algorithm. Second, calculating the common point set in terms of a given function three dimensional entity. Finally, both the intersection volume and irregularity intersection volume are approximated by the number of the common point set. Simulation shows that the proposed method has the advantages in estimation accuracy and computational load.