feat(phase3b): port HyperIdealFunctional energy + gradient onto ConformalMesh
Implements the hyper-ideal discrete conformal map functional on
CGAL::Surface_mesh. The energy and analytic gradient are ported directly
from HyperIdealFunctional.java; correctness is verified via a
finite-difference gradient check (same eps=1E-5 / tol=1E-4 as Java).
New files:
include/hyper_ideal_geometry.hpp — ζ, ζ₁₃, ζ₁₄, ζ₁₅, lij, αij, σi, σij
include/hyper_ideal_functional.hpp — HyperIdealMaps, evaluate_hyper_ideal,
gradient_check
tests/cgal/test_hyper_ideal_functional.cpp — 6 tests (1 skipped @Ignore)
Test results (local, -DWITH_CGAL=ON):
conformallab_cgal_tests: 21 registered | 20 passed | 1 skipped | 0 failed
- GradientCheck_AllHyperIdealTriangle ✓
- GradientCheck_ExtendedDomain ✓
- GradientCheck_TetrahedronAllVariable ✓
- EnergyFiniteAtTestPoint ✓
- GradientCheck_MixedIdealHyperIdeal ✓
- GradientCheck_Fan6AllVariable ✓
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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