TPMS and lattice catalog

pyvcad_metamaterials supplies seven periodic implicit cells and six graph cells. This guide compares those cells on the same rectangular maps, then uses ordinary CSG to fill more familiar part geometries.

Build a finite rectangular map

Every catalog builder receives a CellMap first:

import pyvcad as pv
import pyvcad_metamaterials as mm

cell_map = mm.rectangular_cell_map(
    (pv.Vec3(-15.0, -15.0, -15.0), pv.Vec3(15.0, 15.0, 15.0)),
    cells=(3, 3, 3),
)

Use cells=(nu, nv, nw) when exact repetition count and phase matter. Use cell_size=... when approximate world spacing is more convenient. cell_size is converted to integer counts by rounding upward, so the requested world bounds remain exact and the realized spacing adjusts slightly to fit them.

TPMS catalog

The names in mm.TPMS_NAMES can be passed to mm.tpms(...), and each also has a named helper such as mm.gyroid(...) or mm.schwarz_p(...).

Gyroid

I-WP

Lidinoid

Neovius

Schwarz-D

Schwarz-P

Split-P

The complete interactive gallery is 02_tpms_gallery.py.

Sheet and solid modes

sheet = mm.gyroid(cell_map, mode="sheet", wall_thickness=1.6)
solid = mm.gyroid(cell_map, mode="solid", level=0.0)

Sheet mode: a wall around the level surface

Solid mode: one labyrinth side of the level surface

In sheet mode, wall_thickness is the requested wall thickness in millimetres. In solid mode, level shifts the dividing surface and changes the retained labyrinth. Standard TPMS cells use the local map metric so those controls remain world-unit quantities when the cells are deformed.

See 01_tpms_gyroid.py for the side-by-side interactive example.

Graph lattice catalog

Graph lattices use normalized vertices and edges, then map each repeated segment into world space. mm.LATTICE_NAMES lists the built-in catalog.

Cubic

BCC

FCC

Kelvin

Octet

Diamond

lattice = mm.octet(
    cell_map,
    beam_radius=0.8,
    node_radius=0.9,
    curve_tolerance=0.05,
)

beam_radius controls strut radius in millimetres. node_radius optionally overrides the joint radius; if omitted, joints follow the beam field. curve_tolerance controls subdivision of beams that become curved under a non-linear map.

See 03_strut_lattices.py for the complete interactive catalog.

Fill ordinary geometry

Mapped structures are ordinary nodes, so lattice filling is an Intersection. Build a map over the target’s bounds, build the architected material, and clip it with the target geometry.

sphere = pv.Sphere(pv.Vec3(0.0, 0.0, 0.0), 16.0)
cell_map = mm.rectangular_cell_map(
    (pv.Vec3(-17.0, -17.0, -17.0), pv.Vec3(17.0, 17.0, 17.0)),
    cells=(4, 4, 4),
)
root = pv.Intersection(sphere, mm.gyroid(cell_map, wall_thickness=1.4))

Gyroid clipped to a sphere

3DBenchy with gyroid infill

Utah teapot with octet infill

For imported meshes, call prepare(...) before querying bounding_box(), then construct the rectangular map from the returned bounds. The complete examples are 04_lattice_in_shape.py, 10_benchy_gyroid_infill.py, and 11_teapot_lattice_infill.py.

Parameter summary

Structure	Topology	Primary geometric controls
TPMS sheet	ImplicitUnitCell	wall_thickness, level, map cell count/spacing
TPMS solid	ImplicitUnitCell	level, map cell count/spacing
Graph lattice	GraphUnitCell	beam_radius, node_radius, curve_tolerance, map cell count/spacing

All of these scalar controls can also change across a design. Continue with Attribute-driven metamaterials to grade geometry, cell spacing, and material distribution.