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Wires the two Phase-9a functionals into the Newton-solver layer so
they are operational end-to-end. CGAL test count: 212 → 219 (+7).
Solvers
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* newton_cp_euclidean(mesh, x0, m, tol, max_iter)
- Uses cp_euclidean_hessian — analytic 2×2-per-edge BPS-2010
formula h_jk = sin θ / (cosh Δρ − cos θ).
- SparseQR fallback handles the gauge-singular case when no face
is pinned (caller error, but we recover gracefully).
- Strictly-convex energy ⇒ quadratic convergence near optimum.
* newton_inversive_distance(mesh, x0, m, tol, max_iter, hess_eps)
- Uses an inline FD Hessian (n × gradient evaluations per step) —
mirrors the Phase 4a HyperIdeal solver in spirit.
- Analytic alternative via Glickenstein 2011 eq. (4.6) is tracked
in doc/roadmap/research-track.md as Phase 9a.2-analytic.
- Sensitive to initial point; the test suite always starts from
a natural-theta setup (u = 0 is the equilibrium when
compute_inversive_distance_init_from_mesh was called).
Tests (test_newton_phase9a.cpp, 7 cases)
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* CPEuclidean_NaturalPhi_ClosedTetrahedron_ConvergesInZeroIterations
* CPEuclidean_PerturbedStart_ConvergesBackToEquilibrium
* CPEuclidean_OpenTetrahedron_NaturalPhi_Converges
* InversiveDistance_NaturalTheta_Triangle_ConvergesInZero
* InversiveDistance_PerturbedQuadStrip_Converges
* InversiveDistance_PerturbedTetrahedron_Converges
* CPEuclidean_UsesAnalyticHessian
Regression guard: 3-DOF problem converges in ≤ 10 iterations even
with strong perturbation, confirming the analytic Hessian path is
actually used.
All seven tests pass. Full CGAL suite: 219/219 PASSED, 0 SKIPPED.
Roadmap additions (`doc/roadmap/phases.md`)
───────────────────────────────────────────
New Phase 11+ section flags two Java sub-packages as optional/deferred
ports, recorded for project memory but not roadmap commitments:
* 11a — Schottky uniformisation (Java plugin/schottky/*, ~3000 LoC)
Hyperbolic loxodromic group acting on S²; complement of the
Phase 10c Fuchsian-group representation in H². Requires
Phase 10b period matrix + Möbius-group machinery from Phase 7.
Effort: very large (4-6 weeks).
* 11b — Riemann maps (Java plugin/riemannmap/*, ~1500 LoC)
Discrete Riemann mapping theorem; texture mapping of bounded
planar regions, classical conformal mapping for engineering.
Requires Phase 10b' quasi-isothermic or Phase 9a.1 CP-Euclidean.
Effort: large (3-4 weeks).
Both are explicitly NOT roadmap commitments — they live in the doc so
they aren't re-discovered.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>