Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

TL;DR

This paper introduces a two-stage algorithm for generating variable resolution Delaunay meshes in 2D and 3D using near maximal Poisson-disk sampling, demonstrated on complex fracture networks.

Contribution

The paper presents a novel linear-time method for 2D and 3D mesh generation employing Poisson-disk sampling, effective even without guaranteed quality bounds in 3D.

Findings

Efficient mesh generation in linear time.

High-quality meshes achieved after removing low-quality tetrahedra.

Successful application to complex 3D fracture networks.

Abstract

We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2- and 3-dimensions in linear run time. The effectiveness of the algorithm is demonstrated by generating an unstructured 3D mesh on a discrete fracture network (DFN). Even though Poisson-disk sampling methods do not provide triangulation quality bounds in more than two-dimensions, we found that low quality tetrahedra are infrequent enough and could be successfully removed to obtain high quality balanced three-dimensional meshes with topologically acceptable tetrahedra.