Using Quasi-Monte Carlo Method to Compute Volume of Point Set

Not having to reconstruct any surface,the algorithm first constructs an octree for a point set using a new volume-based refinement method.Then uniformly distributed quas-i random points are generated inside a box enclosing the point set using Niederreiter’s low discrepancy sequences.The volume of the point set can be estimated as the ratio of number of random points that are contained within the point set to the total number of random points generated,multiplied by the volume of the box.By testing on a number of point sets,experiments suggest that the new algorithm is simple,efficient and can work well for closed point sets with arbitrary topology.In addition,by combining the algorithm with smoothing operation,a volume-preserving smoothing is obtained.