feat(phase3d+3e): port EuclideanCyclicFunctional + add SphericalFunctional gauge-fix

Phase 3d — EuclideanCyclicFunctional:
  • euclidean_geometry.hpp: t-value / atan2 corner-angle formula with
    centering trick (μ = (Λ̃₁₂+Λ̃₂₃+Λ̃₃₁)/6) for numerical stability
  • euclidean_functional.hpp: EuclideanMaps bundle, gradient (G_v = Θ_v − Σα_v,
    G_e = α_opp⁺ + α_opp⁻ − φ_e), 10-point GL path-integral energy,
    gradient_check_euclidean — identical halfedge convention to SphericalFunctional
  • test_euclidean_functional.cpp: 11 tests (1 skip) covering angle formula,
    right-isosceles triangle, angle sum = π, degenerate detection, gradient
    checks on triangle/quad-strip/tetrahedron/fan-5/mixed-pinned, NaN check

Phase 3e — Spherical gauge-fix:
  • spherical_gauge_shift(): Newton + backtracking line search to find t*
    where ΣG_v(x + t·1) = 0 (maximises E along the global scale direction);
    bisection used when sign change is detectable, Newton+backtrack otherwise
  • apply_spherical_gauge(): in-place wrapper
  • 3 new tests: GaugeFix_SpherTetVertexZerosSumGv, GaugeFix_ApplyInPlace,
    GaugeFix_AlreadyAtGaugeReturnsTNearZero

Total: 45 cgal tests pass, 3 skipped (@Ignore Hessian stubs, one per functional)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

code/tests/cgal/CMakeLists.txt

@@ -15,8 +15,11 @@ add_executable(conformallab_cgal_tests
     # ── Phase 3b: HyperIdealFunctional ─────────────────────────────────────
     test_hyper_ideal_functional.cpp
 
-    # ── Phase 3c: SphericalFunctional ─────────────────────────────────────
+    # ── Phase 3c + 3e: SphericalFunctional + gauge-fix ────────────────────
     test_spherical_functional.cpp
+
+    # ── Phase 3d: EuclideanCyclicFunctional ───────────────────────────────
+    test_euclidean_functional.cpp
 )
 
 target_include_directories(conformallab_cgal_tests SYSTEM PRIVATE