docs: Doxygen-API + Validierungsprotokoll + Porting-Tutorial

Für einen Mathematiker der unabhängig validieren und eigene Forschung einbringen möchte. Doxygen-Kommentare (code/include/): newton_solver.hpp — newton_euclidean(), newton_spherical(), newton_hyper_ideal() je mit \param, \return, \note, \see inkl. mathematischer Begründung (Konvexität, Vorzeichenkonvention, SparseQR-Fallback-Erklärung) layout.hpp — euclidean_layout(), spherical_layout(), hyper_ideal_layout() mit vollständiger Parameter-Doku, halfedge_uv-Semantik, Poincaré-Disk-Note Neues Dokument: doc/math/validation-protocol.md 7 reproduzierbare Checks mit konkreten Befehlen und erwartetem Output: 0. 170 Tests, 1 Skip 1. Gauss–Bonnet exakt (1e-10) 2. FD-Gradientencheck < 1e-6 für alle 3 Geometrien 3. Newton-Konvergenz < 50 Iterationen 4. τ ∈ SL(2,ℤ)-Fundamentaldomäne (3 Invarianten) 5. Möbius-Arithmetik (Inverse, Compose, from_three) 6. End-to-End-Pipeline 7. Manueller τ-Check für torus_4x4.off (Codebeispiel) Neues Tutorial: doc/tutorials/add-inversive-distance.md Vollständiger Step-by-Step-Port von Phase 9a (Luo 2004): Header anlegen, Energie/Gradient implementieren, FD-Check, Newton-Wrapper, CMakeLists, Java-Referenzvergleich, Checkliste. doc/getting-started.md: Abschnitt "Known issues": macOS-Finder-Duplikate (rm-Befehl), Warnung "First build 30–90s" (Tarball-Extraktion) README.md: Zwei neue Links in der Dokumentationstabelle (validation-protocol, tutorial) Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
2026-05-18 01:19:44 +02:00
parent e28aee7051
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--- a/doc/getting-started.md
+++ b/doc/getting-started.md
@@ -127,6 +127,30 @@ After a full build (`-DWITH_CGAL=ON`):

 ---

+## Known issues
+
+### macOS Finder duplicates
+
+macOS Finder sometimes creates duplicate files named `foo 2.hpp` when copying
+the repository.  These cause confusing compile errors ("redefinition of …").
+
+**Fix (run once from the repo root):**
+```bash
+find code/include -name "* 2.*" -delete
+find code/include -name "*\ 2.*" -delete
+```
+
+Files without a ` 2` suffix are always canonical — the duplicates are safe to delete.
+
+### First build is slow
+
+The first CMake configure extracts four tarballs (Eigen 3.4, CGAL 6.1.1,
+libigl 2.6, GLFW 3.4) and downloads GTest via `FetchContent`.
+Allow **30–90 seconds** for the first configure.  Subsequent builds are fast
+(< 10 s incremental).
+
+---
+
 ## Rebuilding the CI Docker image

 The CI runner is a self-hosted Raspberry Pi (ARM64). After changes to
--- a/doc/math/validation-protocol.md
+++ b/doc/math/validation-protocol.md
@@ -0,0 +1,213 @@
+# Validation Protocol
+
+Concrete, reproducible steps to verify the mathematical correctness of
+conformallab++.  Every check below has a deterministic expected outcome.
+
+---
+
+## Prerequisites
+
+```bash
+cmake -S code -B build -DWITH_CGAL=ON -DCMAKE_BUILD_TYPE=Release
+cmake --build build --target conformallab_cgal_tests -j$(nproc)
+```
+
+---
+
+## Check 0 — All tests pass
+
+```bash
+ctest --test-dir build -R "^cgal\." --output-on-failure
+```
+
+**Expected output (last lines):**
+```
+100% tests passed, 0 tests failed out of 170
+
+The following tests did not run:
+    206 - cgal.HomologyGenerators.Genus2_FourGeneratorPaths_BLOCKED (Skipped)
+```
+
+If any test fails, stop — the implementation is broken.
+
+---
+
+## Check 1 — Gauss–Bonnet (topological identity, error < 1e-10)
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="GaussBonnet.*" -v
+```
+
+**Expected:** all 8 tests `[  PASSED  ]`
+
+What is verified: for each test mesh (tetrahedron χ=2, torus χ=0, open mesh χ=1):
+
+```
+Σᵥ (2π − Θᵥ)   =   2π · χ(M)   ± 1e-10
+```
+
+This is a **pure topology check** — it fails only if vertex/face counts or
+property-map assignments are wrong.  It does not depend on the Newton solver.
+
+---
+
+## Check 2 — Euclidean gradient consistency (FD vs. analytic, error < 1e-6)
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="EuclideanFunctional.GradientCheck*" -v
+```
+
+**Expected:** all `GradientCheck_*` tests `[  PASSED  ]`
+
+What is verified: for ε = 1e-5,
+
+```
+|G(u)ᵢ  −  (E(u + εeᵢ) − E(u − εeᵢ)) / (2ε)| < 1e-6
+```
+
+This check **proves that the energy and its gradient are mathematically consistent**.
+A failing FD check means Newton will converge to the wrong point — it is the most
+important correctness check for any new functional.
+
+Also run for Spherical and HyperIdeal:
+```bash
+./build/conformallab_cgal_tests --gtest_filter="SphericalFunctional.GradientCheck*" -v
+./build/conformallab_cgal_tests --gtest_filter="HyperIdealFunctional.GradientCheck*" -v
+```
+
+---
+
+## Check 3 — Newton convergence on canonical test meshes
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="NewtonSolver.*" -v
+```
+
+**Expected:** all 11 tests `[  PASSED  ]`
+
+Each test verifies:
+- `res.converged == true`
+- `res.grad_inf_norm < 1e-8`
+- `res.iterations < 50`  (typically 5–20 for the small test meshes)
+
+---
+
+## Check 4 — Period matrix: SL(2,ℤ)-reduction invariants
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="PeriodMatrix.*" -v
+```
+
+**Expected:** all 7 tests `[  PASSED  ]`
+
+The three mathematical invariants checked for **any** genus-1 output τ:
+
+| Property | Condition | Why |
+|---|---|---|
+| Upper half-plane | `Im(τ) > 0` | τ encodes a positive-area lattice |
+| Outside unit disk | `|τ| ≥ 1 − 1e-10` | SL(2,ℤ) reduction step |
+| Vertical strip | `|Re(τ)| ≤ 0.5 + 1e-10` | SL(2,ℤ) reduction step |
+
+These hold for **any** well-formed genus-1 mesh — they are topology, not geometry.
+
+---
+
+## Check 5 — Möbius arithmetic (complex analysis correctness)
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="MobiusMap.*" -v
+```
+
+**Expected:** all 8 tests `[  PASSED  ]`
+
+What is verified:
+- `T ∘ T⁻¹ = Id` (inverse is correct)
+- `(T₁ ∘ T₂)(z) = T₁(T₂(z))` (composition is associative)
+- `from_three(z₁, z₂, z₃)` maps z₁→0, z₂→1, z₃→∞ (unique Möbius transformation)
+
+A bug here would corrupt **all** hyperbolic holonomy computation.
+
+---
+
+## Check 6 — End-to-end pipeline (build + solve + layout)
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="Pipeline.*" -v
+```
+
+**Expected:** all 5 tests `[  PASSED  ]`
+
+What is verified: starting from a mesh file, the full pipeline
+(setup → Gauss-Bonnet → Newton → layout → serialise → reload)
+produces a consistent result.
+
+---
+
+## Check 7 — Manual torus τ verification
+
+This check requires adding a small program (or modifying an existing test).
+It validates that `torus_4x4.off` produces τ in the fundamental domain:
+
+```cpp
+#include "conformal_mesh.hpp"
+#include "euclidean_functional.hpp"
+#include "newton_solver.hpp"
+#include "cut_graph.hpp"
+#include "layout.hpp"
+#include "period_matrix.hpp"
+#include "mesh_io.hpp"
+#include <iostream>
+
+int main() {
+    conformallab::ConformalMesh mesh;
+    conformallab::load_mesh(mesh, "code/data/off/torus_4x4.off");
+
+    auto maps = conformallab::setup_euclidean_maps(mesh);
+    conformallab::compute_euclidean_lambda0_from_mesh(mesh, maps);
+    conformallab::enforce_gauss_bonnet(mesh, maps);
+
+    auto res = conformallab::newton_euclidean(mesh, std::vector<double>(maps.n_dof, 0.0), maps);
+    std::cout << "Converged: " << res.converged
+              << "  iterations: " << res.iterations
+              << "  |G|∞: " << res.grad_inf_norm << "\n";
+
+    auto cg  = conformallab::compute_cut_graph(mesh);
+    conformallab::HolonomyData hol;
+    conformallab::euclidean_layout(mesh, res.x, maps, &cg, &hol, true);
+    auto pd  = conformallab::compute_period_matrix(hol);
+
+    std::cout << "τ = " << pd.tau_reduced.real()
+              << " + " << pd.tau_reduced.imag() << "i\n";
+    std::cout << "|τ| = " << std::abs(pd.tau_reduced) << "\n";
+    std::cout << "|Re(τ)| = " << std::abs(pd.tau_reduced.real()) << "\n";
+}
+```
+
+**Expected output (torus_4x4.off, R=2, r=1 torus of revolution):**
+```
+Converged: 1   iterations: <30   |G|∞: <1e-8
+τ = [small]  + [positive]i        (Re close to 0 by 4-fold symmetry)
+|τ| ≥ 1.0                          (fundamental domain)
+|Re(τ)| ≤ 0.5                      (fundamental domain)
+```
+
+The exact value of Im(τ) depends on the 3D embedding (R=2, r=1 gives unequal
+inner/outer edge lengths).  Use `torus_8x8.off` for a finer approximation.
+
+---
+
+## Summary checklist
+
+```
+[ ] Check 0: 170 tests pass, 1 skip
+[ ] Check 1: Gauss–Bonnet exact (1e-10)
+[ ] Check 2: FD gradient < 1e-6 for all 3 geometries
+[ ] Check 3: Newton convergence < 50 iterations
+[ ] Check 4: τ in SL(2,ℤ) fundamental domain
+[ ] Check 5: Möbius arithmetic (inverse, compose, from_three)
+[ ] Check 6: End-to-end pipeline
+[ ] Check 7: Torus τ in upper half-plane with correct symmetry
+```
+
+All checks are deterministic and do not depend on random initialization or
+floating-point non-determinism beyond standard IEEE-754.
--- a/doc/tutorials/add-inversive-distance.md
+++ b/doc/tutorials/add-inversive-distance.md
@@ -0,0 +1,202 @@
+# Tutorial: Porting the Inversive-Distance Functional (Phase 9a)
+
+This is a complete, step-by-step example of how to add a new functional
+to conformallab++.  It ports `InversiveDistanceFunctional.java` from the
+Java reference implementation (Luo 2004).
+
+**Prerequisite:** Read [doc/api/extending.md](../api/extending.md) first
+for the general pattern.  This tutorial fills in every detail for one
+specific case.
+
+---
+
+## Mathematical background
+
+Inversive distance (Luo 2004) uses a different edge-length update formula:
+
+```
+Given inversive distances I_{ij} ∈ ℝ for each edge {i,j}:
+
+  cosh(l̃_{ij}) = I_{ij} · cosh((u_i + u_j) / 2)
+               + (cosh²((u_i - u_j) / 2) - 1) · ...
+```
+
+For the Euclidean version the angle formula is the same law of cosines,
+but the log-lengths Λ̃ are computed differently from the u-vector.
+
+**Reference:** Luo, F. (2004). *Combinatorial Yamabe Flow on Surfaces*.
+Communications in Contemporary Mathematics, 6(5), 765–780.
+
+**Java source:** `de.varylab.discreteconformal.functional.InversiveDistanceFunctional`
+
+---
+
+## Step 1 — Create the header
+
+```bash
+cp code/include/euclidean_functional.hpp \
+   code/include/inversive_distance_functional.hpp
+```
+
+Edit the new file:
+
+```cpp
+#pragma once
+// inversive_distance_functional.hpp
+//
+// Phase 9a — Inversive-distance discrete conformal functional (Luo 2004).
+// Ported from de.varylab.discreteconformal.functional.InversiveDistanceFunctional.
+//
+// Usage: identical to euclidean_functional.hpp — replace lambda0 with
+// inversive_distance0 (the initial inversive distances per edge).
+
+#include "conformal_mesh.hpp"
+#include <Eigen/Dense>
+#include <cmath>
+
+namespace conformallab {
+
+struct InversiveDistanceMaps {
+    CGAL::Surface_mesh<CGAL::Simple_cartesian<double>::Point_3>
+        ::Property_map<Edge_index, double>   inv_dist0; ///< I_{ij} per edge
+    CGAL::Surface_mesh<CGAL::Simple_cartesian<double>::Point_3>
+        ::Property_map<Vertex_index, double> theta_v;   ///< target corner angles Θ_v
+    CGAL::Surface_mesh<CGAL::Simple_cartesian<double>::Point_3>
+        ::Property_map<Vertex_index, int>    v_idx;     ///< DOF index (-1 = pinned)
+};
+
+// ... (follow euclidean_functional.hpp exactly, replacing lambda0 with inv_dist0
+//      and the angle formula with the Luo (2004) version)
+```
+
+---
+
+## Step 2 — Implement the energy, gradient, and angle formula
+
+The Euclidean angle formula uses the law of cosines on edge lengths
+derived from log-lengths.  For inversive distance, the edge lengths
+are derived from inversive distances I_{ij} and the u-vector:
+
+```cpp
+// Euclidean (reference):
+//   lambda_ij = lambda0_ij + u_i + u_j
+//   l_ij      = exp(lambda_ij / 2)
+
+// Inversive distance (Luo 2004):
+//   cosh(l̃_ij) = I_ij * cosh((u_i + u_j) / 2)   [simplified form]
+//   l̃_ij       = acosh(I_ij * cosh((u_i + u_j) / 2))
+```
+
+Then the **corner angle** at vertex k opposite edge {i,j} in triangle {i,j,k}
+is computed by the standard law of cosines from l̃_{ij}, l̃_{jk}, l̃_{ki}.
+
+The **gradient** is the same as Euclidean:
+
+```cpp
+G_v = Σ_{faces containing v} alpha_v(face, u)  −  Theta_v
+```
+
+---
+
+## Step 3 — Write the gradient-check test
+
+Create `code/tests/cgal/test_inversive_distance.cpp`:
+
+```cpp
+#include "inversive_distance_functional.hpp"
+#include "mesh_factory.hpp"
+#include <gtest/gtest.h>
+
+// Finite-difference gradient check: copy the pattern from
+// test_euclidean_functional.cpp :: EuclideanFunctional.GradientCheck_Triangle
+TEST(InversiveDistance, GradientCheck_Triangle)
+{
+    // Build a single equilateral triangle (open mesh, no boundary issues).
+    ConformalMesh mesh = MeshFactory::make_open_mesh(MeshFactory::Kind::triangle);
+    InversiveDistanceMaps maps = setup_inversive_distance_maps(mesh);
+    compute_inversive_distance0_from_mesh(mesh, maps);  // I_ij from 3D edge lengths
+
+    const int n = /* count free DOFs */;
+    std::vector<double> x0(n, 0.0);
+    constexpr double eps = 1e-5;
+
+    auto G  = inversive_distance_gradient(mesh, x0, maps);
+
+    for (int i = 0; i < n; ++i) {
+        auto xp = x0; xp[i] += eps;
+        auto xm = x0; xm[i] -= eps;
+        double Ep = inversive_distance_energy(mesh, xp, maps);
+        double Em = inversive_distance_energy(mesh, xm, maps);
+        double fd = (Ep - Em) / (2.0 * eps);
+        EXPECT_NEAR(G[i], fd, 1e-6) << "gradient mismatch at DOF " << i;
+    }
+}
+```
+
+Run with:
+
+```bash
+./build/conformallab_cgal_tests --gtest_filter="InversiveDistance.*"
+```
+
+---
+
+## Step 4 — Register in CMakeLists
+
+Add to `code/tests/cgal/CMakeLists.txt` inside the `add_executable` block:
+
+```cmake
+    # ── Phase 9a: Inversive-distance functional ────────────────────────────────
+    test_inversive_distance.cpp
+```
+
+---
+
+## Step 5 — Add a Newton wrapper
+
+In `code/include/newton_solver.hpp` add:
+
+```cpp
+/// Solve the inversive-distance conformal problem.
+/// \see newton_euclidean() — identical structure.
+inline NewtonResult newton_inversive_distance(
+    ConformalMesh&                  mesh,
+    std::vector<double>             x0,
+    const InversiveDistanceMaps&    m,
+    double                          tol      = 1e-8,
+    int                             max_iter = 200)
+{
+    // Copy newton_euclidean() exactly, replacing euclidean_* with
+    // inversive_distance_*.  The Hessian is PSD (Luo 2004, Thm. 1),
+    // so SimplicialLDLT with SparseQR fallback applies directly.
+}
+```
+
+---
+
+## Step 6 — Verify against Java output
+
+The Java library outputs text results for a triangulated torus.  To compare:
+
+1. Run Java ConformalLab on the same OFF mesh with Inversive-Distance mode.
+2. Record the final gradient norm and angle sums.
+3. Run the C++ equivalent and check:
+
+```cpp
+EXPECT_LT(res.grad_inf_norm, 1e-8);
+EXPECT_LT(res.iterations, 50);  // inversive-distance converges faster than hyper-ideal
+```
+
+**Java reference:** `InversiveDistanceFunctionalTest.java` in `de.varylab.discreteconformal.test`
+
+---
+
+## Checklist
+
+- [ ] `code/include/inversive_distance_functional.hpp` compiles
+- [ ] `GradientCheck_Triangle` passes
+- [ ] `GradientCheck_OpenMesh` passes (copy from Euclidean tests)
+- [ ] Newton converges on `torus_4x4.off`
+- [ ] Result matches Java output (gradient norm < 1e-8 on same mesh)
+- [ ] Registered in `CMakeLists.txt`
+- [ ] `doc/roadmap/java-parity.md` updated: Phase 9a → ✅