feat(phase4): HyperIdeal Newton solver, SparseQR fallback, examples, docs
Phase 4 complete — 87 CGAL tests pass, 2 skipped. Newton solver (phase4a): - hyper_ideal_hessian.hpp: symmetric FD Hessian (O(ε²), PSD by convexity) - newton_hyper_ideal(): Newton + backtracking for the HyperIdeal functional - detail::solve_with_fallback(): optional bool* fallback_used parameter - solve_linear_system(): public API exposing LDLT→SparseQR fallback SparseQR fallback tests (SparseQRFallback.*): - FullRankSystem_CorrectSolution: LDLT path, fallback_used=false - SingularMatrix_FallbackActivated: zero-pivot → QR activated, fallback_used=true - Euclidean_ClosedMeshNoPinConverges: gauge-mode null space handled via QR HyperIdeal Newton tests (NewtonSolver.HyperIdeal_*): - ConvergesTriangleAllVariable, ResultFieldsConsistent, ConvergesTetrahedron, SparseQRFallbackNoCrash - Natural-target base point (b=1.0, a=0.5) — x=0 is degenerate in log-space Pipeline tests (test_pipeline.cpp): - End-to-end: all three geometries, mesh I/O round-trip, solve+export Example programs (code/examples/): - example_euclidean.cpp: headless Euclidean pipeline - example_hyper_ideal.cpp: headless HyperIdeal pipeline - example_viewer.cpp: interactive libigl viewer with jet colour map README: - Mathematical scope table: C++ vs Java original (18 rows) - "For mathematicians" section: mental model, step-by-step new-functional guide, half-edge traversal snippets, recommended reading 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_pipeline.cpp
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292
code/tests/cgal/test_pipeline.cpp
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// test_pipeline.cpp
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//
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// Phase 4c — End-to-end pipeline tests and library-user examples.
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//
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// These tests exercise the full conformallab++ pipeline as a user would:
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//
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// 1. Build (or load) a mesh
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// 2. Set up maps and assign DOFs
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// 3. Configure target angles / targets
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// 4. Solve with Newton
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// 5. Inspect / export the result
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//
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// Each test mirrors a realistic usage scenario documented in the README.
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//
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// Tests:
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// 1. Pipeline_Euclidean_TriangleToEquilibrium
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// Read mesh → setup Euclidean maps → solve → verify convergence
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// 2. Pipeline_Spherical_TetrahedronToEquilibrium
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// Setup spherical tetrahedron → solve → verify angles sum to 4π
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// 3. Pipeline_HyperIdeal_TriangleRoundTrip
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// Build triangle → setup HyperIdeal → solve → verify G ≈ 0
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// 4. Pipeline_MeshIO_SolveAndExport
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// Build mesh → solve → write OFF → reload → verify vertex count intact
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// 5. Pipeline_AllThreeGeometries_SameTopology
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// Same quad-strip mesh solved under all three geometries: all converge
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#include "conformal_mesh.hpp"
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#include "mesh_builder.hpp"
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#include "mesh_io.hpp"
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#include "euclidean_functional.hpp"
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#include "spherical_functional.hpp"
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#include "hyper_ideal_functional.hpp"
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#include "newton_solver.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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#include <filesystem>
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using namespace conformallab;
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// ────────────────────────────────────────────────────────────────────────────
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// Shared helpers
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// ────────────────────────────────────────────────────────────────────────────
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static void pin_first_vertex_euclidean(ConformalMesh& mesh, EuclideanMaps& maps, int& n)
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{
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auto vit = mesh.vertices().begin();
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Vertex_index v0 = *vit++;
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maps.v_idx[v0] = -1;
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int idx = 0;
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for (; vit != mesh.vertices().end(); ++vit)
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maps.v_idx[*vit] = idx++;
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n = idx;
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}
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static void set_natural_euclidean_theta(ConformalMesh& mesh, EuclideanMaps& maps, int n)
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{
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std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
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auto G = euclidean_gradient(mesh, x0, maps);
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for (auto v : mesh.vertices()) {
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int iv = maps.v_idx[v];
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if (iv < 0) continue;
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maps.theta_v[v] -= G[static_cast<std::size_t>(iv)];
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}
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}
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static std::vector<double> set_natural_hyper_ideal_targets(
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ConformalMesh& mesh, HyperIdealMaps& maps, int n,
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double b_base = 1.0, double a_base = 0.5)
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{
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const auto sz = static_cast<std::size_t>(n);
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std::vector<double> xbase(sz, 0.0);
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for (auto v : mesh.vertices()) {
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int iv = maps.v_idx[v];
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if (iv >= 0) xbase[static_cast<std::size_t>(iv)] = b_base;
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}
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for (auto e : mesh.edges()) {
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int ie = maps.e_idx[e];
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if (ie >= 0) xbase[static_cast<std::size_t>(ie)] = a_base;
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}
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auto G = evaluate_hyper_ideal(mesh, xbase, maps, false).gradient;
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for (auto v : mesh.vertices()) {
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int iv = maps.v_idx[v];
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if (iv < 0) continue;
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maps.theta_v[v] += G[static_cast<std::size_t>(iv)];
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}
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for (auto e : mesh.edges()) {
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int ie = maps.e_idx[e];
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if (ie < 0) continue;
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maps.theta_e[e] += G[static_cast<std::size_t>(ie)];
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}
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return xbase;
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 1 — Euclidean full pipeline: triangle → equilibrium
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//
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// Simulates a user doing:
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// auto mesh = make_triangle();
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// auto maps = setup_euclidean_maps(mesh);
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// compute_euclidean_lambda0_from_mesh(mesh, maps);
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// // … set target angles and DOF indices …
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// auto result = newton_euclidean(mesh, x0, maps);
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// assert(result.converged);
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// ════════════════════════════════════════════════════════════════════════════
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TEST(Pipeline, Euclidean_TriangleToEquilibrium)
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{
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// ── Step 1: build mesh ────────────────────────────────────────────────
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auto mesh = make_triangle();
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// ── Step 2: set up maps ───────────────────────────────────────────────
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auto maps = setup_euclidean_maps(mesh);
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compute_euclidean_lambda0_from_mesh(mesh, maps);
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// ── Step 3: assign DOFs (pin v0) ──────────────────────────────────────
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int n = 0;
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pin_first_vertex_euclidean(mesh, maps, n);
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ASSERT_EQ(n, 2);
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// ── Step 4: choose natural target angles → x* = 0 ────────────────────
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set_natural_euclidean_theta(mesh, maps, n);
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// ── Step 5: solve ─────────────────────────────────────────────────────
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std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
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auto result = newton_euclidean(mesh, x0, maps);
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// ── Step 6: verify ────────────────────────────────────────────────────
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EXPECT_TRUE(result.converged)
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<< "Euclidean pipeline: triangle should converge; "
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"grad_inf_norm = " << result.grad_inf_norm;
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EXPECT_LT(result.grad_inf_norm, 1e-8);
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EXPECT_EQ(static_cast<int>(result.x.size()), n);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 2 — Spherical full pipeline: tetrahedron → equilibrium
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//
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// The spherical tetrahedron equilibrium x* = 0 is built into the maps.
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// After solving, the total angle defect Σ(Θ_v − Σα_v) should be ≈ 0.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(Pipeline, Spherical_TetrahedronToEquilibrium)
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{
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// ── Steps 1–3 ─────────────────────────────────────────────────────────
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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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// ── Step 4: solve ─────────────────────────────────────────────────────
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std::vector<double> x0(static_cast<std::size_t>(n), -0.2);
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auto result = newton_spherical(mesh, x0, maps);
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// ── Step 5: verify convergence ────────────────────────────────────────
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EXPECT_TRUE(result.converged)
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<< "Spherical pipeline: tetrahedron should converge; "
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"grad_inf_norm = " << result.grad_inf_norm;
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EXPECT_LT(result.grad_inf_norm, 1e-8);
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// ── Step 6: verify geometric invariant — total angle defect ≈ 0 ──────
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auto G_final = spherical_gradient(mesh, result.x, maps);
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double total_defect = 0.0;
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for (double gv : G_final) total_defect += gv;
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EXPECT_NEAR(total_defect, 0.0, 1e-7)
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<< "Spherical: total angle defect should vanish at equilibrium";
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 3 — HyperIdeal full pipeline: triangle → equilibrium
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// ════════════════════════════════════════════════════════════════════════════
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TEST(Pipeline, HyperIdeal_TriangleRoundTrip)
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{
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// ── Steps 1–3 ─────────────────────────────────────────────────────────
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auto mesh = make_triangle();
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auto maps = setup_hyper_ideal_maps(mesh);
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int n = assign_all_dof_indices(mesh, maps);
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// ── Step 4: natural targets (equilibrium at b=1.0, a=0.5) ────────────
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auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
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// Verify: gradient at xbase must be ≈ 0 before solving
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auto G_at_base = evaluate_hyper_ideal(mesh, xbase, maps, false).gradient;
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double max_g = 0.0;
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for (double v : G_at_base) max_g = std::max(max_g, std::abs(v));
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ASSERT_LT(max_g, 1e-10) << "Natural target setup: gradient at base should be ~0";
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// ── Step 5: perturb and solve ─────────────────────────────────────────
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std::vector<double> x0 = xbase;
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for (auto& v : x0) v += 0.3;
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auto result = newton_hyper_ideal(mesh, x0, maps);
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// ── Step 6: verify ────────────────────────────────────────────────────
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EXPECT_TRUE(result.converged)
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<< "HyperIdeal pipeline: triangle should converge; "
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"grad_inf_norm = " << result.grad_inf_norm;
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EXPECT_LT(result.grad_inf_norm, 1e-8);
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// Solution should be close to xbase (same equilibrium)
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for (int i = 0; i < n; ++i) {
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EXPECT_NEAR(result.x[static_cast<std::size_t>(i)],
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xbase[static_cast<std::size_t>(i)], 1e-6)
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<< "DOF " << i << " should recover the equilibrium value";
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}
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 4 — Mesh I/O in the pipeline: solve → write → reload → check
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//
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// Demonstrates: compute a conformal factor on a mesh, write it to OFF, reload
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// and check that the mesh topology is preserved.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(Pipeline, MeshIO_SolveAndExport)
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{
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// ── Build and solve ───────────────────────────────────────────────────
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auto mesh = make_quad_strip();
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auto maps = setup_euclidean_maps(mesh);
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compute_euclidean_lambda0_from_mesh(mesh, maps);
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int n = 0;
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pin_first_vertex_euclidean(mesh, maps, n);
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set_natural_euclidean_theta(mesh, maps, n);
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std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
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auto result = newton_euclidean(mesh, x0, maps);
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ASSERT_TRUE(result.converged) << "Solver must converge before export test";
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// ── Write mesh ────────────────────────────────────────────────────────
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const std::string tmp_path = "/tmp/conformallab_pipeline_test.off";
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ASSERT_NO_THROW(save_mesh(tmp_path, mesh));
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ASSERT_TRUE(std::filesystem::exists(tmp_path));
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// ── Reload and verify topology ────────────────────────────────────────
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ConformalMesh mesh2;
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ASSERT_NO_THROW(mesh2 = load_mesh(tmp_path));
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EXPECT_EQ(mesh2.number_of_vertices(), mesh.number_of_vertices())
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<< "Vertex count must survive OFF round-trip";
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EXPECT_EQ(mesh2.number_of_faces(), mesh.number_of_faces())
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<< "Face count must survive OFF round-trip";
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std::filesystem::remove(tmp_path);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 5 — All three geometries, same quad-strip topology
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//
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// Validates that the solver infrastructure works uniformly: the same mesh
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// topology is solvable under Euclidean, Spherical, and HyperIdeal geometries.
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// ════════════════════════════════════════════════════════════════════════════
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TEST(Pipeline, AllThreeGeometries_QuadStrip)
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{
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// ── Euclidean ──────────────────────────────────────────────────────────
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{
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auto mesh = make_quad_strip();
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auto maps = setup_euclidean_maps(mesh);
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compute_euclidean_lambda0_from_mesh(mesh, maps);
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int n = 0;
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pin_first_vertex_euclidean(mesh, maps, n);
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set_natural_euclidean_theta(mesh, maps, n);
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std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
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auto res = newton_euclidean(mesh, x0, maps);
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EXPECT_TRUE(res.converged) << "Euclidean: quad strip should converge";
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}
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// ── HyperIdeal ────────────────────────────────────────────────────────
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{
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auto mesh = make_quad_strip();
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auto maps = setup_hyper_ideal_maps(mesh);
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int n = assign_all_dof_indices(mesh, maps);
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auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
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std::vector<double> x0 = xbase;
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for (auto& v : x0) v += 0.1;
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auto res = newton_hyper_ideal(mesh, x0, maps);
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EXPECT_TRUE(res.converged) << "HyperIdeal: quad strip should converge";
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}
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// ── Spherical (tetrahedron: smallest closed mesh with all vertices free) ─
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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> x0(static_cast<std::size_t>(n), -0.1);
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auto res = newton_spherical(mesh, x0, maps);
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EXPECT_TRUE(res.converged) << "Spherical: tetrahedron should converge";
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}
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}
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