feat(phase3c): port SphericalFunctional onto ConformalMesh; update README
New headers:
- spherical_geometry.hpp: spherical arc length l(λ) and half-angle formula
for interior angles of a spherical triangle (SphericalFaceAngles struct)
- spherical_functional.hpp: SphericalMaps bundle, setup/assign DOF helpers,
compute_lambda0_from_mesh(), gradient (Θ_v − Σα_v; Schläfli edge formula),
energy via 10-point Gauss-Legendre path integral, gradient_check_spherical()
Updated:
- mesh_builder.hpp: add make_spherical_tetrahedron() (vertices on unit sphere)
and make_octahedron_face() (single right-angled spherical triangle)
- tests/cgal/CMakeLists.txt: enable test_spherical_functional.cpp
- README.md: rewrite for CGAL-package goal, two test targets, all headers,
updated project tree, Phase progress table, key design decisions
Tests (cgal.SphericalFunctional.*): 8 active + 1 skip
- OctaFaceAnglesAreRightAngles, SpherTetAngleSumExceedsPi
- GradientCheck_{OctaFaceVertex, SpherTetVertex, SpherTetAllDofs,
SpherFan4Vertex, MixedPinnedVertices}
- AnglesFiniteAtKnownPoint
All 30 cgal.* tests pass (2 @Ignore skips).
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
Tarik Moussa
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code/tests/cgal/test_spherical_functional.cpp
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246
code/tests/cgal/test_spherical_functional.cpp
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// test_spherical_functional.cpp
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//
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// Phase 3c — SphericalFunctional ported to ConformalMesh.
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//
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// Corresponds to de.varylab.discreteconformal.functional.SphericalFunctionalTest.
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//
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// Test map (Java → C++)
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// ──────────────────────
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// testHessian (Ignored) → GradientCheck_Hessian (SKIPPED)
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// testGradientWithHyperIdeal… → GradientCheck_OctaFaceVertex (ported)
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// testGradientInExtendedDomain → GradientCheck_SpherTetVertex (ported)
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// testGradientWithHyperelliptic → GradientCheck_SpherTetAllDofs (ported)
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// testFunctionalAtNaNValue → AnglesFiniteAtKnownPoint (ported)
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//
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// Energy model
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// ────────────
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// The energy is computed as the Schläfli path integral E(x) = ∫₀¹⟨G(tx),x⟩dt
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// using 10-point Gauss-Legendre quadrature. The gradient check therefore
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// verifies that G is curl-free (the integrability / exactness condition of
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// the spherical discrete conformal functional). This is equivalent to the
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// Java FunctionalTest gradient check.
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#include "conformal_mesh.hpp"
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#include "mesh_builder.hpp"
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#include "spherical_functional.hpp"
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#include <gtest/gtest.h>
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#include <cmath>
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#include <vector>
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using namespace conformallab;
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// ════════════════════════════════════════════════════════════════════════════
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// @Ignore in Java: no Hessian implemented
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_Hessian)
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{
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GTEST_SKIP() << "@Ignore in Java – Hessian not implemented";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Angle formula: octahedron-face triangle has all angles = π/2
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//
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// The triangle (1,0,0)–(0,1,0)–(0,0,1) has l_ij = π/2 for all edges.
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// Half-angle formula: s = 3π/4, s_ij = π/4 for all three.
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// All angles = π/2 (right-angled spherical triangle).
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, OctaFaceAnglesAreRightAngles)
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{
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// l_ij = π/2 for all edges (octahedron face on unit sphere)
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const double l = PI_SPHER / 2.0;
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auto fa = spherical_angles(l, l, l);
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ASSERT_TRUE(fa.valid) << "Equilateral spherical triangle must be valid";
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EXPECT_NEAR(PI_SPHER / 2.0, fa.alpha1, 1e-12);
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EXPECT_NEAR(PI_SPHER / 2.0, fa.alpha2, 1e-12);
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EXPECT_NEAR(PI_SPHER / 2.0, fa.alpha3, 1e-12);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Angle sum of a spherical triangle exceeds π (positive curvature)
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//
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// For the spherical tetrahedron face (arccos(−1/3) ≈ 1.9106 per edge):
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// The dihedral angle = arccos(1/3) ≈ 70.53°; by symmetry the face angles
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// (vertex angles of the spherical triangle) are all equal.
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// Angle sum must be > π and equal 3·arccos(1/3) ≈ 3·1.2310 ≈ 3.693 rad.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, SpherTetAngleSumExceedsPi)
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{
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// Edge length of spherical tetrahedron face: arccos(−1/3)
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const double l = std::acos(-1.0 / 3.0);
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auto fa = spherical_angles(l, l, l);
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ASSERT_TRUE(fa.valid);
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EXPECT_GT(fa.alpha1 + fa.alpha2 + fa.alpha3, PI_SPHER)
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<< "Angle sum of spherical triangle must exceed π";
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// By symmetry all three angles must be equal
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EXPECT_NEAR(fa.alpha1, fa.alpha2, 1e-12);
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EXPECT_NEAR(fa.alpha2, fa.alpha3, 1e-12);
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// For a regular spherical tetrahedron with edge arccos(−1/3):
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// half-angle: tan(α/2) = √(sin(l/2)/sin(3l/2)) = √3 → α/2 = π/3 → α = 2π/3.
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// (arccos(1/3) ≈ 1.231 is the 3D dihedral angle of a Euclidean tetrahedron, not this.)
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double expected = 2.0 * PI_SPHER / 3.0; // 120°
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EXPECT_NEAR(fa.alpha1, expected, 1e-10);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Gradient check: octahedron-face triangle, vertex DOFs only
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//
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// Sets λ° from mesh geometry (unit sphere), all u_i = −0.3 (slightly smaller).
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// Mirrors Java testGradientWithHyperIdeal… on a single-triangle mesh.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_OctaFaceVertex)
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{
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auto mesh = make_octahedron_face();
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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int n = assign_vertex_dof_indices(mesh, maps);
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// Small uniform conformal factor: shrink the triangle slightly.
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std::vector<double> x(static_cast<std::size_t>(n), -0.3);
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EXPECT_TRUE(gradient_check_spherical(mesh, x, maps))
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<< "Gradient check failed on octahedron-face triangle (vertex DOFs)";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Gradient check: spherical tetrahedron (4 faces), vertex DOFs only
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//
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// Closed surface; exercises accumulation over multiple faces per vertex.
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// Mirrors Java testGradientInTheExtendedDomain.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_SpherTetVertex)
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{
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auto mesh = make_spherical_tetrahedron();
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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int n = assign_vertex_dof_indices(mesh, maps);
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std::vector<double> x(static_cast<std::size_t>(n), -0.2);
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EXPECT_TRUE(gradient_check_spherical(mesh, x, maps))
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<< "Gradient check failed on spherical tetrahedron (vertex DOFs)";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Gradient check: spherical tetrahedron, all DOFs (vertex + edge)
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//
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// Exercises the edge-gradient branch: G_e = α_opp⁺ + α_opp⁻ − π.
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// Mirrors Java testGradientWithHyperellipticCurve.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_SpherTetAllDofs)
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{
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auto mesh = make_spherical_tetrahedron();
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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int n = assign_all_spherical_dof_indices(mesh, maps);
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// Small but non-zero values; vertex DOFs negative, edge DOFs zero.
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// Edge DOF adjusts the effective log-length Λ_ij = λ°_ij + u_i + u_j + λ_e.
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std::vector<double> x(static_cast<std::size_t>(n), 0.0);
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// Set vertex DOFs (indices 0..3) to -0.2 to keep triangle well-formed.
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for (int i = 0; i < 4; ++i) x[static_cast<std::size_t>(i)] = -0.2;
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EXPECT_TRUE(gradient_check_spherical(mesh, x, maps))
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<< "Gradient check failed on spherical tetrahedron (all DOFs)";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Angles are finite at a known interior point
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//
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// Mirrors Java testFunctionalAtNaNValue: choose DOFs that could hit
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// a degenerate branch (l_ij → 0 or triangle inequality fails) and check
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// the gradient vector is free of NaN/Inf.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, AnglesFiniteAtKnownPoint)
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{
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auto mesh = make_spherical_tetrahedron();
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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int n = assign_vertex_dof_indices(mesh, maps);
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// u_i = -1.5: contracts the triangle heavily but stays non-degenerate.
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std::vector<double> x(static_cast<std::size_t>(n), -1.5);
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auto G = spherical_gradient(mesh, x, maps);
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for (std::size_t i = 0; i < G.size(); ++i) {
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EXPECT_FALSE(std::isnan(G[i])) << "Gradient component " << i << " is NaN";
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EXPECT_FALSE(std::isinf(G[i])) << "Gradient component " << i << " is Inf";
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}
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Gradient check: fan-4 mesh on unit sphere, vertex DOFs only
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//
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// Make a fan of 4 triangles around the north pole (0,0,1);
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// rim vertices projected onto the equator.
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// Exercises high-valence vertex gradient accumulation.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_SpherFan4Vertex)
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{
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// Build a fan with 4 spherical triangles manually (can't use make_fan
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// directly because those vertices are not on the unit sphere).
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ConformalMesh mesh;
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auto center = mesh.add_vertex(Point3(0, 0, 1)); // north pole
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const int n_rim = 4;
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std::vector<Vertex_index> rim(n_rim);
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const double dtheta = 2.0 * PI_SPHER / n_rim;
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const double phi = PI_SPHER / 4.0; // 45° colatitude
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for (int i = 0; i < n_rim; ++i) {
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double theta = i * dtheta;
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rim[i] = mesh.add_vertex(Point3(
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std::sin(phi) * std::cos(theta),
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std::sin(phi) * std::sin(theta),
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std::cos(phi)));
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}
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for (int i = 0; i < n_rim; ++i)
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mesh.add_face(center, rim[i], rim[(i + 1) % n_rim]);
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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int ndof = assign_vertex_dof_indices(mesh, maps);
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std::vector<double> x(static_cast<std::size_t>(ndof), -0.3);
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EXPECT_TRUE(gradient_check_spherical(mesh, x, maps))
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<< "Gradient check failed on spherical fan-4 mesh";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Gradient check: mixed pinned/variable vertices
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//
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// One vertex pinned (u_v = 0 fixed), others variable.
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// Verifies that the gradient accumulation skips pinned vertices correctly.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(SphericalFunctional, GradientCheck_MixedPinnedVertices)
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{
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auto mesh = make_octahedron_face();
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auto maps = setup_spherical_maps(mesh);
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compute_lambda0_from_mesh(mesh, maps);
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// Pin v0, make v1 and v2 variable.
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auto vit = mesh.vertices().begin();
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Vertex_index v0 = *vit++;
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Vertex_index v1 = *vit++;
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Vertex_index v2 = *vit;
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maps.v_idx[v0] = -1; // pinned
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maps.v_idx[v1] = 0;
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maps.v_idx[v2] = 1;
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std::vector<double> x = {-0.2, -0.4};
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EXPECT_TRUE(gradient_check_spherical(mesh, x, maps))
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<< "Gradient check failed for mixed pinned/variable vertices";
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}
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