Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes

TLDR

Generating Monte Carlo distributions efficiently and practically while avoiding common pitfalls is a key challenge. The study proposes a tunable Constrained Poisson‑disk sampling scheme for polygonal meshes to generate customized sampling distributions. Two algorithms implementing the Constrained Poisson‑disk sampling approach are presented. The algorithms are evaluated through an in-depth analysis of their frequency characteristics and performance.

Abstract

This paper deals with the problem of taking random samples over the surface of a 3D mesh describing and evaluating efficient algorithms for generating different distributions. We discuss first the problem of generating a Monte Carlo distribution in an efficient and practical way avoiding common pitfalls. Then, we propose Constrained Poisson-disk sampling, a new Poisson-disk sampling scheme for polygonal meshes which can be easily tweaked in order to generate customized set of points such as importance sampling or distributions with generic geometric constraints. In particular, two algorithms based on this approach are presented. An in-depth analysis of the frequency characterization and performance of the proposed algorithms are also presented and discussed.