platosdf

A genetic evolver that generates 3D shapes defined by G-invariant Signed Distance Functions, optimised for DMLS/SLM metal 3D printing.

Repository: github.com/carlok/platosdf

Mathematical foundation: foundation.tex · formal notes: tex/g_carving_grammars.tex

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Core idea

Every shape in the population is a G-invariant SDF — satisfying f(g·x) = f(x) for all g ∈ G. This is enforced structurally by the grammar, not measured post-hoc.

The three symmetry groups correspond to the Platonic solids (finite irreducible subgroups of O(3)):

Seed	Group	Order
tetrahedron	Td	24
cube	Oh	48
icosahedron	Ih	120

Each shape is a G-grammar: a seed primitive (the initial G-invariant SDF) followed by a sequence of Boolean operations, each carving or adding a G-orbit of child primitives placed inside the fundamental domain FD(G).

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Structure

platosdf/
├── evolver/
│   ├── sdf_metal.py        # Metal/MPS SDF evaluator (PyTorch, Apple Silicon)
│   ├── mutate.py           # Mutation, crossover, tournament selection
│   ├── fitness.py          # DMLS/SLM fitness metrics (15 sub-scores)
│   ├── grammar_name.py     # Human-readable names and POSIX-safe slugs
│   ├── evolver_native.py   # GA main loop (CLI)
│   ├── config.json         # Population size, eval resolution, weights
│   └── tests/              # pytest suite
│       ├── test_mutate.py
│       ├── test_grammar_name.py
│       └── test_fitness.py
├── engine/
│   └── sdf.py              # NumPy SDF evaluator (CPU, server-side mesh export)
├── glb-viewer/
│   ├── index.html          # Three.js GLB viewer with material/light panel
│   └── serve.py            # Local HTTP server
├── tex/
│   └── g_carving_grammars.tex  # Small theorems on G-carving grammars
├── foundation.tex          # Formal mathematical specification
├── PLAN.md                 # Step-by-step build plan
└── PROMPT.txt              # Bootstrap prompt for new sessions

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Setup

python3.11 -m venv .venv
source .venv/bin/activate
pip install torch trimesh scipy scikit-image numpy pytest

Run

For direct upload to an SLM/DMLS service (e.g. weerg, Xometry, i.materialise):

cd evolver
python evolver_native.py \
    --mode resonant \
    --epochs 30 \
    --export-stl \
    --stl-mc-level -0.02 \
    --workers 8

--export-stl writes a .stl alongside every .glb each epoch.
--stl-mc-level -0.02 dilates the solid ~0.5 mm at 80 mm scale — enough to pass the 0.5 mm minimum wall check used by most SLM services. Increase the magnitude (e.g. -0.04) for stricter services or thinner shapes.
--mode resonant constrains placements to group-theoretically natural positions, which tend to produce cleaner, more printable geometry.

The fitness hard gate already rejects shapes below 0.5 mm wall thickness before they reach the STL stage, so every exported STL has passed the minimum wall check.

Resume a previous run:

python evolver_native.py --mode resonant --resume --export-stl --workers 8

Output is written to gallery/ (relative to evolver/):

gallery/
  epoch_0001/
    rank_01_<slug>.glb           # preview mesh (GLB, slight erosion)
    rank_01_<slug>.stl           # print mesh (STL, dilated for SLM wall thickness)
    rank_01_<slug>_grammar.json
    overview.glb                 # all top-k side by side
    fitness_log.json
  manifest.json                  # cross-epoch summary
  population.json                # last population (used by --resume)

GLB viewer

python glb-viewer/serve.py   # → http://localhost:5000

Drag-and-drop any .glb from the gallery. Panel controls: material presets, metalness/roughness sliders, IBL environment, light intensities, turntable.

Test

cd evolver
python -m pytest tests/ -q

---

Grammar encoding

A grammar is a JSON dict:

{
  "seed": {"type": "cube", "radius": 1.0},
  "iterations": [
    {"operation": "subtract", "primitive": "sphere",
     "fd_u": 0.3, "fd_v": 0.1,
     "distance": 0.7, "scale_factor": 0.3, "smooth_radius": 0.02}
  ]
}

fd_u, fd_v are barycentric coordinates in FD(G) — the irreducible spherical triangle for the group derived from the seed. symmetry_group is never stored; it is always derived from seed.type.

Name format: C.-s9u63v35k24d97 +i2u74v20 — seed char, op, primitive, smooth×0.005, u×100, v×100, optional scale (k) and distance (d) when non-default.

---

Fitness

15 weighted sub-scores, all in [0, 1]. Hard gates (non-watertight, islands, thin walls) return fitness 0.

Key weights: min_wall_thickness 0.15 · fractal_dimension 0.16 · curvature_variance 0.12 · normalised_S_V 0.08.

G-invariance is structural (enforced by grammar construction), not a fitness metric.

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Implementation notes

Carving-only grammar — OPERATIONS = ["subtract", "intersect"]. The add (union) operation was removed because orbit copies placed near the seed surface protrude as peninsulas. Carving-only is also physically correct for metal printing: you begin with a solid and remove material.

Mesh cleaning — extract_mesh_metal always returns the single largest connected component, at both eval and save resolution. Fitness gating and GLB export therefore always see the same topology. Only viable individuals (fitness > 0) get a .glb and _grammar.json saved.

Marching cubes level=0.01 — slight erosion (~0.8mm at 80mm print scale) removes necks thinner than ~1.6mm before they can appear as peninsulas in the GLB.

Distance capped at 1.0 — orbit copies placed at distance > seed_radius graze the surface from outside, creating thin fingers via subtract/intersect. Hard cap at 1.0 everywhere (generation, mutation, jitter).

Crossover step cap — crossover is capped at 5 iterations per child. Without the cap, repeated crossover produces grammars with 10–15+ steps and degenerate geometry.

Tetrahedral group generators — Td requires three generators: C3([1,1,1]), C2([1,0,0]), σ_d([1,-1,0]). Using only C3+σ_d yields S3 (order 6) instead of Td (order 24).

Diversity — pop=36, mutation_rate=0.65, fd Gaussian σ=0.22, tournament_k=3, ~12% fresh random individuals injected each epoch.