# TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization

arXiv: https://arxiv.org/abs/2505.04590 · HTML: https://mlsanity.com/paper/2505.04590/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 88 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decomposition](https://mlsanity.com/paper/2110.14373/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [NeRFactor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination](https://mlsanity.com/paper/2106.01970/) (2021)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Kaolin: A PyTorch Library for Accelerating 3D Deep Learning Research](https://mlsanity.com/paper/1911.05063/) (2019)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Deep Geometric Texture Synthesis](https://mlsanity.com/paper/2007.00074/) (2020)
- [Stanford-ORB: A Real-World 3D Object Inverse Rendering Benchmark](https://mlsanity.com/paper/2310.16044/) (2023)

## Built on by (most cited first, 6 of 6)

- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)
- [DiffTrans: Differentiable Geometry-Materials Decomposition for Reconstructing Transparent Objects](https://mlsanity.com/paper/2603.00413/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)
- [Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds](https://mlsanity.com/paper/2607.28855/) (2026)
- [Differentiable Voxelization of Surface Representations](https://mlsanity.com/paper/2608.15934/) (2026)
- [ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction](https://mlsanity.com/paper/2609.06723/) (2026)

## Abstract (arXiv)

We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh - a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation.