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docs(claude): rewrite CLAUDE.md with full project context
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Browse Source 
Incorporates README, architecture doc, and Java ConformalLab source
structure. Adds:
- Long-term CGAL package goal made explicit
- Language policy: all code/comments/docs in English
- Java-to-C++ porting table (what is done, what is Phase 9, what is Phase 10)
- Java class names as reference anchors for future porting work
- "Natural theta" and gradient-check test patterns
- Halfedge traversal conventions
- CI job table with expected pass/skip counts
- Both remotes (origin + Codeberg) sync requirement
- Known quirks (Finder duplicates, protected main, Boost header-only)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Tarik Moussa
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CLAUDE.md
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This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
## What this project is
## Project purpose and long-term goal
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/`.
conformallab++ is a C++17 reimplementation of [ConformalLab](https://github.com/varylab/conformallab) — Stefan Sechelmann's Java research library for discrete conformal geometry (TU Berlin, ~850 commits, v1.0.0 2018). The algorithmic foundation is his dissertation:
The algorithmic foundation is Sechelmann's dissertation:
> *Variational Methods for Discrete Surface Parameterization: Applications and Implementation*, TU Berlin 2016. DOI: 10.14279/depositonce-5415
> Stefan Sechelmann — *Variational Methods for Discrete Surface Parameterization: Applications and Implementation*, TU Berlin 2016.
> DOI: [10.14279/depositonce-5415](https://depositonce.tu-berlin.de/items/8e2988b2-d991-45b5-aad5-9fb7988f3b2f) · CC BY-SA 4.0
**The long-term goal is a CGAL package** — a submission to the CGAL library that brings discrete conformal maps (hyper-ideal, spherical, Euclidean) to the CGAL ecosystem using `CGAL::Surface_mesh` as the underlying halfedge data structure, with a traits-class design compatible with arbitrary CGAL-conforming mesh types.
The project has three distinct phases:
- **Phase 1–7 (done):** Direct port of the Java library algorithms to C++
- **Phase 8–9 (planned):** CGAL package infrastructure + remaining Java features not yet ported (inversive-distance functional, analytic HyperIdeal Hessian, genus-g > 1 fundamental domain)
- **Phase 10+ (research):** New mathematics beyond the Java original — holomorphic differentials, Siegel period matrix Ω ∈ H_g, full uniformization for genus g ≥ 2
## Language
**All code, comments, documentation, commit messages, and test descriptions must be in English.** The project is intended for international collaboration and CGAL submission. Existing German-language comments in older files should be replaced with English when editing those files.
## Build commands
All three modes share the same source root `code/`:
All source lives under `code/`. Three build modes:
```bash
# Mode 1 — fast tests only (no CGAL, no Boost, no display)
# Mode 1 — fast tests, no CGAL, no Boost, no display (CI default)
cmake -S code -B build
cmake --build build --target conformallab_tests -j$(nproc)
ctest --test-dir build --output-on-failure
# Mode 2 — CGAL tests headless (CI mode, requires Boost headers, no wayland/display)
# macOS: brew install boost Linux: apt install libboost-dev
# Mode 2 — CGAL tests, headless (CI full, requires Boost headers only)
# macOS: brew install boost Linux: apt install libboost-dev
cmake -S code -B build -DWITH_CGAL_TESTS=ON
cmake --build build --target conformallab_cgal_tests -j$(nproc)
ctest --test-dir build -R "^cgal\." --output-on-failure
# Mode 3 — full local build (CLI app + viewer, requires Wayland/X11 dev headers)
# Mode 3 — full local build: CLI app + viewer + examples (requires Wayland/X11)
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.
`-DWITH_CGAL=ON` automatically enables `-DWITH_VIEWER=ON`, which pulls in GLFW and requires `wayland-scanner`. Never use this in headless CI.
### 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
# By GTest suite/test name
./build/conformallab_cgal_tests --gtest_filter="NewtonSolver*"
./build/conformallab_tests --gtest_filter="Clausen*"
# By CTest regex (prefix "cgal." for all CGAL tests)
ctest --test-dir build -R "cgal.NewtonSolver" --output-on-failure
```
### Rebuilding the CI Docker image
```bash
docker buildx build \
--platform linux/arm64 \
-f .gitea/docker/Dockerfile.ci-cpp \
-t git.eulernest.eu/conformallab/ci-cpp:latest \
--push \
.gitea/docker/
```
## 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.
All algorithms live in `code/include/*.hpp`. There is no compiled library. The three CMake targets (`conformallab_tests`, `conformallab_cgal_tests`, `conformallab_core`) compile headers directly from their `.cpp` entry points. To add a new algorithm: create a `.hpp` in `code/include/`, add a test in `code/tests/cgal/`, and register the test file in `code/tests/cgal/CMakeLists.txt`.
### Central type: `ConformalMesh`
Defined in `conformal_mesh.hpp`:
`conformal_mesh.hpp` defines the core type:
```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)
This replaces the Java `CoHDS` (half-edge data structure) and its intrusive `CoVertex`/`CoEdge`/`CoFace` types. Data is attached via named CGAL property maps instead of intrusive fields:
| Property map name | Type | Meaning |
|---|---|---|
| `"v:lambda"` | `double` per vertex | log scale factor (conformal variable uᵢ) |
| `"v:theta"` | `double` per vertex | target cone angle Θᵥ |
| `"v:idx"` | `int` per vertex | solver DOF index; `-1` = pinned/boundary |
| `"e:alpha"` | `double` per edge | intersection angle αᵢⱼ (hyperbolic only) |
| `"f:type"` | `int` per face | geometry type (0=Euclidean, 1=Hyperbolic, 2=Spherical) |
`CGAL_DISABLE_GMP` and `CGAL_DISABLE_MPFR` are defined for all CGAL targets — the library deliberately uses `Simple_cartesian<double>` (floating-point, no exact arithmetic) because conformal geometry does not require exact predicates.
### The three geometry modes
Each mode has its own Maps struct + functional + Hessian header:
Each mode has its own Maps struct that bundles all property maps, plus functional, Hessian, and Newton function:
| 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()` |
| Mode | Space | Maps struct | Key headers | Newton function |
|---|---|---|---|---|
| Euclidean | ℝ² | `EuclideanMaps` | `euclidean_functional.hpp`, `euclidean_hessian.hpp` | `newton_euclidean()` |
| Spherical | S² | `SphericalMaps` | `spherical_functional.hpp`, `spherical_hessian.hpp` | `newton_spherical()` |
| Hyper-ideal | H² (Poincaré disk) | `HyperIdealMaps` | `hyper_ideal_functional.hpp`, `hyper_ideal_hessian.hpp` | `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.
HyperIdeal also has edge DOFs (`e_idx[e]`); Euclidean and Spherical are vertex-DOF only. For HyperIdeal: `assign_all_dof_indices(mesh, maps)` assigns all vertex and edge DOFs automatically. For Euclidean/Spherical: pin one vertex manually (`maps.v_idx[first_vertex] = -1`) then assign sequential indices.
### Pipeline
### The full 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
load_mesh() → ConformalMesh (OFF/OBJ/PLY)
setup_*_maps(mesh) → *Maps (property maps created, all zero)
compute_*_lambda0_from_mesh(mesh, m) → λ° initialised from 3-D edge lengths
DOF assignment → v_idx[v] set; -1 = pinned
check_gauss_bonnet(mesh, maps) → throws if Σ(2π−Θᵥ) ≠ 2π·χ(M)
enforce_gauss_bonnet(mesh, maps) → redistributes angle defect uniformly
newton_*(mesh, x0, maps) → NewtonResult{x*, iterations, converged}
compute_cut_graph(mesh) → CutGraph (2g seam edges, tree-cotree)
*_layout(mesh, x*, maps, &cg, &hol) → Layout2D/3D + HolonomyData
normalise_*(layout) → canonical position (PCA / Möbius / Rodrigues)
compute_period_matrix(hol) → PeriodData{τ∈ℍ} (genus 1 flat torus)
compute_fundamental_domain(hol) → FundamentalDomain{vertices, generators}
tiling_neighbourhood(layout, hol) → vector of translated layout copies
save_result_json/xml() → serialised result
```
After `compute_*_lambda0_from_mesh()` the original vertex positions are no longer used — all subsequent computation is in log-length/scale-factor space.
### 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)`
The gradient sign convention differs between modes:
- **Euclidean/HyperIdeal:** `G_v = actual_angle_sum − Θ_v`, H is PSD → `SimplicialLDLT(H)`
- **Spherical:** `G_v = Θ_v − actual_angle_sum`, 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)`.
When `SimplicialLDLT` fails (rank-deficient H — gauge mode on closed mesh without pinned vertex), the solver automatically retries with `Eigen::SparseQR` to find the minimum-norm step orthogonal to the null space. Public API: `solve_linear_system(H, rhs, &used_fallback)`.
### Layout (`layout.hpp`)
The HyperIdeal Hessian is currently a **symmetric finite-difference approximation** (O(ε²), costs n extra gradient evaluations per Newton step). The analytic Hessian via the chain `(bᵢ, aₑ) → lᵢⱼ → ζ₁₃/ζ₁₄/ζ₁₅ → αᵢⱼ/βᵢ` is deferred to Phase 9b.
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)
### Layout and holonomy (`layout.hpp`)
### Test design pattern
BFS-trilateration with a **priority min-heap on BFS depth** (`depth = max(depth[src], depth[tgt]) + 1`). Root face = largest 3-D area face. This minimises trilateration error accumulation compared to simple BFS.
Key output fields:
- `layout.uv[v.idx()]` — primary UV (first/shallowest BFS visit per vertex)
- `layout.halfedge_uv[h.idx()]` — UV of `source(h)` as seen from `face(h)`; at seam halfedges the two opposite halfedges carry *different* UV values, enabling proper GPU texture atlasing without vertex duplication
- `hol.translations[i]` — lattice generator ωᵢ ∈ ℂ (Euclidean/spherical)
- `hol.mobius_maps[i]` — Möbius isometry Tᵢ ∈ SU(1,1) (hyperbolic, Poincaré disk)
`MobiusMap` is defined in `layout.hpp`: T(z) = (az+b)/(cz+d). Key methods: `from_three()` (fit to 3 point correspondences via 3×3 complex linear system), `compose()`, `inverse()`, `apply(Vector2d)`.
### Key mathematical reference for each header
| Header | Java original | Key reference |
|---|---|---|
| `hyper_ideal_geometry.hpp` | `HyperIdealGeometry.java` | Springborn (2020) — ζ₁₃/ζ₁₄/ζ₁₅ functions |
| `euclidean_hessian.hpp` | `EuclideanHessian.java` | Pinkall & Polthier (1993) — cotangent Laplacian |
| `spherical_hessian.hpp` | `SphericalHessian.java` | ∂α/∂u from spherical law of cosines |
| `cut_graph.hpp` | `CuttingUtility.java` | Erickson & Whittlesey (SODA 2005) — tree-cotree |
| `period_matrix.hpp` | `PeriodMatrixUtility.java` | Sechelmann (2016) §4 — SL(2,ℤ) reduction |
| `gauss_bonnet.hpp` | (distributed across Java) | Gauss–Bonnet: Σ(2π−Θᵥ) = 2π·χ(M) |
### Java features not yet ported (Phase 9)
The Java library under `de.varylab.discreteconformal` contains these items not yet in C++:
| Java class | Planned C++ header | Phase |
|---|---|---|
| `InversiveDistanceFunctional` | `inversive_distance_functional.hpp` | 9a |
| Analytic HyperIdeal Hessian | `hyper_ideal_hessian.hpp` (replace FD) | 9b |
| 4g-polygon boundary walk in `FundamentalDomainUtility` | `fundamental_domain.hpp` (extend) | 9c |
| `DiscreteHarmonicFormUtility` | Phase 10a prerequisite | 10 |
| `DiscreteHolomorphicFormUtility` | Phase 10a | 10 |
| `HomologyUtility`, `CanonicalBasisUtility` | Phase 10 | 10 |
When porting a Java class, locate the original in `de.varylab.discreteconformal.*` at [github.com/varylab/conformallab](https://github.com/varylab/conformallab) and use it as the reference implementation.
## Test design patterns
### "Natural theta" — constructing a known equilibrium at x* = 0
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);
// Evaluate gradient at x=0; set target angles = actual angle sums → x*=0 by definition
std::vector<double> x0(n_dofs, 0.0);
auto G0 = 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 */;
maps.theta_v[v] -= G0[maps.v_idx[v]]; // shift so G(x=0) = 0
```
This is used in virtually every Newton convergence test — it avoids hardcoding specific angle values.
### Gradient check pattern
```cpp
// Copy from any test_*_functional.cpp — GradientCheck_* test suite
double eps = 1e-5;
for (int i = 0; i < n; ++i) {
xp[i] += eps; auto Gp = euclidean_gradient(mesh, xp, maps);
xm[i] -= eps; auto Gm = euclidean_gradient(mesh, xm, maps);
double fd = (energy(xp) - energy(xm)) / (2*eps);
EXPECT_NEAR(G[i], fd, 1e-7);
xp[i] = xm[i] = x0[i];
}
```
All new functionals must have a gradient-check test before being considered complete.
### Halfedge traversal
```cpp
for (auto f : mesh.faces()) {
auto h0 = mesh.halfedge(f); // canonical halfedge of face
auto h1 = mesh.next(h0);
auto h2 = mesh.next(h1);
Vertex_index v1 = mesh.source(h0); // = mesh.target(h2)
Vertex_index v2 = mesh.source(h1);
Vertex_index v3 = mesh.source(h2);
// Angle at v3 is opposite to h0 (edge v1–v2)
// h_alpha[h0] = α₃, h_alpha[h1] = α₁, h_alpha[h2] = α₂
bool is_boundary = mesh.is_border(mesh.opposite(h0));
}
```
### Attaching custom data to the mesh
```cpp
auto [my_map, created] = mesh.add_property_map<Vertex_index, double>("v:my_data", 0.0);
my_map[v] = 3.14;
```
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
Two jobs in `.gitea/workflows/cpp-tests.yml`:
Docker image: `git.eulernest.eu/conformallab/ci-cpp:latest` (Ubuntu 22.04 ARM64). Dockerfile at `.gitea/docker/Dockerfile.ci-cpp`.
| Job | CMake flags | Deps | Triggers on |
|---|---|---|---|
| `test-fast` | *(none)* | Eigen + GTest only | all branches |
| `test-cgal` | `-DWITH_CGAL_TESTS=ON` | + Boost | `main`, `dev`, PRs only |
## Known issues / conventions
Runner: `eulernest` — self-hosted Raspberry Pi, ARM64, Ubuntu 22.04. Docker image: `git.eulernest.eu/conformallab/ci-cpp:latest`. `test-cgal` needs `test-fast` to pass first (`needs: test-fast`).
- 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.
Expected results: **36 non-CGAL tests pass**, **158 CGAL tests pass, 2 skipped** (intentional `GTEST_SKIP` stubs for genus-2 homology and analytic HyperIdeal Hessian — these are Java features deferred to Phase 9).
## Known quirks
- **Finder duplicate files**: `include/` contains files like `clausen 2.hpp`, `hyper_ideal_utility 2.hpp` — macOS Finder duplicates. Always use the canonical name without ` 2`. These should be deleted.
- **`test-fast` also runs stubs**: `conformallab_tests` (non-CGAL) contains `GTEST_SKIP`-based stubs for functionals that need CGAL. This is intentional — those tests document what was in the Java port scope but requires the CGAL mesh type.
- **Boost is header-only**: CGAL 6.x uses only Boost headers (`Boost.Config`, `Boost.Graph`). No compiled Boost libraries are needed. `find_package(Boost REQUIRED)` only locates the include path.
- **`main` branch is protected** on `origin` (Gitea). Push to `dev`, then merge via pull request. Codeberg `main` can be pushed to directly.
- **Both remotes must stay in sync**: `origin` = `git.eulernest.eu` (CI runs here), `codeberg` = `codeberg.org/TMoussa/ConformalLabpp` (public mirror). Push to both after every significant change.