feat(phase7): Java-parity layout — priority BFS, halfedge_uv, Möbius holonomy, period matrix, fundamental domain — 158 tests
Phase 7 adds seven features ported from the original Java ConformalLab:
layout.hpp
- Priority BFS (min-heap on BFS depth) replaces FIFO queue, minimising
trilateration error accumulation from the root face outward.
- MobiusMap struct: T(z)=(az+b)/(cz+d), identity/inverse/compose,
from_three (3×3 complex least-squares fit), apply(Vector2d).
- halfedge_uv[h.idx()] = UV of source(h) in face(h); seam halfedges
carry the virtual unfolded position, enabling proper GPU texture atlases.
- Hyperbolic holonomy stored as MobiusMap per cut edge (SU(1,1) isometry).
- best_root_face: largest 3-D area face, 1.5× interior bonus.
- normalise_euclidean also transforms halfedge_uv (centroid + PCA).
- Face-area-weighted iterative Möbius centering (Fréchet mean, Phase 7).
period_matrix.hpp (new)
- PeriodData: lattice generators ω_i as complex numbers, τ = ω₂/ω₁ ∈ ℍ.
- reduce_to_fundamental_domain: SL(2,ℤ) reduction via alternating S/T steps.
- is_in_fundamental_domain, compute_period_matrix.
- NOTE: Siegel matrix Ω for genus g>1 intentionally deferred.
fundamental_domain.hpp (new)
- FundamentalDomain: CCW parallelogram {0, ω₁, ω₁+ω₂, ω₂} for genus 1.
- edge_identifications, generators stored.
- 4g-polygon boundary-walk for g>1 marked TODO(Phase 8) with full algorithm
outline and literature references.
- tiling_copy / tiling_neighbourhood for universal cover visualisation.
Tests: 121 → 158 (+37 Phase 7 tests covering all new features).
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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