TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid

TetraSDF is a new analytic isosurface extraction framework for neural signed distance functions that tries to bridge a familiar tradeoff in reconstruction pipelines. Sampling-based methods like Marching Cubes are easy to use, but they approximate the surface on a grid and can introduce discretization error. Pure analytic approaches can be exact, but they often lean on plain ReLU MLPs that struggle to represent the high-frequency detail many modern SDFs need.

The core idea is to pair a ReLU MLP with a multi-resolution tetrahedral positional encoder. Because the encoder uses barycentric interpolation, the representation stays globally continuous piecewise affine, which lets the method track ReLU linear regions through an encoder-induced polyhedral complex. In practical terms, that means the zero-level set can be recovered exactly as a triangle mesh rather than approximated from samples.

The method also adds a fixed analytic input preconditioner derived from the encoder’s metric to reduce directional bias and stabilize training. Across multiple benchmarks, TetraSDF matches or exceeds existing grid-based encoders on SDF reconstruction accuracy while still extracting the network’s own surface faithfully. For engine and tools teams, the appeal is obvious: better reconstruction quality without giving up exact surface extraction, which matters for asset generation, scan cleanup, and any workflow that depends on tight geometric fidelity.