Perturbing Slivers in 3D Delaunay Meshes

Abstract

Summary. Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of well-shaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicity. The solution which explicitly perturbs the slivers through random vertex relocation and Delaunay connectivity update is very effective but slow. In this paper we present a perturbation algorithm which favors deterministic over random perturbation. The added value is an improved efficiency and effectiveness. Our experimental study applies the proposed algorithm to meshes obtained by Delaunay refinement as well as to carefully optimized meshes.

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

“…We cannot ensure that the global minimum is obtained, but we give experimental results that show the practical benefit of our mixed Newton/global optimization framework. However, slivers are not totally eliminated, thus requiring a postprocessing with sliver perturbation [31]. (2) Our method needs to fix the vertices on the boundary.…”

“…In [32,31], the sliver perturbation method is proposed. It can effectively remove slivers, though it may not We now compare the global ODT method with the interleaved method [32] and the Stellar method [20], using a model with uniform density in Figure 16.…”

Multi-material adaptive volume remesher

“…A first solution, called sliver exudation [23], turns the triangulation into a weighted Delaunay triangulation to address this problem. An alternative approach is to perturb slivers through vertex relocation and Delaunay connectivity update [24]. In a more general setting, the quality can be improved using optimization based-smoothing and local topological operations such as edge flip or removal [25].…”

Connectivity Oblivious Merging of Triangulations

“…Recently, these challenges have been one of the drivers of the development of pointbased (hybrid) approaches [2]. An alternative solution to this problem involves focusing only on triangulations whose connectivity can be implicitly derived from geometric constraints [3], [4], [5], such as Delaunay Triangulations (DT) [6]. However, these approaches are rather limited, since in some cases the underlying meshes do not comply with the required geometric constraints, thus falling back to the case where one needs to explicitly manage mesh connectivity [7].…”