feat: compute the first Brillouin zone from the reciprocal lattice

[timurbazhirov]

Adds ReciprocalLattice.brillouinZone — the first Brillouin zone as polygonal faces, computed from the lattice we already have.

Why

Consumers illustrate the Brillouin zone with a static PNG per lattice type: @mat3ra/wove derives /images/brillouin_zone/<lattice>.png from the material and renders it through an injectable component (@mat3ra/move's BrillouinZoneImage is one). Two problems with that:

1. The asset ships in no package — only the web app serves those files, so every other consumer (standalone demos, Storybook, embedders) renders a broken image. The path is also absolute, so it cannot resolve under a non-root deployment base.
2. One image per type cannot be right for every material of that type. Non-cubic systems have axial-ratio freedom: a graphene monolayer and bulk GaN are both HEX, but the monolayer's vacuum padding flattens its zone. A per-type image shows them identically.

made already owns the reciprocal lattice and its reciprocalVectors, so the zone can simply be derived here instead.

What

• src/js/lattice/reciprocal/brillouin_zone.ts — computeBrillouinZone(reciprocalVectors). The zone is the set of points closer to the origin than to any other reciprocal lattice point, i.e. the intersection of half-spaces k·G ≤ |G|²/2; vertices are the plane triple-intersections satisfying every other half-space, and faces group the vertices on each plane (ordered counter-clockwise about the face normal, so they can be drawn directly).
• ReciprocalLattice.brillouinZone getter returning those faces, or null for a degenerate lattice.

No existing behaviour changes; this is additive.

Validation

Tested against the repo's material fixtures rather than hand-made vectors (tests/js/lattice/brillouin_zone.ts, 7 tests):

fixture	lattice	expected solid	faces / vertices
Silicon	FCC	truncated octahedron	14 (8 hex + 6 square) / 24
Na4Cl4	cubic	cube	6 / 8
Graphene	hexagonal	hexagonal prism	8 (2 hex + 6 rect) / 12
Si slab	—	flattened along the vacuum axis	—

Plus invariants on all four: Euler characteristic V − E + F = 2, and every vertex at least as close to the origin as to a neighbouring reciprocal lattice point. Existing lattice and lattice_reciprocal suites still pass (14 tests).

Follow-ups (not in this PR)

• @mat3ra/move: render this zone, superseding the <img>-based BrillouinZoneImage.
• @mat3ra/wove: pass the provider's material/lattice to the injected component instead of latticeType + a dead imgSrc.
• With symmetryPoints alongside, labelling Γ/X/L on the drawn zone and overlaying the k-path becomes straightforward — something a static image never allowed.

Context: mat3ra/workflow-designer#12 (SOF-8024), where this shipped first as a local stopgap.

🤖 Generated with Claude Code

https://claude.ai/code/session_01FFFpkKD3zHysJXgAbT2uYV

---

Generated by Claude Code