TetraSDF: Precise Mesh Extraction with Multi-resolution Tetrahedral Grid

Extracting meshes that exactly match the zero-level set of neural signed distance functions (SDFs) remains challenging. Sampling-based methods introduce discretization error, while continuous piecewise affine (CPWA) analytic approaches apply only to plain ReLU MLPs. We present TetraSDF, a precise analytic meshing framework for SDFs represented by a ReLU MLP composed with a multiresolution tetrahedral positional encoder. The encoder’s barycentric interpolation preserves global CPWA structure, enabling us to track ReLU linear regions within an encoderinduced polyhedral complex. A fixed analytic input preconditioner derived from the encoder’s metric further reduces directional bias and stabilizes training. Across multiple benchmarks, TetraSDF matches or surpasses existing gridbased encoders in SDF reconstruction accuracy, and its analytic extractor produces highly self-consistent meshes that remain faithful to the learned isosurfaces, all with practical runtime and memory efficiency.