# TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid

arXiv: https://arxiv.org/abs/2511.16273 · HTML: https://mlsanity.com/paper/2511.16273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 47 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [PermutoSDF: Fast Multi-View Reconstruction with Implicit Surfaces using Permutohedral Lattices](https://mlsanity.com/paper/2211.12562/) (2022)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [NSML: Meet the MLaaS platform with a real-world case study](https://mlsanity.com/paper/1810.09957/) (2018)
- [Tetra-NeRF: Representing Neural Radiance Fields Using Tetrahedra](https://mlsanity.com/paper/2304.09987/) (2023)
- [CamP: Camera Preconditioning for Neural Radiance Fields](https://mlsanity.com/paper/2308.10902/) (2023)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks](https://mlsanity.com/paper/2008.09052/) (2020)
- [Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks](https://mlsanity.com/paper/2002.06597/) (2020)

## Abstract (arXiv)

Extracting an explicit surface that exactly matches the zero-level set of a neural signed distance function (SDF) remains challenging. Sampling-based isosurfacing methods such as Marching Cubes introduce discretization error. In contrast, continuous piecewise affine (CPWA) analytic approaches typically require plain ReLU MLPs, which limits the ability to learn high-frequency SDFs in practice. We present TetraSDF, an analytic isosurface extraction framework for SDFs that retains the expressiveness of grid-based encoders while enabling exact zero-level set extraction, by representing the SDF with a ReLU MLP composed with a multi-resolution tetrahedral positional encoder. Our positional encoder's barycentric interpolation preserves a global CPWA structure, allowing us to track ReLU linear regions within an encoder-induced polyhedral complex. We further introduce a fixed analytic input preconditioner derived from the encoder's metric to reduce directional bias, thereby stabilizing training. Across multiple benchmarks, TetraSDF matches or surpasses existing grid-based encoders in SDF reconstruction accuracy, while faithfully recovering the network's zero-level set as a triangle mesh.