feat(p1): CLI extensions + quality measures + stereographic layout
Implement Phase-Session P1 quick wins (4 independent additions):
9h.1: Add --tol and --max-iter CLI options to conformallab_core
- Newton solver tolerance [default 1e-8]
- Newton iteration limit [default 200]
- Thread both through run_euclidean / run_spherical / run_hyper_ideal
- Update CLI parameter table in documentation
9h.2: Add -g cp_euclidean and -g inversive_distance geometry routes
- run_cp_euclidean() & run_inversive_distance() pipelines (~60 lines each)
- Face-based DOF assignment for CP-Euclidean
- Vertex-based DOF assignment for Inversive-Distance
- Both integrated into CLI geometry validator (IsMember)
9g.1: Create conformal_quality.hpp with validation measures
- IsothermicityMeasure: metric anisotropy (conformality deviation)
- DiscreteConformalEquivalenceMeasure: length-cross-ratio residuals
- FlippedTriangles: detects inverted/degenerate triangles
- LengthCrossRatio: discrete conformal invariant computation
- ConvergenceUtility: aggregated convergence statistics (max/mean/sum)
- Ported from Java: plugin/visualizer + convergence utilities
- Includes sanity tests validating finite outputs on valid layouts
9d.3: Create stereographic_layout.hpp for S² → ℂ projection
- Stereographic projection from north pole: S² → ℂ ∪ {∞}
- Inverse projection: ℂ → S² for round-trip validation
- Möbius centring: centres the 2-D point cloud at origin
- stereographic_layout(Layout3D) -> Layout2D conversion
- Round-trip tests: south pole, equator, random sphere points
- Tests: projection/inverse consistency, north pole handling
Test results: 336/336 CGAL tests pass (272 pre-existing + 64 new from all phases)
- conformal_quality.cpp: 13 new tests (measures, isothermic, dce, convergence)
- stereographic_layout.cpp: 10 new tests (projection, inverse, round-trip, layout)
Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>
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