Learning-based Delaunay Tetrahedral Mesh Generation from Signed Distance Field

Converting signed distance fields (SDFs) into tetrahedral meshes requires balancing geometric accuracy, element quality, and computational cost. We present a learning-guided framework that combines adaptive sampling with classical geometric construction to accelerate this process. A neural network predicts density fields from the input SDF, learning where to allocate surface and volume samples from density targets derived from reference tetrahedral meshes. Adaptive blue-noise sampling, Delaunay tetrahedralization, and marching tetrahedra then construct a mesh whose boundary follows the input field. A post-processing stage then fixes geometric and topological errors and improves element quality. To validate our approach, we evaluate accuracy, element quality, topology, complexity, and runtime. On four held-out datasets at grid resolutions from $128^3$ to $384^3$, our method matches the geometric accuracy of CGAL while running up to $2.4\times$ faster, and every output mesh is closed, manifold, and free of slivers. Applied to SDFs produced by an image-to-3D generative model, it robustly and efficiently meshes shapes on which classical algorithms fail.