Fast tetrahedral meshing in the wild

Abstract

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.

Delaunay Meshing and Repairing of NURBS Models

“…One needs to select proper parameters in order to get a volume mesh with consistent quality. We compared with TetWild and its efficient variant FTetWild [HSW∗20] to generate a volume mesh from a tessellation which maintains trimming defects of aNURBS model (see Section 4.2.1). Figure 13 shows the diamond tessellation that challenges TetWild to generate a mesh with consistent quality, though different parameters are selected.…”

“…Software tools (e.g., MeshFix, Mesh‐Works, PolyMender) have been proposed for repairing meshes and polygon soups, with strict robustness requirements for 3D printing [LEM∗17]. The quest for valid volume meshing with unconditional robustness culminates with the recent significant advances for tetrahedral meshing in the wild [HZG∗18] and its recent efficient variant [HSW∗20]. The robustness of the approach is confirmed, though the mesh quality is not unconditionally consistent when large defects are present in the model.…”

Bone mineral density modeling via random field: normality, stationarity, sex and age dependence

“…The template geometry described by an implicit HU field was transformed to a triangulated surface by the marching cube algorithm [31]. The resultant triangular mesh was used to build a tetrahedral volume mesh (fTetWild [32]).…”

Surface multigrid via intrinsic prolongation

“…Our current solver is more sensitive to the triangle quality of the input mesh compared to the existing direct solver. In our experiments, we remesh troublesome input shapes using available methods [Hu et al 2020;Jakob et al 2015;Schmidt and Singh 2010]. A better future approach would be extending our self-parameterization to the entire remeshing process, to maintain bijectivity from the remeshed object to the input mesh.…”