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Phase 9a-Newton: newton_cp_euclidean + newton_inversive_distance
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
───────
* 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)
────────────────────────────────────────
* 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>
2026-05-21 21:10:00 +02:00

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# tests/cgal/CMakeLists.txt
#
# CGAL-dependent test target. Only built when -DWITH_CGAL=ON.
# Requires Boost (find_package(Boost REQUIRED) is called in the root CMakeLists).
#
# Run with:
# cmake -S code -B build -DWITH_CGAL=ON
# cmake --build build --target conformallab_cgal_tests
# ctest --test-dir build -R cgal
add_executable(conformallab_cgal_tests
# ── Phase 3a: mesh infrastructure ──────────────────────────────────────
test_conformal_mesh.cpp
# ── Phase 3b: HyperIdealFunctional ─────────────────────────────────────
test_hyper_ideal_functional.cpp
# ── Phase 3c + 3e: SphericalFunctional + gauge-fix ────────────────────
test_spherical_functional.cpp
# ── Phase 3d: EuclideanCyclicFunctional ───────────────────────────────
test_euclidean_functional.cpp
# ── Phase 3f: Hessians (cotangent Laplacian, spherical + Euclidean) ───
test_euclidean_hessian.cpp
test_spherical_hessian.cpp
# ── Phase 9b: Hyper-ideal Hessian — block-FD vs full-FD validation ───
# Verifies the O(F·36) block-local Hessian agrees with the
# O(F·n) full-FD baseline. Java upstream has no Hessian at all
# (HyperIdealFunctional.hasHessian() returns false) — both
# variants are conformallab++ extensions beyond the port.
test_hyper_ideal_hessian.cpp
# ── Phase 4a: Newton solver ────────────────────────────────────────────
test_newton_solver.cpp
# ── Phase 4b: Mesh I/O (CGAL::IO) ─────────────────────────────────────
test_mesh_io.cpp
# ── Phase 4c: End-to-end pipeline + user examples ─────────────────────
test_pipeline.cpp
# ── Phase 5: Layout / embedding + serialization ────────────────────────
test_layout.cpp
# ── Phase 6: GaussBonnet, cut graph, exact trilateration, normalisation
test_phase6.cpp
# ── Phase 7: Java-parity layout — MobiusMap, priority BFS, halfedge_uv,
# period matrix, fundamental domain, tiling
test_phase7.cpp
# ── Java parity: geometry utility tests ──────────────────────────────────
# Ported from CuttinUtilityTest, UnwrapUtilityTest,
# ConvergenceUtilityTests, HomologyTest (tests 16).
# Test 7 (genus-2 homology) as GTEST_SKIP stub until Phase 8.
test_geometry_utils.cpp
# ── Scalability smoke tests ────────────────────────────────────────────────
# Newton convergence on large real-world meshes (cathead, brezel, brezel2).
# Assert correctness only (< 30 iterations, ||G|| < 1e-8).
# Wall-clock time is printed for documentation but NOT asserted,
# so the tests remain stable on slow CI hardware (Raspberry Pi ARM64).
test_scalability_smoke.cpp
# ── Phase 8 MVP: new CGAL-style public API ────────────────────────────────
# First client of Conformal_map_traits.h + Discrete_conformal_map.h.
# Acceptance probe before Phase 9a (Inversive-Distance) lands.
test_cgal_traits_mvp.cpp
# ── Phase 9a.1: CPEuclideanFunctional (BPS 2010 circle packing) ──────────
# Face-based circle-packing functional ported from
# CPEuclideanFunctional.java. Reference: Bobenko-Pinkall-Springborn 2010.
test_cp_euclidean_functional.cpp
# ── Phase 9a.2: InversiveDistance (Luo 2004 + Glickenstein 2011) ─────────
# Vertex-based inversive-distance circle-packing functional. No Java
# reference; implemented from the literature. Cross-validated against
# EuclideanCyclicFunctional at the natural initial geometry (u = 0).
test_inversive_distance_functional.cpp
# ── Phase 9a: Newton solvers for the two new circle-packing functionals ──
# Convergence tests for newton_cp_euclidean (analytic Hessian) and
# newton_inversive_distance (FD Hessian).
test_newton_phase9a.cpp
)
target_include_directories(conformallab_cgal_tests SYSTEM PRIVATE
${CMAKE_SOURCE_DIR}/deps/eigen-3.4.0
${CMAKE_SOURCE_DIR}/deps/CGAL-6.1.1/include
${CMAKE_SOURCE_DIR}/deps/single_includes
${Boost_INCLUDE_DIRS}
)
target_include_directories(conformallab_cgal_tests PRIVATE
${CMAKE_SOURCE_DIR}/include
)
target_compile_definitions(conformallab_cgal_tests PRIVATE
CGAL_DISABLE_GMP
CGAL_DISABLE_MPFR
# Data directory — absolute path to code/data/ at build time.
# Used by tests that load real mesh files (cathead.obj, brezel2.obj, …).
CONFORMALLAB_DATA_DIR="${CMAKE_SOURCE_DIR}/data"
)
# Suppress warnings from CGAL/Boost headers
target_compile_options(conformallab_cgal_tests PRIVATE
$<$<CXX_COMPILER_ID:GNU,Clang,AppleClang>:-Wno-unused-parameter>
)
target_link_libraries(conformallab_cgal_tests PRIVATE GTest::gtest_main)
include(GoogleTest)
gtest_discover_tests(conformallab_cgal_tests
TEST_PREFIX "cgal."
DISCOVERY_TIMEOUT 60
)