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
@@ -106,5 +106,10 @@ if(WITH_CGAL)
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RUNTIME_OUTPUT_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/bin)
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endif()
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# ── Example programs (require WITH_CGAL; viewer example also needs WITH_VIEWER) ─
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if(WITH_CGAL)
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add_subdirectory(examples)
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endif()
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# ── Tests (always) ────────────────────────────────────────────────────────────
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add_subdirectory(tests)
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49
code/examples/CMakeLists.txt
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49
code/examples/CMakeLists.txt
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@@ -0,0 +1,49 @@
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# examples/CMakeLists.txt
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#
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# Example programs for conformallab++.
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# All examples require -DWITH_CGAL=ON.
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# example_viewer additionally requires -DWITH_VIEWER=ON.
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#
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# Run after building:
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# ./build/examples/example_euclidean [input.off] [output.off]
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# ./build/examples/example_hyper_ideal [input.off] [output.off]
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# ./build/examples/example_viewer [input.off] (requires WITH_VIEWER)
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# ── Shared include paths for all examples ─────────────────────────────────────
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set(EXAMPLE_INCLUDES
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${CMAKE_SOURCE_DIR}/deps/eigen-3.4.0
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${CMAKE_SOURCE_DIR}/deps/CGAL-6.1.1/include
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${Boost_INCLUDE_DIRS}
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)
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set(EXAMPLE_PRIVATE_INCLUDES
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${CMAKE_SOURCE_DIR}/include
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)
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set(EXAMPLE_DEFS
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CGAL_DISABLE_GMP
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CGAL_DISABLE_MPFR
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)
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# ── example_euclidean ─────────────────────────────────────────────────────────
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add_executable(example_euclidean example_euclidean.cpp)
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target_include_directories(example_euclidean SYSTEM PRIVATE ${EXAMPLE_INCLUDES})
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target_include_directories(example_euclidean PRIVATE ${EXAMPLE_PRIVATE_INCLUDES})
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target_compile_definitions(example_euclidean PRIVATE ${EXAMPLE_DEFS})
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# ── example_hyper_ideal ───────────────────────────────────────────────────────
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add_executable(example_hyper_ideal example_hyper_ideal.cpp)
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target_include_directories(example_hyper_ideal SYSTEM PRIVATE ${EXAMPLE_INCLUDES})
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target_include_directories(example_hyper_ideal PRIVATE ${EXAMPLE_PRIVATE_INCLUDES})
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target_compile_definitions(example_hyper_ideal PRIVATE ${EXAMPLE_DEFS})
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# ── example_viewer (requires WITH_VIEWER) ─────────────────────────────────────
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if(WITH_VIEWER)
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add_executable(example_viewer example_viewer.cpp)
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target_include_directories(example_viewer SYSTEM PRIVATE
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${EXAMPLE_INCLUDES}
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${CMAKE_SOURCE_DIR}/deps/libigl-2.6.0/include
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${CMAKE_SOURCE_DIR}/deps/libigl-glad/include
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)
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target_include_directories(example_viewer PRIVATE ${EXAMPLE_PRIVATE_INCLUDES})
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target_compile_definitions(example_viewer PRIVATE ${EXAMPLE_DEFS})
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target_link_libraries(example_viewer PRIVATE viewer)
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endif()
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117
code/examples/example_euclidean.cpp
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117
code/examples/example_euclidean.cpp
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@@ -0,0 +1,117 @@
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// example_euclidean.cpp
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//
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// conformallab++ — Euclidean discrete conformal map (headless example)
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//
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// This program demonstrates the full library pipeline for the EUCLIDEAN
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// discrete conformal functional:
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//
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// 1. Load a triangle mesh from an OFF file
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// 2. Set up the Euclidean functional maps
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// 3. Pin one vertex (gauge fix for open surfaces)
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// 4. Set target angles via "natural equilibrium" (x* = x_input)
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// 5. Solve with Newton + backtracking line search
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// 6. Print per-vertex conformal factors u_i = x[v_idx[v]]
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// 7. Save the result mesh (same geometry, solver state printed)
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//
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// Build (requires -DWITH_CGAL=ON):
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// cmake -S code -B build -DWITH_CGAL=ON
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// cmake --build build --target example_euclidean
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// ./build/examples/example_euclidean [input.off] [output.off]
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//
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// If no input file is given the built-in make_quad_strip() mesh is used.
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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 "newton_solver.hpp"
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#include <iostream>
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#include <string>
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#include <vector>
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using namespace conformallab;
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int main(int argc, char* argv[])
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{
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// ── Step 1: obtain mesh ───────────────────────────────────────────────
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ConformalMesh mesh;
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std::string input_path = (argc > 1) ? argv[1] : "";
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std::string output_path = (argc > 2) ? argv[2] : "/tmp/conformallab_euclidean_out.off";
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if (input_path.empty()) {
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std::cout << "[example_euclidean] No input file given — using make_quad_strip().\n";
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mesh = make_quad_strip();
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} else {
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std::cout << "[example_euclidean] Loading mesh from: " << input_path << "\n";
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try { mesh = load_mesh(input_path); }
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catch (const std::exception& e) {
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std::cerr << "Error loading mesh: " << e.what() << "\n";
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return 1;
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}
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}
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std::cout << "[example_euclidean] Mesh: "
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<< mesh.number_of_vertices() << " vertices, "
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<< mesh.number_of_faces() << " faces.\n";
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// ── Step 2: set up functional 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: pin the first vertex (gauge fix) ──────────────────────────
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auto vit = mesh.vertices().begin();
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Vertex_index v_pinned = *vit++;
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maps.v_idx[v_pinned] = -1; // pinned: u[v_pinned] = 0 (fixed)
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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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const int n = idx;
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std::cout << "[example_euclidean] DOFs: " << n << " (1 vertex pinned).\n";
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// ── Step 4: natural equilibrium — set theta_v = actual angle sum at x=0 ─
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// After this step x* = 0 is the equilibrium (no deformation).
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// In a real application you would set theta_v = desired angle (e.g. 2π
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// for flat disks, or the cone angles for a cone metric).
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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 G0 = 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) maps.theta_v[v] -= G0[static_cast<std::size_t>(iv)];
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}
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}
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// ── Step 5: solve from a small perturbation to demonstrate Newton ─────
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std::vector<double> x0(static_cast<std::size_t>(n), -0.05);
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std::cout << "[example_euclidean] Solving Newton system…\n";
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auto result = newton_euclidean(mesh, x0, maps, /*tol=*/1e-9, /*max_iter=*/100);
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// ── Step 6: report ────────────────────────────────────────────────────
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if (result.converged) {
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std::cout << "[example_euclidean] Converged in " << result.iterations
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<< " iterations. ||G||_inf = " << result.grad_inf_norm << "\n";
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} else {
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std::cout << "[example_euclidean] Did NOT converge after " << result.iterations
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<< " iterations. ||G||_inf = " << result.grad_inf_norm << "\n";
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}
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std::cout << "[example_euclidean] Per-vertex conformal factors u_i:\n";
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for (auto v : mesh.vertices()) {
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int iv = maps.v_idx[v];
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double u = (iv >= 0) ? result.x[static_cast<std::size_t>(iv)] : 0.0;
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std::cout << " v" << v << " u = " << u;
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if (iv < 0) std::cout << " (pinned)";
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std::cout << "\n";
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}
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// ── Step 7: write output mesh ─────────────────────────────────────────
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try {
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save_mesh(output_path, mesh);
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std::cout << "[example_euclidean] Mesh saved to: " << output_path << "\n";
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} catch (const std::exception& e) {
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std::cerr << "Warning: could not write output: " << e.what() << "\n";
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}
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return result.converged ? 0 : 1;
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}
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147
code/examples/example_hyper_ideal.cpp
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147
code/examples/example_hyper_ideal.cpp
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@@ -0,0 +1,147 @@
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// example_hyper_ideal.cpp
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//
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// conformallab++ — Hyper-ideal discrete conformal map (headless example)
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//
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// Demonstrates the full library pipeline for the HYPER-IDEAL discrete conformal
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// functional (Springborn 2020). The hyper-ideal functional operates in
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// hyperbolic geometry: vertices have "horoball radii" (DOF b_i) and edges have
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// "intersection lengths" (DOF a_e). The energy is strictly convex, so Newton
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// converges globally from any valid starting point.
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//
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// Pipeline:
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// 1. Load (or synthesise) a triangle mesh
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// 2. Set up HyperIdeal maps + assign all vertex and edge DOFs
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// 3. Choose equilibrium base point (b=1.0, a=0.5) and set natural targets
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// 4. Perturb and solve with Newton
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// 5. Print DOF values at equilibrium
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// 6. Save result mesh
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//
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// Build (requires -DWITH_CGAL=ON):
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// cmake -S code -B build -DWITH_CGAL=ON
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// cmake --build build --target example_hyper_ideal
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// ./build/examples/example_hyper_ideal [input.off] [output.off]
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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 "hyper_ideal_functional.hpp"
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#include "newton_solver.hpp"
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#include <iostream>
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#include <string>
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#include <vector>
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#include <cmath>
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using namespace conformallab;
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int main(int argc, char* argv[])
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{
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// ── Step 1: obtain mesh ───────────────────────────────────────────────
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ConformalMesh mesh;
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std::string input_path = (argc > 1) ? argv[1] : "";
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std::string output_path = (argc > 2) ? argv[2] : "/tmp/conformallab_hyper_ideal_out.off";
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if (input_path.empty()) {
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std::cout << "[example_hyper_ideal] No input file — using make_triangle().\n";
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mesh = make_triangle();
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} else {
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std::cout << "[example_hyper_ideal] Loading mesh from: " << input_path << "\n";
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try { mesh = load_mesh(input_path); }
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catch (const std::exception& e) {
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std::cerr << "Error loading mesh: " << e.what() << "\n";
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return 1;
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}
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}
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std::cout << "[example_hyper_ideal] Mesh: "
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<< mesh.number_of_vertices() << " vertices, "
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<< mesh.number_of_faces() << " faces.\n";
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// ── Step 2: set up functional maps ────────────────────────────────────
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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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std::cout << "[example_hyper_ideal] DOFs: " << n
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<< " (" << mesh.number_of_vertices() << " vertex + "
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<< mesh.number_of_edges() << " edge).\n";
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// ── Step 3: choose equilibrium base point and set natural targets ─────
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//
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// x = 0 is degenerate for the HyperIdeal functional (log-space).
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// We pick a valid base point (b_i = b_base, a_e = a_base), evaluate
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// the gradient there, and absorb it into the target angles so that
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// G(xbase) = 0. This makes xbase the equilibrium x*.
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//
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// In a real application you would set theta_v / theta_e to the desired
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// hyperbolic angle targets (e.g. from a reference mesh).
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const double b_base = 1.0; // horoball radii at equilibrium
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const double a_base = 0.5; // edge-length DOFs at equilibrium
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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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// G = Σβ − theta_target; absorb G(xbase) into targets so G(xbase) = 0
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auto G0 = 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) maps.theta_v[v] += G0[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) maps.theta_e[e] += G0[static_cast<std::size_t>(ie)];
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}
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// ── Step 4: perturb and solve ─────────────────────────────────────────
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const double perturb = 0.25;
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std::vector<double> x0 = xbase;
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for (auto& v : x0) v += perturb;
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double g_start = 0.0;
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for (double v : G0) g_start = std::max(g_start, std::abs(v));
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std::cout << "[example_hyper_ideal] Starting Newton from perturbation +" << perturb
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<< " (G at xbase = " << g_start << ").\n";
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auto result = newton_hyper_ideal(mesh, x0, maps, /*tol=*/1e-9, /*max_iter=*/200);
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// ── Step 5: report ────────────────────────────────────────────────────
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if (result.converged) {
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std::cout << "[example_hyper_ideal] Converged in " << result.iterations
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<< " iterations. ||G||_inf = " << result.grad_inf_norm << "\n";
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} else {
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std::cout << "[example_hyper_ideal] Did NOT converge after " << result.iterations
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<< " iterations. ||G||_inf = " << result.grad_inf_norm << "\n";
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}
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std::cout << "[example_hyper_ideal] DOF values at equilibrium:\n";
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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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std::cout << " v" << v
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<< " b = " << result.x[static_cast<std::size_t>(iv)]
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<< " (expected " << b_base << ")\n";
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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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std::cout << " e" << e
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<< " a = " << result.x[static_cast<std::size_t>(ie)]
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<< " (expected " << a_base << ")\n";
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}
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// ── Step 6: write output mesh ─────────────────────────────────────────
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try {
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save_mesh(output_path, mesh);
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std::cout << "[example_hyper_ideal] Mesh saved to: " << output_path << "\n";
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} catch (const std::exception& e) {
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std::cerr << "Warning: could not write output: " << e.what() << "\n";
|
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}
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|
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return result.converged ? 0 : 1;
|
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}
|
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150
code/examples/example_viewer.cpp
Normal file
150
code/examples/example_viewer.cpp
Normal file
@@ -0,0 +1,150 @@
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// example_viewer.cpp
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//
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// conformallab++ — Interactive viewer example (requires -DWITH_VIEWER=ON)
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//
|
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// This example demonstrates the full end-to-end pipeline WITH visual output:
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//
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// 1. Load (or synthesise) a mesh
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// 2. Compute the Euclidean discrete conformal map (Newton solver)
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// 3. Display the result in an interactive libigl / GLFW window
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// • Left pane: input mesh, coloured by per-vertex conformal factor u_i
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// • Right pane: a flat parameterisation (future, placeholder)
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//
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// The viewer is split into two data sets using libigl's multi-mesh API so
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// users can inspect geometry and solution simultaneously.
|
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//
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// Build (requires -DWITH_CGAL=ON -DWITH_VIEWER=ON):
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||||
// cmake -S code -B build -DWITH_CGAL=ON -DWITH_VIEWER=ON
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// cmake --build build --target example_viewer
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// ./build/examples/example_viewer [input.off]
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||||
//
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// Navigation (libigl default):
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||||
// Mouse drag — rotate
|
||||
// Scroll — zoom
|
||||
// C — toggle camera mode (trackball / 2D)
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||||
// Z / X / Y — snap to axis-aligned view
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||||
// Q / Esc — quit
|
||||
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||||
#include "conformal_mesh.hpp"
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||||
#include "mesh_builder.hpp"
|
||||
#include "mesh_io.hpp"
|
||||
#include "euclidean_functional.hpp"
|
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#include "mesh_utils.hpp"
|
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#include "newton_solver.hpp"
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||||
#include <igl/opengl/glfw/Viewer.h>
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||||
#include <Eigen/Dense>
|
||||
#include <iostream>
|
||||
#include <string>
|
||||
#include <vector>
|
||||
#include <cmath>
|
||||
#include <algorithm>
|
||||
|
||||
using namespace conformallab;
|
||||
|
||||
// ── Jet colour map: scalar → RGB ─────────────────────────────────────────────
|
||||
static Eigen::RowVector3d jet(double t)
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||||
{
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||||
t = std::max(0.0, std::min(1.0, t));
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||||
double r = std::clamp(1.5 - std::abs(4.0 * t - 3.0), 0.0, 1.0);
|
||||
double g = std::clamp(1.5 - std::abs(4.0 * t - 2.0), 0.0, 1.0);
|
||||
double b = std::clamp(1.5 - std::abs(4.0 * t - 1.0), 0.0, 1.0);
|
||||
return {r, g, b};
|
||||
}
|
||||
|
||||
int main(int argc, char* argv[])
|
||||
{
|
||||
// ── Step 1: load or synthesise mesh ───────────────────────────────────
|
||||
ConformalMesh mesh;
|
||||
std::string input_path = (argc > 1) ? argv[1] : "";
|
||||
|
||||
if (input_path.empty()) {
|
||||
std::cout << "[example_viewer] No input file — using make_quad_strip().\n";
|
||||
mesh = make_quad_strip();
|
||||
} else {
|
||||
std::cout << "[example_viewer] Loading: " << input_path << "\n";
|
||||
try { mesh = load_mesh(input_path); }
|
||||
catch (const std::exception& e) {
|
||||
std::cerr << "Error: " << e.what() << "\n";
|
||||
return 1;
|
||||
}
|
||||
}
|
||||
|
||||
std::cout << "[example_viewer] Mesh: "
|
||||
<< mesh.number_of_vertices() << " vertices, "
|
||||
<< mesh.number_of_faces() << " faces.\n";
|
||||
|
||||
// ── Step 2: solve the Euclidean discrete conformal map ────────────────
|
||||
auto maps = setup_euclidean_maps(mesh);
|
||||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
|
||||
// Pin first vertex
|
||||
auto vit = mesh.vertices().begin();
|
||||
maps.v_idx[*vit++] = -1;
|
||||
int idx = 0;
|
||||
for (; vit != mesh.vertices().end(); ++vit)
|
||||
maps.v_idx[*vit] = idx++;
|
||||
const int n = idx;
|
||||
|
||||
// Natural equilibrium
|
||||
{
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
|
||||
auto G0 = euclidean_gradient(mesh, x0, maps);
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv >= 0) maps.theta_v[v] -= G0[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
}
|
||||
|
||||
// Perturb and solve
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.08);
|
||||
auto result = newton_euclidean(mesh, x0, maps, 1e-9, 200);
|
||||
|
||||
if (result.converged)
|
||||
std::cout << "[example_viewer] Converged in " << result.iterations << " iterations.\n";
|
||||
else
|
||||
std::cout << "[example_viewer] Warning: did not converge fully "
|
||||
"(||G||_inf = " << result.grad_inf_norm << ").\n";
|
||||
|
||||
// ── Step 3: build Eigen V / F for libigl ─────────────────────────────
|
||||
using Kernel = CGAL::Simple_cartesian<double>;
|
||||
Eigen::MatrixXd V;
|
||||
Eigen::MatrixXi F;
|
||||
mesh_utils::cgal_to_eigen<Kernel>(mesh, V, F);
|
||||
|
||||
// Per-vertex colour: conformal factor u_i, mapped via jet palette
|
||||
const int nv = static_cast<int>(V.rows());
|
||||
Eigen::MatrixXd C(nv, 3);
|
||||
|
||||
// Collect all u values to normalise
|
||||
std::vector<double> u_all(static_cast<std::size_t>(nv), 0.0);
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv >= 0)
|
||||
u_all[static_cast<std::size_t>(v.idx())] = result.x[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
double u_min = *std::min_element(u_all.begin(), u_all.end());
|
||||
double u_max = *std::max_element(u_all.begin(), u_all.end());
|
||||
double u_range = (u_max > u_min) ? (u_max - u_min) : 1.0;
|
||||
|
||||
for (int vi = 0; vi < nv; ++vi) {
|
||||
double t = (u_all[static_cast<std::size_t>(vi)] - u_min) / u_range;
|
||||
C.row(vi) = jet(t);
|
||||
}
|
||||
|
||||
// ── Step 4: launch interactive viewer ─────────────────────────────────
|
||||
igl::opengl::glfw::Viewer viewer;
|
||||
viewer.data().set_mesh(V, F);
|
||||
viewer.data().set_colors(C);
|
||||
viewer.data().show_lines = true;
|
||||
viewer.data().show_overlay = true;
|
||||
|
||||
// Status text overlay
|
||||
viewer.data().add_label(
|
||||
Eigen::Vector3d(V.col(0).mean(), V.col(1).mean(), V.col(2).maxCoeff()),
|
||||
"Euclidean conformal factor u_i (jet: blue=min, red=max)");
|
||||
|
||||
std::cout << "[example_viewer] Launching viewer. Press Q or Esc to quit.\n";
|
||||
viewer.launch();
|
||||
|
||||
return 0;
|
||||
}
|
||||
87
code/include/hyper_ideal_hessian.hpp
Normal file
87
code/include/hyper_ideal_hessian.hpp
Normal file
@@ -0,0 +1,87 @@
|
||||
#pragma once
|
||||
// hyper_ideal_hessian.hpp
|
||||
//
|
||||
// Phase 4a — Hessian of the hyper-ideal discrete conformal functional.
|
||||
//
|
||||
// ┌──────────────────────────────────────────────────────────────────────────┐
|
||||
// │ Implementation strategy │
|
||||
// │ │
|
||||
// │ The hyper-ideal functional involves angle functions (ζ, σ, α, β) │
|
||||
// │ composed through several nested layers (lij → ζ13/14/15 → β/α). │
|
||||
// │ Deriving closed-form Hessian entries analytically through all these │
|
||||
// │ layers is feasible but lengthy; an analytical Hessian is left for a │
|
||||
// │ future phase. │
|
||||
// │ │
|
||||
// │ Here we compute the Hessian by symmetric finite differences of the │
|
||||
// │ gradient, which is exact to O(ε²) and sufficient for Newton's method │
|
||||
// │ at the meshes typical in Phase 4 (< 500 DOFs): │
|
||||
// │ │
|
||||
// │ H[i,j] = (G(x + ε·eⱼ)[i] − G(x − ε·eⱼ)[i]) / (2ε) │
|
||||
// │ │
|
||||
// │ The hyper-ideal energy is strictly convex (Springborn 2020), so H is │
|
||||
// │ positive semi-definite everywhere and Eigen::SimplicialLDLT applies │
|
||||
// │ directly. │
|
||||
// └──────────────────────────────────────────────────────────────────────────┘
|
||||
|
||||
#include "hyper_ideal_functional.hpp"
|
||||
#include <Eigen/Sparse>
|
||||
#include <vector>
|
||||
#include <cmath>
|
||||
|
||||
namespace conformallab {
|
||||
|
||||
// ── Numerical Hessian via symmetric finite differences ────────────────────────
|
||||
//
|
||||
// Returns the n×n sparse Hessian, where n = hyper_ideal_dimension(mesh, m).
|
||||
// eps: finite-difference step size (default 1e-5 gives ~1e-10 relative error).
|
||||
inline Eigen::SparseMatrix<double> hyper_ideal_hessian(
|
||||
ConformalMesh& mesh,
|
||||
const std::vector<double>& x,
|
||||
const HyperIdealMaps& m,
|
||||
double eps = 1e-5)
|
||||
{
|
||||
const int n = hyper_ideal_dimension(mesh, m);
|
||||
std::vector<Eigen::Triplet<double>> trips;
|
||||
trips.reserve(static_cast<std::size_t>(n * n)); // dense upper bound
|
||||
|
||||
std::vector<double> xp = x, xm = x;
|
||||
|
||||
for (int j = 0; j < n; ++j) {
|
||||
const std::size_t sj = static_cast<std::size_t>(j);
|
||||
xp[sj] = x[sj] + eps;
|
||||
xm[sj] = x[sj] - eps;
|
||||
|
||||
auto Gp = evaluate_hyper_ideal(mesh, xp, m, /*energy=*/false).gradient;
|
||||
auto Gm = evaluate_hyper_ideal(mesh, xm, m, /*energy=*/false).gradient;
|
||||
|
||||
xp[sj] = xm[sj] = x[sj]; // restore
|
||||
|
||||
for (int i = 0; i < n; ++i) {
|
||||
double val = (Gp[static_cast<std::size_t>(i)]
|
||||
- Gm[static_cast<std::size_t>(i)]) / (2.0 * eps);
|
||||
if (std::abs(val) > 1e-15)
|
||||
trips.emplace_back(i, j, val);
|
||||
}
|
||||
}
|
||||
|
||||
Eigen::SparseMatrix<double> H(n, n);
|
||||
H.setFromTriplets(trips.begin(), trips.end());
|
||||
return H;
|
||||
}
|
||||
|
||||
// ── Symmetrised Hessian ───────────────────────────────────────────────────────
|
||||
//
|
||||
// The FD Hessian is symmetric in exact arithmetic; floating-point rounding
|
||||
// can introduce tiny asymmetries. This helper returns (H + Hᵀ)/2.
|
||||
inline Eigen::SparseMatrix<double> hyper_ideal_hessian_sym(
|
||||
ConformalMesh& mesh,
|
||||
const std::vector<double>& x,
|
||||
const HyperIdealMaps& m,
|
||||
double eps = 1e-5)
|
||||
{
|
||||
auto H = hyper_ideal_hessian(mesh, x, m, eps);
|
||||
Eigen::SparseMatrix<double> Ht = H.transpose();
|
||||
return (H + Ht) * 0.5;
|
||||
}
|
||||
|
||||
} // namespace conformallab
|
||||
@@ -1,27 +1,39 @@
|
||||
#pragma once
|
||||
// newton_solver.hpp
|
||||
//
|
||||
// Phase 4a — Newton solver for the discrete conformal functionals.
|
||||
// Phase 4a — Newton solver for all three discrete conformal functionals.
|
||||
//
|
||||
// Solves G(x) = 0 where G is the gradient of the discrete conformal energy:
|
||||
// G_v = Θ_v − Σ_f α_v^f (angle-sum residual at each vertex DOF)
|
||||
// Solves G(x) = 0 where G is the gradient of the discrete conformal energy.
|
||||
//
|
||||
// Algorithm per iteration:
|
||||
// 1. Compute gradient G(x)
|
||||
// 2. Check convergence: max|G_i| < tol → done
|
||||
// 3. Compute sparse Hessian H(x)
|
||||
// 4. Factorize and solve the Newton system:
|
||||
// Euclidean: H · Δx = −G (H is PSD → SimplicialLDLT directly)
|
||||
// Spherical: (−H) · Δx = G (H is NSD → negate to get PSD matrix)
|
||||
// 5. Backtracking line search: halve α until ||G(x+α·Δx)|| < ||G(x)||
|
||||
// 6. x ← x + α·Δx, go to 1
|
||||
// ┌──────────────────────────────────────────────────────────────────────────┐
|
||||
// │ Gradient sign conventions │
|
||||
// │ Euclidean / Spherical: G_v = Θ_v − Σ α_v (target − actual) │
|
||||
// │ HyperIdeal: G_v = Σ β_v − Θ_v (actual − target) │
|
||||
// │ │
|
||||
// │ All solvers use the same Newton step Δx = −H⁻¹·G │
|
||||
// │ │
|
||||
// │ Hessian sign at equilibrium │
|
||||
// │ Euclidean: H PSD → SimplicialLDLT on H │
|
||||
// │ Spherical: H NSD → SimplicialLDLT on −H (solve (−H)Δx = G) │
|
||||
// │ HyperIdeal: H PSD → SimplicialLDLT on H (analytical H: future) │
|
||||
// └──────────────────────────────────────────────────────────────────────────┘
|
||||
//
|
||||
// SparseQR fallback:
|
||||
// When SimplicialLDLT reports a failure (e.g. singular H on a closed mesh
|
||||
// without a pinned vertex), the solver automatically retries with
|
||||
// Eigen::SparseQR, which finds the minimum-norm Newton step orthogonal to
|
||||
// the null space. This handles the gauge mode on closed surfaces without
|
||||
// requiring the caller to pin a vertex explicitly.
|
||||
//
|
||||
// Requires:
|
||||
// Eigen::SimplicialLDLT (part of Eigen's sparse Cholesky module)
|
||||
// Eigen::SimplicialLDLT, Eigen::SparseQR (Eigen sparse module)
|
||||
|
||||
#include "euclidean_hessian.hpp"
|
||||
#include "spherical_hessian.hpp"
|
||||
#include "hyper_ideal_hessian.hpp"
|
||||
#include <Eigen/SparseCholesky>
|
||||
#include <Eigen/SparseQR>
|
||||
#include <Eigen/OrderingMethods>
|
||||
#include <Eigen/Dense>
|
||||
#include <algorithm>
|
||||
#include <cmath>
|
||||
@@ -41,6 +53,58 @@ struct NewtonResult {
|
||||
|
||||
namespace detail {
|
||||
|
||||
// Solve A·Δx = rhs with SimplicialLDLT; on failure fall back to SparseQR.
|
||||
// Returns Δx. ok is set to false only if both solvers fail.
|
||||
// If fallback_used is non-null, it is set to true iff SparseQR was needed.
|
||||
inline Eigen::VectorXd solve_with_fallback(
|
||||
const Eigen::SparseMatrix<double>& A,
|
||||
const Eigen::VectorXd& rhs,
|
||||
bool& ok,
|
||||
bool* fallback_used = nullptr)
|
||||
{
|
||||
if (fallback_used) *fallback_used = false;
|
||||
|
||||
Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> ldlt(A);
|
||||
if (ldlt.info() == Eigen::Success) {
|
||||
Eigen::VectorXd dx = ldlt.solve(rhs);
|
||||
if (ldlt.info() == Eigen::Success) { ok = true; return dx; }
|
||||
}
|
||||
// Fallback: SparseQR — handles singular/rank-deficient H (gauge modes).
|
||||
if (fallback_used) *fallback_used = true;
|
||||
Eigen::SparseQR<Eigen::SparseMatrix<double>, Eigen::COLAMDOrdering<int>> qr(A);
|
||||
if (qr.info() == Eigen::Success) {
|
||||
Eigen::VectorXd dx = qr.solve(rhs);
|
||||
if (qr.info() == Eigen::Success) { ok = true; return dx; }
|
||||
}
|
||||
ok = false;
|
||||
return Eigen::VectorXd::Zero(rhs.size());
|
||||
}
|
||||
|
||||
} // namespace detail
|
||||
|
||||
// ── Public linear-system solver (SparseQR fallback) ──────────────────────────
|
||||
//
|
||||
// Solve A·x = rhs with Eigen::SimplicialLDLT; if that fails (singular or
|
||||
// rank-deficient A), retry with Eigen::SparseQR which finds the minimum-norm
|
||||
// solution orthogonal to the null space.
|
||||
//
|
||||
// This is the same primitive used internally by all three Newton solvers.
|
||||
// Exposing it publicly lets callers (tests, downstream code) reuse the logic
|
||||
// and — via the optional fallback_used pointer — verify which code path ran.
|
||||
//
|
||||
// fallback_used – if non-null, set to true iff SparseQR was invoked
|
||||
// Returns Eigen::VectorXd::Zero(rhs.size()) if both solvers fail.
|
||||
inline Eigen::VectorXd solve_linear_system(
|
||||
const Eigen::SparseMatrix<double>& A,
|
||||
const Eigen::VectorXd& rhs,
|
||||
bool* fallback_used = nullptr)
|
||||
{
|
||||
bool ok = false;
|
||||
return detail::solve_with_fallback(A, rhs, ok, fallback_used);
|
||||
}
|
||||
|
||||
namespace detail { // re-open for the remaining helpers
|
||||
|
||||
// Backtracking line search: find the largest α in {1, 0.5, 0.25, …} such that
|
||||
// ||G(x + α·Δx)||₂ < ||G(x)||₂. Returns the accepted step (α may stay 1).
|
||||
template <typename GradFn>
|
||||
@@ -109,14 +173,11 @@ inline NewtonResult newton_euclidean(
|
||||
return res;
|
||||
}
|
||||
|
||||
// ── Hessian + factorisation ───────────────────────────────────────────
|
||||
// ── Hessian + solve H·Δx = −G (SparseQR fallback for singular H) ──
|
||||
auto H = euclidean_hessian(mesh, x, m);
|
||||
solver.compute(H);
|
||||
if (solver.info() != Eigen::Success) break;
|
||||
|
||||
// ── Newton step: solve H·Δx = −G ────────────────────────────────────
|
||||
Eigen::VectorXd dx = solver.solve(-G);
|
||||
if (solver.info() != Eigen::Success) break;
|
||||
bool ok = false;
|
||||
Eigen::VectorXd dx = detail::solve_with_fallback(H, -G, ok);
|
||||
if (!ok) break;
|
||||
|
||||
// ── Backtracking line search ──────────────────────────────────────────
|
||||
double norm0 = G.norm();
|
||||
@@ -157,8 +218,6 @@ inline NewtonResult newton_spherical(
|
||||
res.iterations = 0;
|
||||
res.grad_inf_norm = 0.0;
|
||||
|
||||
Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> solver;
|
||||
|
||||
for (int iter = 0; iter < max_iter; ++iter) {
|
||||
// ── Gradient ──────────────────────────────────────────────────────────
|
||||
auto G_std = spherical_gradient(mesh, x, m);
|
||||
@@ -173,15 +232,12 @@ inline NewtonResult newton_spherical(
|
||||
return res;
|
||||
}
|
||||
|
||||
// ── Hessian: negate to get PSD matrix ────────────────────────────────
|
||||
auto H = spherical_hessian(mesh, x, m);
|
||||
auto negH = Eigen::SparseMatrix<double>(-H);
|
||||
solver.compute(negH);
|
||||
if (solver.info() != Eigen::Success) break;
|
||||
|
||||
// ── Newton step: solve (−H)·Δx = G ─────────────────────────────────
|
||||
Eigen::VectorXd dx = solver.solve(G);
|
||||
if (solver.info() != Eigen::Success) break;
|
||||
// ── Hessian: negate to get PSD; solve (−H)·Δx = G ──────────────────
|
||||
auto H = spherical_hessian(mesh, x, m);
|
||||
auto negH = Eigen::SparseMatrix<double>(-H);
|
||||
bool ok = false;
|
||||
Eigen::VectorXd dx = detail::solve_with_fallback(negH, G, ok);
|
||||
if (!ok) break;
|
||||
|
||||
// ── Backtracking line search ──────────────────────────────────────────
|
||||
double norm0 = G.norm();
|
||||
@@ -201,4 +257,70 @@ inline NewtonResult newton_spherical(
|
||||
return res;
|
||||
}
|
||||
|
||||
// ── HyperIdeal Newton solver ──────────────────────────────────────────────────
|
||||
//
|
||||
// Solves G(x) = 0 for the hyper-ideal discrete conformal functional.
|
||||
//
|
||||
// Gradient sign convention (opposite to Euclidean/Spherical):
|
||||
// G_v = Σ β_v − Θ_v, G_e = Σ α_e − θ_e (actual − target)
|
||||
//
|
||||
// The hyper-ideal energy is strictly convex (Springborn 2020), so H is PSD
|
||||
// and SimplicialLDLT (with SparseQR fallback) applies directly.
|
||||
//
|
||||
// The Hessian is computed by symmetric finite differences of G (see
|
||||
// hyper_ideal_hessian.hpp); replace with an analytical Hessian in Phase 5.
|
||||
inline NewtonResult newton_hyper_ideal(
|
||||
ConformalMesh& mesh,
|
||||
std::vector<double> x0,
|
||||
const HyperIdealMaps& m,
|
||||
double tol = 1e-8,
|
||||
int max_iter = 200,
|
||||
double hess_eps = 1e-5)
|
||||
{
|
||||
std::vector<double> x = x0;
|
||||
const int n = static_cast<int>(x.size());
|
||||
|
||||
NewtonResult res;
|
||||
res.converged = false;
|
||||
res.iterations = 0;
|
||||
res.grad_inf_norm = 0.0;
|
||||
|
||||
for (int iter = 0; iter < max_iter; ++iter) {
|
||||
// ── Gradient ──────────────────────────────────────────────────────────
|
||||
auto G_std = evaluate_hyper_ideal(mesh, x, m, /*energy=*/false).gradient;
|
||||
Eigen::Map<const Eigen::VectorXd> G(G_std.data(), n);
|
||||
|
||||
double inf_norm = G.cwiseAbs().maxCoeff();
|
||||
if (inf_norm < tol) {
|
||||
res.converged = true;
|
||||
res.grad_inf_norm = inf_norm;
|
||||
res.iterations = iter;
|
||||
res.x = x;
|
||||
return res;
|
||||
}
|
||||
|
||||
// ── Hessian (numerical FD) + solve H·Δx = −G ─────────────────────────
|
||||
auto H = hyper_ideal_hessian_sym(mesh, x, m, hess_eps);
|
||||
bool ok = false;
|
||||
Eigen::VectorXd dx = detail::solve_with_fallback(H, -G, ok);
|
||||
if (!ok) break;
|
||||
|
||||
// ── Backtracking line search ──────────────────────────────────────────
|
||||
double norm0 = G.norm();
|
||||
x = detail::line_search(x, dx, norm0,
|
||||
[&](const std::vector<double>& xnew) {
|
||||
return evaluate_hyper_ideal(mesh, xnew, m, false).gradient;
|
||||
});
|
||||
|
||||
res.iterations = iter + 1;
|
||||
}
|
||||
|
||||
auto G_final = evaluate_hyper_ideal(mesh, x, m, false).gradient;
|
||||
double inf_final = 0.0;
|
||||
for (double v : G_final) inf_final = std::max(inf_final, std::abs(v));
|
||||
res.grad_inf_norm = inf_final;
|
||||
res.x = x;
|
||||
return res;
|
||||
}
|
||||
|
||||
} // namespace conformallab
|
||||
|
||||
@@ -30,6 +30,9 @@ add_executable(conformallab_cgal_tests
|
||||
|
||||
# ── Phase 4b: Mesh I/O (CGAL::IO) ─────────────────────────────────────
|
||||
test_mesh_io.cpp
|
||||
|
||||
# ── Phase 4c: End-to-end pipeline + user examples ─────────────────────
|
||||
test_pipeline.cpp
|
||||
)
|
||||
|
||||
target_include_directories(conformallab_cgal_tests SYSTEM PRIVATE
|
||||
|
||||
@@ -20,7 +20,9 @@
|
||||
#include "conformal_mesh.hpp"
|
||||
#include "mesh_builder.hpp"
|
||||
#include "hyper_ideal_functional.hpp"
|
||||
#include "hyper_ideal_hessian.hpp"
|
||||
#include <gtest/gtest.h>
|
||||
#include <Eigen/Dense>
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
|
||||
@@ -52,9 +54,19 @@ static std::vector<double> make_x_all_variable(
|
||||
// @Ignore in Java: no Hessian implemented
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(HyperIdealFunctional, GradientCheck_Hessian)
|
||||
TEST(HyperIdealFunctional, HessianSymmetryCheck)
|
||||
{
|
||||
GTEST_SKIP() << "@Ignore in Java – Hessian not implemented in the functional";
|
||||
// Hessian is now implemented (numerical FD). Verify it is symmetric.
|
||||
auto mesh = make_triangle();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
std::vector<double> x(static_cast<std::size_t>(n), 0.5);
|
||||
auto H = hyper_ideal_hessian_sym(mesh, x, maps);
|
||||
|
||||
Eigen::MatrixXd Hd(H);
|
||||
EXPECT_NEAR((Hd - Hd.transpose()).norm(), 0.0, 1e-8)
|
||||
<< "HyperIdeal Hessian must be symmetric";
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
@@ -1,12 +1,14 @@
|
||||
// test_newton_solver.cpp
|
||||
//
|
||||
// Phase 4a — Newton solver tests.
|
||||
// Phase 4 — Newton solver tests.
|
||||
//
|
||||
// Design principle:
|
||||
// We test convergence to a KNOWN equilibrium. For the spherical tetrahedron
|
||||
// x* = 0 is built-in (G(0) ≈ 0 by construction). For Euclidean meshes we
|
||||
// use "natural theta": set theta_v[v] = actual angle sum at x=0, which makes
|
||||
// x* = 0 the exact equilibrium by definition.
|
||||
// For HyperIdeal we use the same "natural target" trick at a valid base point
|
||||
// (b=1.0, a=0.5), since x=0 is degenerate for the HyperIdeal functional.
|
||||
//
|
||||
// Tests:
|
||||
// Spherical:
|
||||
@@ -19,12 +21,26 @@
|
||||
// 5. Converges (triangle, 1 pinned vertex, natural theta).
|
||||
// 6. Converges (quad strip, 1 pinned vertex, natural theta).
|
||||
// 7. Converges with explicitly chosen mixed pinned/variable layout.
|
||||
//
|
||||
// HyperIdeal:
|
||||
// 8. Converges on triangle (all variable, natural targets).
|
||||
// 9. Result fields self-consistent.
|
||||
// 10. Converges on tetrahedron (10 DOFs, larger mesh).
|
||||
// 11. SparseQR: result consistent (valid starting region).
|
||||
//
|
||||
// SparseQR fallback (direct unit tests):
|
||||
// 12. solve_linear_system recovers correct solution on rank-deficient matrix.
|
||||
// 13. solve_linear_system sets fallback_used=true on a singular matrix.
|
||||
// 14. Euclidean Newton on closed tetrahedron (no pinned vertex) converges
|
||||
// via SparseQR gauge-mode handling.
|
||||
|
||||
#include "conformal_mesh.hpp"
|
||||
#include "mesh_builder.hpp"
|
||||
#include "euclidean_functional.hpp"
|
||||
#include "spherical_functional.hpp"
|
||||
#include "hyper_ideal_functional.hpp"
|
||||
#include "newton_solver.hpp"
|
||||
#include <Eigen/Dense>
|
||||
#include <gtest/gtest.h>
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
@@ -233,3 +249,252 @@ TEST(NewtonSolver, Euclidean_ConvergesMixedPinned)
|
||||
"grad_inf_norm = " << res.grad_inf_norm;
|
||||
EXPECT_LT(res.grad_inf_norm, 1e-8);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Helper: set HyperIdeal target angles to actual sums at a non-degenerate
|
||||
// base point (b_base, a_base), making that point the equilibrium x*.
|
||||
//
|
||||
// Note: x = 0 is degenerate for the HyperIdeal functional (log-space; the
|
||||
// functional requires b_i > 0 / a_e > 0). We therefore choose a valid base
|
||||
// point, evaluate G there, and absorb G into the targets so that G(xbase) = 0.
|
||||
// Newton tests then start from a perturbation of xbase.
|
||||
//
|
||||
// Returns xbase so callers can construct a perturbed starting point.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
static std::vector<double> set_natural_hyper_ideal_targets(
|
||||
ConformalMesh& mesh, HyperIdealMaps& maps, int n,
|
||||
double b_base = 1.0, double a_base = 0.5)
|
||||
{
|
||||
const auto sz = static_cast<std::size_t>(n);
|
||||
std::vector<double> xbase(sz, 0.0);
|
||||
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv >= 0) xbase[static_cast<std::size_t>(iv)] = b_base;
|
||||
}
|
||||
for (auto e : mesh.edges()) {
|
||||
int ie = maps.e_idx[e];
|
||||
if (ie >= 0) xbase[static_cast<std::size_t>(ie)] = a_base;
|
||||
}
|
||||
|
||||
// G = Σβ - theta_target (initial target = 0 → G = Σβ = "actual" angles)
|
||||
auto G = evaluate_hyper_ideal(mesh, xbase, maps, /*energy=*/false).gradient;
|
||||
|
||||
// Set target := actual so that G(xbase) = actual - target = 0
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv < 0) continue;
|
||||
maps.theta_v[v] += G[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
for (auto e : mesh.edges()) {
|
||||
int ie = maps.e_idx[e];
|
||||
if (ie < 0) continue;
|
||||
maps.theta_e[e] += G[static_cast<std::size_t>(ie)];
|
||||
}
|
||||
|
||||
return xbase;
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// HyperIdeal 1 — Triangle, all DOFs variable, converges from perturbation
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(NewtonSolver, HyperIdeal_ConvergesTriangleAllVariable)
|
||||
{
|
||||
auto mesh = make_triangle();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
// xbase = (b=1.0, a=0.5) is the equilibrium after natural-target setup.
|
||||
auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
|
||||
|
||||
// Perturb by +0.2 uniformly
|
||||
std::vector<double> x0 = xbase;
|
||||
for (auto& v : x0) v += 0.2;
|
||||
|
||||
auto res = newton_hyper_ideal(mesh, x0, maps, /*tol=*/1e-7, /*max_iter=*/100);
|
||||
|
||||
EXPECT_TRUE(res.converged)
|
||||
<< "Newton (HyperIdeal, triangle) should converge; "
|
||||
"grad_inf_norm = " << res.grad_inf_norm;
|
||||
EXPECT_LT(res.grad_inf_norm, 1e-7);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// HyperIdeal 2 — Result fields self-consistent
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(NewtonSolver, HyperIdeal_ResultFieldsConsistent)
|
||||
{
|
||||
auto mesh = make_triangle();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
|
||||
|
||||
std::vector<double> x0 = xbase;
|
||||
for (auto& v : x0) v += 0.1;
|
||||
|
||||
auto res = newton_hyper_ideal(mesh, x0, maps, /*tol=*/1e-7, /*max_iter=*/100);
|
||||
|
||||
EXPECT_EQ(static_cast<int>(res.x.size()), n);
|
||||
|
||||
// Reported grad_inf_norm must match re-computed gradient at res.x
|
||||
auto G = evaluate_hyper_ideal(mesh, res.x, maps, false).gradient;
|
||||
double actual_inf = 0.0;
|
||||
for (double v : G) actual_inf = std::max(actual_inf, std::abs(v));
|
||||
EXPECT_NEAR(actual_inf, res.grad_inf_norm, 1e-9);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// HyperIdeal 3 — Tetrahedron (10 DOFs): 4 vertex b-vals + 6 edge a-vals
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(NewtonSolver, HyperIdeal_ConvergesTetrahedron)
|
||||
{
|
||||
auto mesh = make_tetrahedron();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
|
||||
|
||||
// Perturb by +0.15
|
||||
std::vector<double> x0 = xbase;
|
||||
for (auto& v : x0) v += 0.15;
|
||||
|
||||
auto res = newton_hyper_ideal(mesh, x0, maps, /*tol=*/1e-7, /*max_iter=*/200);
|
||||
|
||||
EXPECT_TRUE(res.converged)
|
||||
<< "Newton (HyperIdeal, tetrahedron) should converge; "
|
||||
"grad_inf_norm = " << res.grad_inf_norm;
|
||||
EXPECT_LT(res.grad_inf_norm, 1e-7);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// HyperIdeal 4 — SparseQR fallback: solver returns a result (no crash)
|
||||
//
|
||||
// With all targets = 0 the equilibrium is not at x=0 but the solver should
|
||||
// at minimum not crash and return a consistent result struct.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(NewtonSolver, HyperIdeal_SparseQRFallbackNoCrash)
|
||||
{
|
||||
auto mesh = make_triangle();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
// Leave targets at their default (0): solver tries to solve but the
|
||||
// "equilibrium" is at some unknown x*. With valid starting point the
|
||||
// Hessian is positive-definite and the solver should not crash.
|
||||
// We don't assert convergence — just that the result struct is consistent.
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), 1.0);
|
||||
// Mix vertex / edge DOFs: b=1.0, a=0.5 (valid region of the functional)
|
||||
for (auto e : mesh.edges()) {
|
||||
int ie = maps.e_idx[e];
|
||||
if (ie >= 0) x0[static_cast<std::size_t>(ie)] = 0.5;
|
||||
}
|
||||
auto res = newton_hyper_ideal(mesh, x0, maps, /*tol=*/1e-7, /*max_iter=*/50);
|
||||
|
||||
// Struct fields must always be populated
|
||||
EXPECT_EQ(static_cast<int>(res.x.size()), n);
|
||||
EXPECT_GE(res.iterations, 0);
|
||||
EXPECT_FALSE(std::isnan(res.grad_inf_norm));
|
||||
EXPECT_FALSE(std::isinf(res.grad_inf_norm));
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// SparseQR fallback — Test 12: solve_linear_system recovers correct solution
|
||||
//
|
||||
// The public API solve_linear_system(A, rhs) must return the correct answer
|
||||
// for a well-conditioned full-rank system (LDLT path taken).
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(SparseQRFallback, FullRankSystem_CorrectSolution)
|
||||
{
|
||||
// Build a simple 3×3 diagonal PD matrix: A = diag(1, 2, 3)
|
||||
Eigen::SparseMatrix<double> A(3, 3);
|
||||
A.insert(0, 0) = 1.0;
|
||||
A.insert(1, 1) = 2.0;
|
||||
A.insert(2, 2) = 3.0;
|
||||
A.makeCompressed();
|
||||
|
||||
Eigen::VectorXd rhs(3);
|
||||
rhs << 1.0, 4.0, 9.0; // solution = [1, 2, 3]
|
||||
|
||||
bool fallback = true; // expect it to be set to false (LDLT succeeds)
|
||||
Eigen::VectorXd x = conformallab::solve_linear_system(A, rhs, &fallback);
|
||||
|
||||
EXPECT_FALSE(fallback) << "Full-rank system: LDLT should succeed (no SparseQR needed)";
|
||||
EXPECT_NEAR(x[0], 1.0, 1e-12);
|
||||
EXPECT_NEAR(x[1], 2.0, 1e-12);
|
||||
EXPECT_NEAR(x[2], 3.0, 1e-12);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// SparseQR fallback — Test 13: fallback_used=true on a singular matrix
|
||||
//
|
||||
// Construct a symmetric 3×3 matrix of rank 1 where LDLT fails (the (2,2)
|
||||
// pivot is zero). SparseQR finds the minimum-norm least-squares solution.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(SparseQRFallback, SingularMatrix_FallbackActivated)
|
||||
{
|
||||
// A = [[2, 0, 0],
|
||||
// [0, 0, 0], ← zero pivot → LDLT failure
|
||||
// [0, 0, 3]]
|
||||
// rhs compatible with the row space: [2, 0, 3] → solution [1, 0, 1]
|
||||
Eigen::SparseMatrix<double> A(3, 3);
|
||||
A.insert(0, 0) = 2.0;
|
||||
// row/col 1 deliberately all-zero
|
||||
A.insert(2, 2) = 3.0;
|
||||
A.makeCompressed();
|
||||
|
||||
Eigen::VectorXd rhs(3);
|
||||
rhs << 2.0, 0.0, 3.0;
|
||||
|
||||
bool fallback = false;
|
||||
Eigen::VectorXd x = conformallab::solve_linear_system(A, rhs, &fallback);
|
||||
|
||||
EXPECT_TRUE(fallback) << "Singular matrix: SparseQR fallback must be triggered";
|
||||
// SparseQR min-norm solution: x[0]=1, x[1]=0, x[2]=1
|
||||
EXPECT_NEAR(x[0], 1.0, 1e-10);
|
||||
EXPECT_NEAR(x[1], 0.0, 1e-10);
|
||||
EXPECT_NEAR(x[2], 1.0, 1e-10);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// SparseQR fallback — Test 14: Euclidean Newton on a closed mesh, no pinning
|
||||
//
|
||||
// make_tetrahedron() is a closed surface (4 vertices, 4 faces). Without a
|
||||
// pinned vertex the Euclidean Hessian has a 1-D null space (uniform scale
|
||||
// gauge mode): H·1 = 0. SimplicialLDLT fails on this rank-deficient H;
|
||||
// SparseQR finds the min-norm Newton step orthogonal to the null space.
|
||||
//
|
||||
// The gradient always lives in the row space of H (Σ G_v = 0 by angle-sum
|
||||
// invariance), so the SparseQR step is also the Newton step and the solver
|
||||
// converges to the natural equilibrium.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(SparseQRFallback, Euclidean_ClosedMeshNoPinConverges)
|
||||
{
|
||||
auto mesh = make_tetrahedron();
|
||||
auto maps = setup_euclidean_maps(mesh);
|
||||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
|
||||
// Assign all 4 vertices as free DOFs (no pinning).
|
||||
int idx = 0;
|
||||
for (auto v : mesh.vertices())
|
||||
maps.v_idx[v] = idx++;
|
||||
const int n = idx; // = 4
|
||||
|
||||
// Natural theta: equilibrium at x* = 0.
|
||||
set_natural_euclidean_theta(mesh, maps, n);
|
||||
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
|
||||
auto res = newton_euclidean(mesh, x0, maps, /*tol=*/1e-8, /*max_iter=*/100);
|
||||
|
||||
EXPECT_TRUE(res.converged)
|
||||
<< "Euclidean Newton on closed tetrahedron (no pin) must converge via SparseQR; "
|
||||
"grad_inf_norm = " << res.grad_inf_norm;
|
||||
EXPECT_LT(res.grad_inf_norm, 1e-8);
|
||||
}
|
||||
|
||||
292
code/tests/cgal/test_pipeline.cpp
Normal file
292
code/tests/cgal/test_pipeline.cpp
Normal file
@@ -0,0 +1,292 @@
|
||||
// test_pipeline.cpp
|
||||
//
|
||||
// Phase 4c — End-to-end pipeline tests and library-user examples.
|
||||
//
|
||||
// These tests exercise the full conformallab++ pipeline as a user would:
|
||||
//
|
||||
// 1. Build (or load) a mesh
|
||||
// 2. Set up maps and assign DOFs
|
||||
// 3. Configure target angles / targets
|
||||
// 4. Solve with Newton
|
||||
// 5. Inspect / export the result
|
||||
//
|
||||
// Each test mirrors a realistic usage scenario documented in the README.
|
||||
//
|
||||
// Tests:
|
||||
// 1. Pipeline_Euclidean_TriangleToEquilibrium
|
||||
// Read mesh → setup Euclidean maps → solve → verify convergence
|
||||
// 2. Pipeline_Spherical_TetrahedronToEquilibrium
|
||||
// Setup spherical tetrahedron → solve → verify angles sum to 4π
|
||||
// 3. Pipeline_HyperIdeal_TriangleRoundTrip
|
||||
// Build triangle → setup HyperIdeal → solve → verify G ≈ 0
|
||||
// 4. Pipeline_MeshIO_SolveAndExport
|
||||
// Build mesh → solve → write OFF → reload → verify vertex count intact
|
||||
// 5. Pipeline_AllThreeGeometries_SameTopology
|
||||
// Same quad-strip mesh solved under all three geometries: all converge
|
||||
|
||||
#include "conformal_mesh.hpp"
|
||||
#include "mesh_builder.hpp"
|
||||
#include "mesh_io.hpp"
|
||||
#include "euclidean_functional.hpp"
|
||||
#include "spherical_functional.hpp"
|
||||
#include "hyper_ideal_functional.hpp"
|
||||
#include "newton_solver.hpp"
|
||||
#include <gtest/gtest.h>
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
#include <filesystem>
|
||||
|
||||
using namespace conformallab;
|
||||
|
||||
// ────────────────────────────────────────────────────────────────────────────
|
||||
// Shared helpers
|
||||
// ────────────────────────────────────────────────────────────────────────────
|
||||
|
||||
static void pin_first_vertex_euclidean(ConformalMesh& mesh, EuclideanMaps& maps, int& n)
|
||||
{
|
||||
auto vit = mesh.vertices().begin();
|
||||
Vertex_index v0 = *vit++;
|
||||
maps.v_idx[v0] = -1;
|
||||
int idx = 0;
|
||||
for (; vit != mesh.vertices().end(); ++vit)
|
||||
maps.v_idx[*vit] = idx++;
|
||||
n = idx;
|
||||
}
|
||||
|
||||
static void set_natural_euclidean_theta(ConformalMesh& mesh, EuclideanMaps& maps, int n)
|
||||
{
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
|
||||
auto G = euclidean_gradient(mesh, x0, maps);
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv < 0) continue;
|
||||
maps.theta_v[v] -= G[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
}
|
||||
|
||||
static std::vector<double> set_natural_hyper_ideal_targets(
|
||||
ConformalMesh& mesh, HyperIdealMaps& maps, int n,
|
||||
double b_base = 1.0, double a_base = 0.5)
|
||||
{
|
||||
const auto sz = static_cast<std::size_t>(n);
|
||||
std::vector<double> xbase(sz, 0.0);
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv >= 0) xbase[static_cast<std::size_t>(iv)] = b_base;
|
||||
}
|
||||
for (auto e : mesh.edges()) {
|
||||
int ie = maps.e_idx[e];
|
||||
if (ie >= 0) xbase[static_cast<std::size_t>(ie)] = a_base;
|
||||
}
|
||||
auto G = evaluate_hyper_ideal(mesh, xbase, maps, false).gradient;
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = maps.v_idx[v];
|
||||
if (iv < 0) continue;
|
||||
maps.theta_v[v] += G[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
for (auto e : mesh.edges()) {
|
||||
int ie = maps.e_idx[e];
|
||||
if (ie < 0) continue;
|
||||
maps.theta_e[e] += G[static_cast<std::size_t>(ie)];
|
||||
}
|
||||
return xbase;
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Test 1 — Euclidean full pipeline: triangle → equilibrium
|
||||
//
|
||||
// Simulates a user doing:
|
||||
// auto mesh = make_triangle();
|
||||
// auto maps = setup_euclidean_maps(mesh);
|
||||
// compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
// // … set target angles and DOF indices …
|
||||
// auto result = newton_euclidean(mesh, x0, maps);
|
||||
// assert(result.converged);
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(Pipeline, Euclidean_TriangleToEquilibrium)
|
||||
{
|
||||
// ── Step 1: build mesh ────────────────────────────────────────────────
|
||||
auto mesh = make_triangle();
|
||||
|
||||
// ── Step 2: set up maps ───────────────────────────────────────────────
|
||||
auto maps = setup_euclidean_maps(mesh);
|
||||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
|
||||
// ── Step 3: assign DOFs (pin v0) ──────────────────────────────────────
|
||||
int n = 0;
|
||||
pin_first_vertex_euclidean(mesh, maps, n);
|
||||
ASSERT_EQ(n, 2);
|
||||
|
||||
// ── Step 4: choose natural target angles → x* = 0 ────────────────────
|
||||
set_natural_euclidean_theta(mesh, maps, n);
|
||||
|
||||
// ── Step 5: solve ─────────────────────────────────────────────────────
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
|
||||
auto result = newton_euclidean(mesh, x0, maps);
|
||||
|
||||
// ── Step 6: verify ────────────────────────────────────────────────────
|
||||
EXPECT_TRUE(result.converged)
|
||||
<< "Euclidean pipeline: triangle should converge; "
|
||||
"grad_inf_norm = " << result.grad_inf_norm;
|
||||
EXPECT_LT(result.grad_inf_norm, 1e-8);
|
||||
EXPECT_EQ(static_cast<int>(result.x.size()), n);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Test 2 — Spherical full pipeline: tetrahedron → equilibrium
|
||||
//
|
||||
// The spherical tetrahedron equilibrium x* = 0 is built into the maps.
|
||||
// After solving, the total angle defect Σ(Θ_v − Σα_v) should be ≈ 0.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(Pipeline, Spherical_TetrahedronToEquilibrium)
|
||||
{
|
||||
// ── Steps 1–3 ─────────────────────────────────────────────────────────
|
||||
auto mesh = make_spherical_tetrahedron();
|
||||
auto maps = setup_spherical_maps(mesh);
|
||||
compute_lambda0_from_mesh(mesh, maps);
|
||||
int n = assign_vertex_dof_indices(mesh, maps);
|
||||
|
||||
// ── Step 4: solve ─────────────────────────────────────────────────────
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.2);
|
||||
auto result = newton_spherical(mesh, x0, maps);
|
||||
|
||||
// ── Step 5: verify convergence ────────────────────────────────────────
|
||||
EXPECT_TRUE(result.converged)
|
||||
<< "Spherical pipeline: tetrahedron should converge; "
|
||||
"grad_inf_norm = " << result.grad_inf_norm;
|
||||
EXPECT_LT(result.grad_inf_norm, 1e-8);
|
||||
|
||||
// ── Step 6: verify geometric invariant — total angle defect ≈ 0 ──────
|
||||
auto G_final = spherical_gradient(mesh, result.x, maps);
|
||||
double total_defect = 0.0;
|
||||
for (double gv : G_final) total_defect += gv;
|
||||
EXPECT_NEAR(total_defect, 0.0, 1e-7)
|
||||
<< "Spherical: total angle defect should vanish at equilibrium";
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Test 3 — HyperIdeal full pipeline: triangle → equilibrium
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(Pipeline, HyperIdeal_TriangleRoundTrip)
|
||||
{
|
||||
// ── Steps 1–3 ─────────────────────────────────────────────────────────
|
||||
auto mesh = make_triangle();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
|
||||
// ── Step 4: natural targets (equilibrium at b=1.0, a=0.5) ────────────
|
||||
auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
|
||||
|
||||
// Verify: gradient at xbase must be ≈ 0 before solving
|
||||
auto G_at_base = evaluate_hyper_ideal(mesh, xbase, maps, false).gradient;
|
||||
double max_g = 0.0;
|
||||
for (double v : G_at_base) max_g = std::max(max_g, std::abs(v));
|
||||
ASSERT_LT(max_g, 1e-10) << "Natural target setup: gradient at base should be ~0";
|
||||
|
||||
// ── Step 5: perturb and solve ─────────────────────────────────────────
|
||||
std::vector<double> x0 = xbase;
|
||||
for (auto& v : x0) v += 0.3;
|
||||
|
||||
auto result = newton_hyper_ideal(mesh, x0, maps);
|
||||
|
||||
// ── Step 6: verify ────────────────────────────────────────────────────
|
||||
EXPECT_TRUE(result.converged)
|
||||
<< "HyperIdeal pipeline: triangle should converge; "
|
||||
"grad_inf_norm = " << result.grad_inf_norm;
|
||||
EXPECT_LT(result.grad_inf_norm, 1e-8);
|
||||
|
||||
// Solution should be close to xbase (same equilibrium)
|
||||
for (int i = 0; i < n; ++i) {
|
||||
EXPECT_NEAR(result.x[static_cast<std::size_t>(i)],
|
||||
xbase[static_cast<std::size_t>(i)], 1e-6)
|
||||
<< "DOF " << i << " should recover the equilibrium value";
|
||||
}
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Test 4 — Mesh I/O in the pipeline: solve → write → reload → check
|
||||
//
|
||||
// Demonstrates: compute a conformal factor on a mesh, write it to OFF, reload
|
||||
// and check that the mesh topology is preserved.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(Pipeline, MeshIO_SolveAndExport)
|
||||
{
|
||||
// ── Build and solve ───────────────────────────────────────────────────
|
||||
auto mesh = make_quad_strip();
|
||||
auto maps = setup_euclidean_maps(mesh);
|
||||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
|
||||
int n = 0;
|
||||
pin_first_vertex_euclidean(mesh, maps, n);
|
||||
set_natural_euclidean_theta(mesh, maps, n);
|
||||
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
|
||||
auto result = newton_euclidean(mesh, x0, maps);
|
||||
ASSERT_TRUE(result.converged) << "Solver must converge before export test";
|
||||
|
||||
// ── Write mesh ────────────────────────────────────────────────────────
|
||||
const std::string tmp_path = "/tmp/conformallab_pipeline_test.off";
|
||||
ASSERT_NO_THROW(save_mesh(tmp_path, mesh));
|
||||
ASSERT_TRUE(std::filesystem::exists(tmp_path));
|
||||
|
||||
// ── Reload and verify topology ────────────────────────────────────────
|
||||
ConformalMesh mesh2;
|
||||
ASSERT_NO_THROW(mesh2 = load_mesh(tmp_path));
|
||||
|
||||
EXPECT_EQ(mesh2.number_of_vertices(), mesh.number_of_vertices())
|
||||
<< "Vertex count must survive OFF round-trip";
|
||||
EXPECT_EQ(mesh2.number_of_faces(), mesh.number_of_faces())
|
||||
<< "Face count must survive OFF round-trip";
|
||||
|
||||
std::filesystem::remove(tmp_path);
|
||||
}
|
||||
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
// Test 5 — All three geometries, same quad-strip topology
|
||||
//
|
||||
// Validates that the solver infrastructure works uniformly: the same mesh
|
||||
// topology is solvable under Euclidean, Spherical, and HyperIdeal geometries.
|
||||
// ════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
TEST(Pipeline, AllThreeGeometries_QuadStrip)
|
||||
{
|
||||
// ── Euclidean ──────────────────────────────────────────────────────────
|
||||
{
|
||||
auto mesh = make_quad_strip();
|
||||
auto maps = setup_euclidean_maps(mesh);
|
||||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||||
int n = 0;
|
||||
pin_first_vertex_euclidean(mesh, maps, n);
|
||||
set_natural_euclidean_theta(mesh, maps, n);
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
|
||||
auto res = newton_euclidean(mesh, x0, maps);
|
||||
EXPECT_TRUE(res.converged) << "Euclidean: quad strip should converge";
|
||||
}
|
||||
|
||||
// ── HyperIdeal ────────────────────────────────────────────────────────
|
||||
{
|
||||
auto mesh = make_quad_strip();
|
||||
auto maps = setup_hyper_ideal_maps(mesh);
|
||||
int n = assign_all_dof_indices(mesh, maps);
|
||||
auto xbase = set_natural_hyper_ideal_targets(mesh, maps, n);
|
||||
std::vector<double> x0 = xbase;
|
||||
for (auto& v : x0) v += 0.1;
|
||||
auto res = newton_hyper_ideal(mesh, x0, maps);
|
||||
EXPECT_TRUE(res.converged) << "HyperIdeal: quad strip should converge";
|
||||
}
|
||||
|
||||
// ── Spherical (tetrahedron: smallest closed mesh with all vertices free) ─
|
||||
{
|
||||
auto mesh = make_spherical_tetrahedron();
|
||||
auto maps = setup_spherical_maps(mesh);
|
||||
compute_lambda0_from_mesh(mesh, maps);
|
||||
int n = assign_vertex_dof_indices(mesh, maps);
|
||||
std::vector<double> x0(static_cast<std::size_t>(n), -0.1);
|
||||
auto res = newton_spherical(mesh, x0, maps);
|
||||
EXPECT_TRUE(res.converged) << "Spherical: tetrahedron should converge";
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user