# Fast Tetrahedral Meshing in the Wild

arXiv: https://arxiv.org/abs/1908.03581 · HTML: https://mlsanity.com/paper/1908.03581/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2019.

## Built on by (most cited first, 30 of 35)

- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [Learning Skeletal Articulations with Neural Blend Shapes](https://mlsanity.com/paper/2105.02451/) (2021)
- [GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation](https://mlsanity.com/paper/2406.14927/) (2024)
- [Recent Trends in 3D Reconstruction of General Non-Rigid Scenes](https://mlsanity.com/paper/2403.15064/) (2024)
- [NeuManifold: Neural Watertight Manifold Reconstruction with Efficient and High-Quality Rendering Support](https://mlsanity.com/paper/2305.17134/) (2023)
- [PAT3D: Physics-Augmented Text-to-3D Scene Generation](https://mlsanity.com/paper/2511.21978/) (2025)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [Neural Impostor: Editing Neural Radiance Fields with Explicit Shape Manipulation](https://mlsanity.com/paper/2310.05391/) (2023)
- [TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation](https://mlsanity.com/paper/2210.05735/) (2022)
- [Robust Biharmonic Skinning Using Geometric Fields](https://mlsanity.com/paper/2406.00238/) (2024)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Neural Green's Functions](https://mlsanity.com/paper/2511.01924/) (2025)
- [Learning Body-Aware 3D Shape Generative Models](https://mlsanity.com/paper/2112.07022/) (2021)
- [TwinTac: A Wide-Range, Highly Sensitive Tactile Sensor with Real-to-Sim Digital Twin Sensor Model](https://mlsanity.com/paper/2509.10063/) (2025)
- [Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary](https://mlsanity.com/paper/2202.02568/) (2022)
- [Split, Merge, and Refine: Fitting Tight Bounding Boxes via Over-Segmentation and Iterative Search](https://mlsanity.com/paper/2304.04336/) (2023)
- [Smoothness and continuity of cost functionals for ECG mismatch computation](https://mlsanity.com/paper/2201.04487/) (2022)
- [Pop-Out Motion: 3D-Aware Image Deformation via Learning the Shape Laplacian](https://mlsanity.com/paper/2203.15235/) (2022)
- [XVoxel-Based Parametric Design Optimization of Feature Models](https://mlsanity.com/paper/2303.15316/) (2023)
- [CageNet: A Meta-Framework for Learning on Wild Meshes](https://mlsanity.com/paper/2505.18772/) (2025)
- [MechStyle: Augmenting Generative AI with Mechanical Simulation to Create Stylized and Structurally Viable 3D Models](https://mlsanity.com/paper/2509.20571/) (2025)
- [VibraVerse: A Large-Scale Geometry-Acoustics Alignment Dataset for Physically-Consistent Multimodal Learning](https://mlsanity.com/paper/2511.20422/) (2025)
- [Deep Feature Deformation Weights](https://mlsanity.com/paper/2601.12527/) (2026)
- [GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems](https://mlsanity.com/paper/2607.01128/) (2026)
- [Learning-Based Biharmonic Augmentation for Point Cloud Classification](https://mlsanity.com/paper/2311.06070/) (2023)
- [M2DNeRF: Multi-Modal Decomposition NeRF with 3D Feature Fields](https://mlsanity.com/paper/2405.05010/) (2024)
- [Deformable NeRF using Recursively Subdivided Tetrahedra](https://mlsanity.com/paper/2410.04402/) (2024)
- [Snap-and-tune: combining deep learning and test-time optimization for high-fidelity cardiovascular volumetric meshing](https://mlsanity.com/paper/2506.08280/) (2025)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)

## Abstract (arXiv)

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.