# Test Suites

## `conformallab_tests` — always built (no CGAL)

Pure-math tests, only Eigen required. Covers Java utilities ported in Phase 1–2.

| File | What it tests |
|---|---|
| `test_clausen.cpp` | Clausen Cl₂, Lobachevsky Л, ImLi₂ — values at known points |
| `test_hyper_ideal_utility.cpp` | Tetrahedron volumes (Meyerhoff / Kolpakov–Mednykh) |
| `test_matrix_utility.cpp` | Matrix helpers |
| `test_surface_curve_utility.cpp` | Surface curve utilities |
| `test_discrete_elliptic_utility.cpp` | Discrete elliptic functions |
| `test_p2_utility.cpp` | P2 projective utilities |
| `test_hyper_ideal_visualization_utility.cpp` | Poincaré disk projection, circumcircle |

**Total: 23 tests, 0 skipped.**

---

## `conformallab_cgal_tests` — built with `-DWITH_CGAL_TESTS=ON` or `-DWITH_CGAL=ON`

All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists).

| Suite | File | Tests | What is verified |
|---|---|---:|---|
| `ConformalMeshTopology` | `test_conformal_mesh.cpp` | 4 | Euler characteristic, vertex/edge/face counts |
| `ConformalMeshTraversal` | `test_conformal_mesh.cpp` | 4 | Halfedge iteration, valence, opposite |
| `ConformalMeshProperties` | `test_conformal_mesh.cpp` | 5 | Property maps (λ, θ, idx, α, geometry type) |
| `ConformalMeshValidity` | `test_conformal_mesh.cpp` | 1 | CGAL validity for all factory meshes |
| `HyperIdealFunctional` | `test_hyper_ideal_functional.cpp` | 7 | FD gradient checks + Hessian symmetry |
| `SphericalFunctional` | `test_spherical_functional.cpp` | 12 | Angle formula + gradient + gauge-fix + cross-module Hessian check |
| `EuclideanFunctional` | `test_euclidean_functional.cpp` | 12 | Angle formula + gradient + cross-module Hessian check |
| `EuclideanHessian` | `test_euclidean_hessian.cpp` | 9 | Cotangent Laplacian structure, FD agreement, PSD, null space |
| `SphericalHessian` | `test_spherical_hessian.cpp` | 8 | Derivative correctness, NSD at equilibrium |
| `NewtonSolver` | `test_newton_solver.cpp` | 11 | Convergence: Euclidean ×3, Spherical ×4, HyperIdeal ×4 |
| `SparseQRFallback` | `test_newton_solver.cpp` | 3 | Full-rank LDLT · singular matrix → QR · closed mesh gauge mode |
| `MeshIO` | `test_mesh_io.cpp` | 6 | OFF/OBJ round-trips, error handling |
| `Pipeline` | `test_pipeline.cpp` | 5 | End-to-end: build → setup → solve → export → reload |
| `Layout` | `test_layout.cpp` | 6 | Edge-length preservation (Eucl./Spher.), Poincaré disk layout |
| `Serialization` | `test_layout.cpp` | 2 | JSON and XML round-trips (DOF vector + layout UVs) |
| `GaussBonnet` | `test_phase6.cpp` | 12 | χ, genus, sum/RHS, deficit, check, enforce |
| `CutGraph` | `test_phase6.cpp` | 6 | Tree-cotree, open/closed meshes, flag–index consistency |
| `HyperbolicTrilateration` | `test_phase6.cpp` | 4 | Möbius + law of cosines: exact distances, disk interior, off-origin |
| `Normalisation` | `test_phase6.cpp` | 4 | Euclidean centroid, length ratios, Möbius centring |
| `MobiusMap` | `test_phase7.cpp` | 8 | Identity, inverse, compose, `from_three`, `apply(Vector2d)` |
| `BestRootFace` | `test_phase7.cpp` | 2 | Valid root face selection, interior bonus |
| `HalfedgeUV` | `test_phase7.cpp` | 4 | Size = #halfedges, seam consistency, boundary halfedges = 0 |
| `PriorityBFS` | `test_phase7.cpp` | 3 | Success, no seam on open meshes, all vertices placed |
| `NormaliseEuclidean` | `test_phase7.cpp` | 2 | UV centroid = 0, halfedge_uv centroid = 0 |
| `PeriodMatrix` | `test_phase7.cpp` | 7 | τ ∈ ℍ, SL(2,ℤ) reduction, exception outside ℍ |
| `FundamentalDomain` | `test_phase7.cpp` | 7 | Genus-1 parallelogram CCW, generators, g > 1 empty |
| `TilingCopy/Neighbourhood` | `test_phase7.cpp` | 4 | Translation correct, tile count |
| `CuttingUtility` | `test_geometry_utils.cpp` | 3 | `point_in_triangle_2d`: false, true, unit triangle (Java CuttingUtilityTest) |
| `UnwrapUtility` | `test_geometry_utils.cpp` | 2 | Corner angle: collinear → π, equilateral → π/3 (Java UnwrapUtilityTest) |
| `ConvergenceUtility` | `test_geometry_utils.cpp` | 6 | Circumradius + scale-invariant R_f/√A (Java ConvergenceUtilityTests) |
| `EuclideanLayout` | `test_geometry_utils.cpp` | 2 | Euclidean layout round-trip edge lengths |
| `SphericalLayout` | `test_geometry_utils.cpp` | 1 | Spherical layout on unit sphere |
| `HomologyGenerators` | `test_geometry_utils.cpp` | 1 | Genus-2 cut graph: χ = −2, 4 cut edges (`brezel2.obj`) |
| `SmokeEuclidean` | `test_scalability_smoke.cpp` | 3 | Smoke tests on real meshes: CatHead (open), Brezel genus-1, Brezel2 genus-2 |

**Total: 227 tests, 0 skipped.**

---

## Running tests

```bash
# All CGAL tests
ctest --test-dir build -R "^cgal\." --output-on-failure

# One suite
./build/conformallab_cgal_tests --gtest_filter="PeriodMatrix*"

# One specific test
./build/conformallab_cgal_tests --gtest_filter="PeriodMatrix.TauInUpperHalfPlane"

# Verbose output with timing
./build/conformallab_cgal_tests --gtest_filter="NewtonSolver*" --gtest_print_time=1
```
