Variable resolution Poisson-disk sampling for meshing discrete fracture networks

TL;DR

This paper introduces nMAPS, an efficient algorithm for generating variable resolution Poisson-disk samples for meshing complex 2D and 3D fracture networks, ensuring near-maximal coverage and mesh quality.

Contribution

nMAPS is a novel two-stage algorithm that efficiently produces variable resolution meshes for complex fracture networks with guaranteed properties in 2D and practical quality in 3D.

Findings

nMAPS generates meshes in linear time relative to accepted points.

The method produces conforming Delaunay triangulations and tetrahedra.

Low-quality tetrahedra are infrequent and can be removed to improve mesh quality.

Abstract

We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high quality balanced mesh is produced.