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Phase 9b: Hyper-ideal Hessian — block-FD optimisation (96× speed-up)
Replaces the O(n·F) full-FD Hessian with an O(F·36) block-local variant
that exploits the per-face locality of the hyper-ideal functional.  Both
variants are kept (full-FD as correctness reference, block-FD as default)
and proven to match to FD rounding tolerance on all test configurations.

Java parity note
────────────────
HyperIdealFunctional.java line 295-298 declares:
    public boolean hasHessian() { return false; }
i.e. the upstream Java functional has NO Hessian implementation, analytic
or numerical.  Both Hessian variants in this file are conformallab++
extensions beyond the Java port.  Analytic Hessian via Schläfli-type
differentiation through (b_i, a_e) → l_ij → ζ_13/ζ_14/ζ_15 → α_ij/β_i
is deferred to a future PR.

Implementation
──────────────
* code/include/hyper_ideal_functional.hpp
  - New pure-math helper face_angles_from_local_dofs() takes 6 input DOFs
    (b1, b2, b3, a12, a23, a31) + variability flags and returns the 6
    output angles (β1, β2, β3, α12, α23, α31).
  - Used by block-FD Hessian as the inner loop; identical semantics to
    the existing compute_face_angles().

* code/include/hyper_ideal_hessian.hpp
  - hyper_ideal_hessian_block_fd()  — new, default production path
  - hyper_ideal_hessian_block_fd_sym() — symmetrised variant
  - hyper_ideal_hessian()  — full-FD baseline, kept for cross-validation
  - hyper_ideal_hessian_sym() — symmetrised baseline
  - Header docblock documents speed-up curve: ~33× at cathead.obj scale,
    ~1166× at brezel.obj scale.

Tests (7 new in test_hyper_ideal_hessian.cpp)
─────────────────────────────────────────────
* PureHelperMatchesMeshHelper — refactor sanity
* BlockFD_MatchesFullFD_ClosedTetrahedron
* BlockFD_MatchesFullFD_Open3FaceMesh (boundary edge path)
* BlockFD_MatchesFullFD_PinnedDOFs    (partial-DOF path)
* BlockFD_IsPSD                       (Springborn 2020 convexity)
* BlockFD_SparsityMatchesFaceAdjacency (structural correctness)
* BlockFD_FasterThanFullFD           (performance assertion: ≥ 3×)

Measured speed-up on the 200-face tet strip (603 DOFs):
    full-FD:   226 591 µs
    block-FD:    2 347 µs
    ratio:        96.5×
The assertion uses ≥ 3× to leave wide CI-hardware tolerance.

Test count
──────────
CGAL suite: 184 → 191 (+7).  Zero skips.

Why not full analytic now
─────────────────────────
Full analytic Hessian via the chain rule
    (b_i, a_e) → l_ij → ζ_{13,14,15} → α_ij / β_i
requires Schläfli-type differentiation with multiple cases for the
ideal / hyper-ideal vertex mix.  It would add another ~6× over
block-FD but at significantly higher implementation and verification
cost.  Block-FD already removes the practical bottleneck for meshes
up to ~10k faces; analytic optimisation can land later when justified
by a concrete profiling result.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
2026-05-21 20:58:33 +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
)
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
)