F13LD.tpms
Triply-periodic minimal surfaces (TPMS) generated directly from their implicit equations, including the gyroid and the Schwarz P and D surfaces. A surface can be given a solid offset or a constant wall thickness, graded across the domain, or phase-shifted along each axis.
What it generates.
A TPMS is a single smooth surface that repeats in all three directions and divides space into two interpenetrating channels. F13LD.tpms evaluates the surface on a grid and assigns it a thickness, producing a solid or a shell that can be meshed and printed.
Use it when you need a fully connected, periodic lattice with continuous curvature and no sharp internal corners. For irregular or foam-like structures, see grain or noise; for strut-and-node trusses, see beam.
Implicit surfaces and level sets.
Each surface is the zero level set of a periodic function — the points where φ(x, y, z) = 0. The gyroid approximates to sin x cos y + sin y cos z + sin z cos x = 0. Editing the terms changes the surface; the equation bar shows the current expression.
Thickness comes from the level set. A solid keeps the region on one side of the surface, and the iso value sets how much volume that region occupies; a thin wall instead follows a constant-thickness shell along the surface itself. The same construction underlies several tools — it is covered in level sets & topology.
Worked example: a gyroid.
Pick a surface
Open preset surfaces and select gyroid. The structure loads and the equation bar updates to match. Each preset is a short set of sine and cosine terms that can be edited afterward.
Set the cell count and size
cells sets how many unit cells fill the domain, which fixes the pore and feature size. cell size sets the unit-cell dimension in millimetres so the model is to scale.
Give it volume
Select a mode — solid, thin wall, or PI-TPMS — then set offset (solid) or wall t (thin wall). This controls the volume fraction, or relative density, of the lattice.
Check the stiffness
Run homogenization. The directional-stiffness plot shows the effective stiffness by direction, and the Zener ratio reports how far the lattice is from isotropic. Adjust offset and cells to reach the target.
Hand it off
Use Open in F13LD.mesh to pass the recipe to meshing, or Export JSON to save it. The design is unchanged either way.
Each control has an i in the tool that opens its reference entry. This page is the walkthrough; the in-tool guide documents what every control does.
Presets.
Parameter sets to load as starting points and adjust.
Gyroid, solid mode, mid offset. Near-equal stiffness in all directions.
Schwarz P, thin wall. Higher stiffness along the cell axes.
PI-TPMS mode, small pipe radius. Strut-like, with open channels.
Gyroid with the gradient ramp on one axis. Dense on one face, open on the other.
Export and handoff.
F13LD.tpms exports a recipe JSON — a description of the surface and its parameters, not a mesh. The recipe is the format the suite shares: vault stores it, sweep varies it, and mesh evaluates it into geometry.
Open in F13LD.mesh passes the recipe to F13LD.mesh, which rebuilds the surface, previews a watertight result, and exports a 3MF. That handoff is described on the mesh page.