MAGMA

Magma Tri-hex Pattern — Design Note (locked)

Third Magma infill pattern, after Triangle and Rectilinear. This note is the implementation reference; the design below is settled.

Terminology: a tri-hex injection unit is a manifold — one hub + N equal-length vent legs. The U-tube (triangle/square) is the degenerate 1-leg manifold.

1. Lattice — trihexagonal tiling

• Hexagon cells (hubs) + up/down triangle cells (vents) filling the gaps.
• Bipartite: a hex borders only triangles (6), a triangle borders only hexes (3); ratio 2 triangles : 1 hex.
• Edges remain 3 line families at 60°, so the toolpath stays triangle-like (single-wall, continuous sweeps) — FillMagmaTriHex is close to the triangle toolpath with the hex/triangle window logic.
• CellId.kind distinguishes HEX / TRI_UP / TRI_DOWN (the field already exists).
• MagmaLattice::neighbors() returns bipartite neighbors (vents for a hub, hubs for a vent), so the solver gets hub↔vent edges for free.

2. Injection model — the manifold

• A hub-tube = a hub cell over a layer range [start, cap], window(s) at the bottom (start), injected at the cap.
• Vent legs: each leg spans the SAME [start, cap] as its hub-tube — legs are equal length, because windows are pinned to the tube bottom (no adjustable/partial legs). Plastic enters each leg at the bottom window, fills up to the cap, air escapes at the cap (the print surface at injection time).
• One injection fills the hub + all its legs together.

3. Solver — UNCHANGED

• Feed the existing tube solver the bipartite hub↔vent lattice.
• Standard cell-exclusive matching (NoOverlap per cell) → each hub-tube gets exactly ONE vent (the primary leg), each vent serves ≤1 hub: a bipartite U-tube matching.
• This schedules hub-tube ranges with stagger / height / stacking AND guarantees feasibility (every scheduled hub-tube has ≥1 leg → can inject / vent air).
• Zero solver code change. A hex having 6 candidate vents instead of 3 is just more edges; the matching, runs, segments, stagger, and CP-SAT model are identical.

4. Extra-vent sweep — NEW, per vent, runs after the solver

Goal: maximize filled vent volume by adding extra legs to the already-scheduled hub-tubes. Runs after greedy and after CP-SAT (same code either way).

For each vent V:

1. Unavailable mask = layers where V is geometry-absent (part blocks the cell) ∪ layers already claimed by the solver’s primary matching. Both are treated identically.
2. Candidates = the bordering hub-tubes’ ranges [start, cap].
3. Delete any candidate that crosses an unavailable layer — a block/claim inside the range would trap air (no escape) → infeasible.
4. The surviving available layers form present-runs. Per run:
   • candidates = hub-tubes fully contained in the run,
   • pick the non-overlapping subset covering the most layers = weighted interval scheduling (exact; sort-by-cap + DP, or brute-force the handful of candidates),
   • tiebreak toward the least-loaded hub (evenness; minor — legs are low-volume),
   • assign V (those layers) as legs of the chosen hub-tubes. - Per vent independent (hubs are uncapped). A vent may be a leg of multiple stacked hub-tubes at different (non-overlapping) heights — each fed from its own tube’s bottom window, which lines up with the plug below by construction.

The sweep is purely additive: feasibility was already secured by the solver’s matching, so it can never strand a hub.

5. Finalize

• Each hub-tube now knows its hub + all legs (primary + extras) → an InjectionUnit.
• Windows: trihex_window_cuts (pattern-owned, like triangle_window_cuts / square_window_cuts) emits one gap per (hub, leg) at the tube bottom.
• Volume: sum over {hub + each leg} of (per-layer actual clipped area × height)
  • each window’s volume. compute_volumes already sums per-cell per-layer, so this is just a sum over the manifold’s members — no per-kind geometry needed.

6. Data model

• UTubePair → InjectionUnit { CellId hub; std::vector<CellId> vents; start/end layer; volume_mm3; injection_center; window_center_layer; … } with cell_a()/ cell_b() accessors so the 2-cell pair is the 1-leg special case.
• Triangle/square produce 1-leg units; their call sites change cell_a→hub, cell_b→vents[0]. compute_volumes / injection / viz iterate vents.

7. Geometry / misc

• Per-cell clipped area carries each vent’s volume → no per-kind geometry methods.
• Hex hub geometry (edge_length, inset_open_area, opening_diameter, inscribed_radius, neighbor_centroid_distance (hex↔triangle), auto_window_height, interior_for_opening) drops into a HexGeometry (MagmaGeometry impl) used for the hub.
• max_neighbors() returns the max (6); neighbors() already returns variable arity.
• Crater-iron start radius is already principled (derived from the per-tube seal depth); feed it the per-kind neighbour opening + hex↔triangle neighbor_centroid_distance for the neighbour-clearance cap.
• Injection-edge preference (interior/exterior) is moot for tri-hex (hub is the hex).
• Dropdown icon: param_magmatrihex.svg (placeholder copy of the triangle art).

8. New vs reused

• NEW: trihexagonal lattice + hex geometry; the extra-vent sweep; trihex_window_cuts; the InjectionUnit generalization.
• REUSED unchanged: the tube solver (greedy + CP-SAT), runs/segments/stagger/ height bounds, presence scan, crater iron, injection sequence, preview viz.

This site is open source. Improve this page.