feat(phase5): Layout, CLI, JSON/XML serialisation — 95 tests
Phase 5 complete:
layout.hpp
- euclidean_layout(): BFS unfolding in ℝ² using trilaterate_2d
- spherical_layout(): BFS on S² using trilaterate_sph (spherical law of cosines)
- hyper_ideal_layout(): BFS in Poincaré disk (tanh(d/2) Euclidean approx)
- save_layout_off(): convenience OFF writer for 2-D and 3-D layouts
serialization.hpp
- save/load_result_json(): nlohmann/json; stores DOF vector + uv/pos layout
- save/load_result_xml(): hand-written writer/parser; same schema
conformallab_cli.cpp (rewritten)
- CLI11 interface: -i/-o/-g/-j/-x/-s/-v
- Dispatches to euclidean / spherical / hyper_ideal pipeline
- Runs Newton, computes layout, saves OFF + JSON + XML
examples/example_layout.cpp
- Full round-trip demo: solve → layout → JSON/XML → reload → verify
tests/cgal/test_layout.cpp (8 tests)
- Euclidean_PreservesEdgeLengths, CorrectVertexCount, TriangleIsNonDegenerate
- Spherical_PreservesArcLengths, PositionsOnUnitSphere
- HyperIdeal_SuccessAndFinitePositions
- Serialization.JSON_RoundTrip, XML_RoundTrip
All 95 CGAL tests pass (2 skipped — Hessian stubs unchanged).
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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