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+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## What this project is
+
+conformallab++ is a C++ reimplementation of Stefan Sechelmann's [ConformalLab](https://github.com/varylab/conformallab) Java library (TU Berlin, 2016). It solves one precise problem: given a triangulated surface, find a conformally equivalent metric satisfying prescribed curvature (angle-sum) constraints at each vertex. All code lives in `code/`.
+
+The algorithmic foundation is Sechelmann's dissertation:
+> *Variational Methods for Discrete Surface Parameterization: Applications and Implementation*, TU Berlin 2016. DOI: 10.14279/depositonce-5415
+
+## Build commands
+
+All three modes share the same source root `code/`:
+
+```bash
+# Mode 1 — fast tests only (no CGAL, no Boost, no display)
+cmake -S code -B build
+cmake --build build --target conformallab_tests -j$(nproc)
+ctest --test-dir build --output-on-failure
+
+# Mode 2 — CGAL tests headless (CI mode, requires Boost headers, no wayland/display)
+# macOS: brew install boost   Linux: apt install libboost-dev
+cmake -S code -B build -DWITH_CGAL_TESTS=ON
+cmake --build build --target conformallab_cgal_tests -j$(nproc)
+ctest --test-dir build -R "^cgal\." --output-on-failure
+
+# Mode 3 — full local build (CLI app + viewer, requires Wayland/X11 dev headers)
+cmake -S code -B build -DWITH_CGAL=ON
+cmake --build build -j$(nproc)
+```
+
+**Important:** `-DWITH_CGAL=ON` automatically enables `-DWITH_VIEWER=ON`, which pulls in GLFW and requires `wayland-scanner`. Use `-DWITH_CGAL_TESTS=ON` for headless environments.
+
+### Running a single test
+
+```bash
+# Non-CGAL test by name
+ctest --test-dir build -R "Clausen" --output-on-failure
+
+# CGAL test by name (prefix is always "cgal.")
+ctest --test-dir build -R "cgal.NewtonSolver" --output-on-failure
+
+# Or run the binary directly for full GTest output
+./build/conformallab_cgal_tests --gtest_filter="NewtonSolver*"
+./build/conformallab_tests       --gtest_filter="Clausen*"
+```
+
+## Architecture
+
+### Everything is header-only
+
+All algorithms live in `code/include/*.hpp`. There is no compiled library. The CMake targets (`conformallab_tests`, `conformallab_cgal_tests`, `conformallab_core`) all compile the headers directly via their test or app `.cpp` files.
+
+### Central type: `ConformalMesh`
+
+Defined in `conformal_mesh.hpp`:
+```cpp
+using ConformalMesh = CGAL::Surface_mesh<Point3>;  // CGAL::Simple_cartesian<double>
+```
+Algorithms attach data via CGAL named property maps rather than intrusive vertex/edge types (replacing the Java CoHDS/CoVertex/CoEdge pattern). Property map naming convention:
+- `"v:lambda"` — per-vertex log scale factor (the conformal variable uᵢ)
+- `"v:theta"` — per-vertex target cone angle
+- `"v:idx"` — solver DOF index (`-1` = pinned/boundary)
+- `"e:alpha"` — per-edge intersection angle (hyperbolic geometry only)
+
+### The three geometry modes
+
+Each mode has its own Maps struct + functional + Hessian header:
+
+| Mode | Headers | Maps struct | Newton function |
+|------|---------|-------------|----------------|
+| Euclidean (ℝ²) | `euclidean_functional.hpp`, `euclidean_hessian.hpp` | `EuclideanMaps` | `newton_euclidean()` |
+| Spherical (S²) | `spherical_functional.hpp`, `spherical_hessian.hpp` | `SphericalMaps` | `newton_spherical()` |
+| Hyper-ideal (H²) | `hyper_ideal_functional.hpp`, `hyper_ideal_hessian.hpp` | `HyperIdealMaps` | `newton_hyper_ideal()` |
+
+Setup follows the same pattern for all three:
+```cpp
+EuclideanMaps maps = setup_euclidean_maps(mesh);
+compute_euclidean_lambda0_from_mesh(mesh, maps);   // initialise λ° from 3-D positions
+maps.v_idx[*mesh.vertices().begin()] = -1;         // pin one vertex (gauge fix)
+int idx = 0;
+for (auto v : mesh.vertices()) if (maps.v_idx[v] != -1) maps.v_idx[v] = idx++;
+```
+After `compute_*_lambda0_from_mesh()` the solver works entirely in scale-factor space; original vertex positions are no longer used.
+
+### Pipeline
+
+```
+load_mesh()                    → ConformalMesh
+setup_*_maps()                 → *Maps  (property maps attached)
+compute_*_lambda0_from_mesh()  → λ° initialised
+check/enforce_gauss_bonnet()   → Σ(2π−Θᵥ) = 2π·χ(M)  [mandatory for closed meshes]
+newton_*()                     → NewtonResult.x  (converged scale factors)
+compute_cut_graph()            → CutGraph  (2g seam edges, closed meshes only)
+euclidean/spherical/hyper_ideal_layout()  → Layout2D/3D + HolonomyData
+normalise_*()                  → canonical position
+compute_period_matrix()        → PeriodData  τ∈ℍ  (genus 1 flat torus)
+compute_fundamental_domain()   → FundamentalDomain + tiling
+save_result_json/xml()         → serialised result
+```
+
+### Newton solver (`newton_solver.hpp`)
+
+Sign conventions differ between modes — the solver handles this internally:
+- Euclidean/HyperIdeal: `G_v = actual − target`, H is PSD → `SimplicialLDLT(H)`
+- Spherical: `G_v = target − actual`, H is NSD → `SimplicialLDLT(−H)`
+
+When `SimplicialLDLT` fails (rank-deficient H on closed meshes without pinned vertex), the solver automatically retries with `SparseQR` to find the minimum-norm step. This is the gauge-mode fallback — public API: `solve_linear_system(H, rhs, &used_fallback)`.
+
+### Layout (`layout.hpp`)
+
+BFS-trilateration using a min-heap on BFS depth (priority BFS). Root face = largest 3-D area face. Key output fields:
+- `layout.uv[v.idx()]` — primary UV (first/shallowest BFS visit)
+- `layout.halfedge_uv[h.idx()]` — UV of `source(h)` as seen from `face(h)` — seam-aware for GPU texture atlasing
+- `hol.translations[i]` — lattice generators ωᵢ (Euclidean/spherical)
+- `hol.mobius_maps[i]` — Möbius isometry Tᵢ ∈ SU(1,1) (hyperbolic)
+
+### Test design pattern
+
+Tests use the **"natural theta"** trick to construct a known equilibrium at `x* = 0`:
+```cpp
+// Evaluate gradient at x=0, use actual angle sums as targets → x*=0 by construction
+evaluate_euclidean_gradient(mesh, x0, maps);
+for (auto v : mesh.vertices())
+    if (maps.v_idx[v] >= 0)
+        maps.theta_v[v] = /* actual angle sum from gradient evaluation */;
+```
+Gradient checks use finite differences: perturb `xᵢ ± ε`, verify `G(x) ≈ ∂E/∂x`.
+
+## CI pipeline
+
+Two jobs defined in `.gitea/workflows/cpp-tests.yml`:
+- **`test-fast`** — no flags, Eigen+GTest only, runs on all branches
+- **`test-cgal`** — `-DWITH_CGAL_TESTS=ON`, requires Boost (installed at runtime until Docker image is rebuilt), runs on `main`/`dev`/PRs only, needs `test-fast` to pass first
+
+Docker image: `git.eulernest.eu/conformallab/ci-cpp:latest` (Ubuntu 22.04 ARM64). Dockerfile at `.gitea/docker/Dockerfile.ci-cpp`.
+
+## Known issues / conventions
+
+- Files ending in ` 2.hpp` (e.g. `clausen 2.hpp`, `hyper_ideal_utility 2.hpp`) are macOS Finder duplicates — ignore them, use the canonical name without ` 2`.
+- `CGAL_DISABLE_GMP` and `CGAL_DISABLE_MPFR` are defined for all CGAL targets — CGAL runs in exact-predicates-inexact-constructions mode with `Simple_cartesian<double>`, which is intentional (conformal geometry does not need exact arithmetic).
+- All deps are bundled as tarballs in `code/deps/tarballs/` and extracted at CMake configure time — no internet access needed at build time except for GTest (fetched via `FetchContent`).
+- The `test-fast` job intentionally includes stubs that call `GTEST_SKIP()` — 2 intentional skips are expected in the CGAL suite, not regressions.