Tetrahedral meshing via maximal Poisson-disk sampling

Abstract

In this paper, we propose a simple yet effective method to generate 3D-conforming tetrahedral meshes from closed 2-manifold surfaces. Our approach is inspired by recent work on maximal Poisson-disk sampling (MPS), which can generate well-distributed point sets in arbitrary domains. We first perform MPS on the boundary of the input domain, we then sample the interior of the domain, and we finally extract the tetrahedral mesh from the samples by using 3D Delaunay or regular triangulation for uniform or adaptive sampling, respectively. We also propose an efficient optimization strategy to protect the domain boundaries and to remove slivers to improve the meshing quality. We present various experimental results to illustrate the efficiency and the robustness of our proposed approach. We demonstrate that the performance and quality (e.g., minimal dihedral angle) of our approach are superior to current state-of-the-art optimization-based approaches.

Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh

“…This approach, while being effective at creating a high quality, isotropic, 3D Delaunay mesh, is inefficient with respect to use of computing resources [74]. Other methods, such as Poisson disk sampling in 3D [75,76] may prove to be a more efficient approach, but has not been implemented or utilized for the calculations presented here.…”

Reconstrucción virtual tridimensional de entornos urbanos complejos

“…Esto hace que sean menos precisos, aunque si son más rápidos. Estos métodos se dividen en dos categorías: los enfoques basados en Voronoi/Delaunay Dey and Goswami (2004); Lhuillier (2018); dou y los basados en crecimiento de malla Digne (2014); Guo et al (2016); Morel et al (2018).…”

Sliver-suppressing tetrahedral mesh optimization with gradient-based shape matching energy

“…Tetrahedral mesh generation has been studied for several decades [5], and these approaches can be categorized as advancing front methods [6,7,8], octreebased methods [9,10], Delaunay-based tetrahedral methods [11], Poisson-disk sampling methods [2], etc.…”

“…In this paper, we focus on the tetrahedral mesh generation. There are several measurements for tetrahedral mesh quality, and dihedral angle is one of the most important criteria [1,2], since badly-shaped tetrahedrons with tiny dihedral angles (i.e., sliver) can severely affect numerical simulation [3].…”