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

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