A Large Scale Extended Algorithm for 2D Halton Points with Low-Discrepancy Sequences

Abstract

Random discrete points have important application value in meshless PDE equation discretization, molecular dynamics simulation, point cloud imaging and so on. There are many common methods to generate random points, such as Monte Carlo, Gibbs Sampling, and Hammersley series and etc. But Halton random point algorithm has a defect that it only generates discrete points in [0,1]2 region. However, in practical applications, it is necessary to be able to generate discrete points on any area. This paper proposed a new Halton points extension algorithm to solve this defects. We defined a linear operator which can transform discrete points from [0,1]2 region into any plane region. Two examples are given, the extension algorithm respectively includes square, rectangular and polar coordinates region. The numerical results show that our method is accurate, effective and more general, it also enhanced the application range by our method.