Fourier-Latent Diffusion for Constrained Generation of Triply Periodic Minimal Surfaces
2026-08-03 • Graphics
Graphics
AI summaryⓘ
The authors developed a method to create special 3D surfaces called triply periodic minimal surfaces (TPMS) that have very low curvature, meaning they are very smooth and mathematically minimal. They made a big collection of over 18,000 unique TPMS shapes by carefully building small surface patches and combining them while keeping symmetry and periodic patterns. Then, they trained a machine learning model (a diffusion model with transformers) to generate new TPMS designs in a compressed space that respects these patterns. Their system can create new shapes, modify existing ones, and meet specific design rules, helping with applications that need customized minimal surface structures.
Triply Periodic Minimal SurfaceDiffusion ModelTransformerFourier Latent SpaceMean CurvaturePeriodic Boundary ConditionsSurface SymmetryInverse DesignHomogenized Elastic Properties
Authors
Shu Yan, Bohan Wang
Abstract
We propose a diffusion-based generative framework for controllable generation of triply periodic minimal surface (TPMS) structures with low residual mean curvature.Existing TPMS generation approaches are often restricted to a small set of canonical families or produce TPMS-like approximations that deviate from exact minimality. To enable this generative framework, we first construct a large-scale dataset of over 18K unique TPMS by enumerating admissible boundary loops on mirrorable fundamental bounding volumes and solving for diverse minimal-surface patches. Each surface is then projected onto a compact Fourier latent space that explicitly enforces periodicity and $D_{2h}$ symmetry. Next, a transformer-based diffusion model is trained in this latent space to support unconditional sampling, deterministic inversion, local editing, and conditional generation under user-specified constraints. Experiments demonstrate that the model generates diverse, low-curvature TPMS candidates that, under conditioning, satisfy sparse geometric constraints and match target homogenized linear elastic properties, providing a practical tool for TPMS inverse design.