# CLAUDE.md

This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.

## Project purpose and long-term goal

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:

> 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 four distinct phase blocks (updated 2026-05-22):
- **Phase 1–7 (done, v0.7.0):** Direct port of the Java library algorithms to C++.
- **Phase 8a MVP + 8b-Lite (done, v0.9.0):** CGAL public-API surface for all five DCE models via `<CGAL/Discrete_*.h>`.  Phase 8a.2 (generic FaceGraph), 8c (manuals), 8d (CGAL-test-format), 8e (YAML pipeline) deferred on-demand.
- **Phase 9a + 9b (done, v0.9.0):** Two new functionals (CP-Euclidean port, Inversive-Distance research), two new Newton solvers, block-FD HyperIdeal Hessian.
- **Phase 9b-analytic + 9c (planned):** Full analytic HyperIdeal Hessian via Schläfli identity (research, see `doc/roadmap/research-track.md`); 4g-polygon fundamental domain for genus g > 1 (mixed port + research).
- **Phase 10+ (research):** 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 source lives under `code/`. Three build modes:

```bash
# 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 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 + examples (requires Wayland/X11)
cmake -S code -B build -DWITH_CGAL=ON
cmake --build build -j$(nproc)
```

`-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
# 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 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`

`conformal_mesh.hpp` defines the core type:
```cpp
using ConformalMesh = CGAL::Surface_mesh<Point3>;  // CGAL::Simple_cartesian<double>
```

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 five DCE models

Each model has its own Maps struct that bundles all property maps, plus a functional, optional Hessian, Newton solver, and (since v0.9.0) a CGAL public-API entry function:

| Model | Space | DOFs | Maps struct | Key headers | Newton function | CGAL entry |
|---|---|---|---|---|---|---|
| Euclidean | ℝ² | vertex | `EuclideanMaps` | `euclidean_functional.hpp`, `euclidean_hessian.hpp` | `newton_euclidean()` | `discrete_conformal_map_euclidean()` |
| Spherical | S² | vertex | `SphericalMaps` | `spherical_functional.hpp`, `spherical_hessian.hpp` | `newton_spherical()` | `discrete_conformal_map_spherical()` |
| Hyper-ideal | H² (Poincaré disk) | vertex + edge | `HyperIdealMaps` | `hyper_ideal_functional.hpp`, `hyper_ideal_hessian.hpp` (block-FD, Phase 9b) | `newton_hyper_ideal()` | `discrete_conformal_map_hyper_ideal()` |
| CP-Euclidean (BPS 2010) | face-based circle packing | **face** | `CPEuclideanMaps` | `cp_euclidean_functional.hpp` | `newton_cp_euclidean()` | `discrete_circle_packing_euclidean()` |
| Inversive-Distance (Luo 2004) | vertex-based circle packing | vertex | `InversiveDistanceMaps` | `inversive_distance_functional.hpp` | `newton_inversive_distance()` | `discrete_inversive_distance_map()` |

DOF-assignment patterns:
- **Vertex-only models** (Euclidean, Spherical, Inversive-Distance): pin one vertex manually (`maps.v_idx[first_vertex] = -1`) then assign sequential indices.  The CGAL public entries do this automatically with the "natural-theta" trick (so calling them with no arguments returns x = 0 as the equilibrium).
- **HyperIdeal**: `assign_all_dof_indices(mesh, maps)` assigns vertex + edge DOFs automatically.
- **CP-Euclidean**: face-based — `assign_cp_euclidean_face_dof_indices(mesh, maps, pinned_face)` pins one face and indexes the rest.

### The full pipeline

```
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`)

Gradient sign convention differs across the five models:
- **Euclidean / Spherical / Inversive-Distance:** `G_v = Θ_v − actual_angle_sum` (target minus actual).
- **HyperIdeal:** `G_v = actual_angle_sum − Θ_v` (actual minus target).
- **CP-Euclidean:** `G_f = φ_f − Σ_{h:face(h)=f} (p(θ*,Δρ) + θ*)` (face-based; see `cp_euclidean_functional.hpp` header for the full formula).

Hessian sign and solver per model:
- **Euclidean:** H is PSD (cotangent Laplacian) → `SimplicialLDLT(H)`.
- **Spherical:** H is NSD (concave energy) → `SimplicialLDLT(−H)` (sign flip inside `newton_spherical`).
- **HyperIdeal:** H is PSD (strictly convex) → `SimplicialLDLT(H)`.  Phase 9b uses a **block-FD Hessian** (per-face 6×6 local block, ~96× speed-up vs full FD on V=200).  Full analytic Hessian via the chain `(bᵢ, aₑ) → lᵢⱼ → ζ₁₃/ζ₁₄/ζ₁₅ → αᵢⱼ/βᵢ` is planned research — see `doc/roadmap/research-track.md` Phase 9b-analytic.
- **CP-Euclidean:** analytic 2×2-per-edge `h_jk = sin θ / (cosh Δρ − cos θ)` (BPS 2010), strictly convex → `SimplicialLDLT(H)`.
- **Inversive-Distance:** FD Hessian (inline in `newton_inversive_distance`).  Analytic via Glickenstein 2011 eq. (4.6) is planned research (Phase 9a.2-analytic).

When `SimplicialLDLT` fails (rank-deficient H — gauge mode on a closed mesh without pinned vertex/face), 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 and holonomy (`layout.hpp`)

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

```cpp
// 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] -= 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;
```

## CI pipeline

Two jobs in `.gitea/workflows/cpp-tests.yml`:

| Job | CMake flags | Deps | Triggers on |
|---|---|---|---|
| `test-fast` | *(none)* | Eigen + GTest only | all branches |
| `test-cgal` | `-DWITH_CGAL_TESTS=ON` | + Boost | pull requests only |

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`).

Expected results: full test suite passing, 0 skipped, 0 failed.  The canonical counts live in `doc/api/tests.md` — do not hardcode them anywhere else (see [`doc/release-policy.md`](doc/release-policy.md)).

## Release state

Current release: **v0.9.0** (tag on `main`, released 2026-05-22).
Phases 1–9a complete, Phase 8b-Lite CGAL API surface complete (all 5 DCE models reachable via `<CGAL/Discrete_*.h>`), Phase 9b block-FD HyperIdeal Hessian shipped (~96× speed-up).  Next planned milestones: Phase 9c (4g-polygon, genus g > 1) and Phase 9b-analytic (Schläfli identity).  See `doc/release-policy.md` for the version-tag policy and `doc/roadmap/phases.md` for the phase plan.

## Phase 8 strategic decisions (2026-05-19)

The CGAL-package architecture was frozen on 2026-05-19.  Full design:
[`doc/api/cgal-package.md`](doc/api/cgal-package.md).  Key decisions:

| Decision | Choice |
|---|---|
| Submission to upstream CGAL | **Pre-submission-ready, not bound.** 12+ months horizon. |
| License | **MIT preserved** (no LGPL switch). |
| Mesh-type flexibility | **Generic `FaceGraph + HalfedgeGraph`** in target design; MVP starts Surface_mesh-only. |
| Parameter style | **Named Parameters** (`CGAL::parameters::...`). |
| Default kernel | **`Simple_cartesian<double>`** (status quo). |
| Backward compatibility | **Dual-layer wrapper** — `code/include/*.hpp` stays as implementation, `include/CGAL/*.h` is thin wrapper.  No algorithm duplication. |
| Implementation strategy | **Hybrid MVP** — minimum Phase 8 (traits + one wrapper) first, then Phase 9 in full, then Phase 8 extensions only on concrete demand. |
| Phase-8 MVP acceptance test | **Phase 9a (Inversive-Distance)** as the first new client of the new traits API. |

### Implementation sequence (committed)

```
1. Phase 7.5  Doxygen + cleanup                         done ✅
2. Phase 8 MVP — traits + one euclidean wrapper         3–5 days
3. Phase 9a — Inversive-Distance against new traits     3–5 days
4. Phase 9b — analytic HyperIdeal Hessian               1 week
5. Phase 9c — 4g-polygon for genus g > 1                1 week
   → port really complete, v0.9.0 release
```

Phase 8 extensions (8a.2 generic FaceGraph, 8c full Doxygen manuals, 8d
CGAL-format tests, 8e YAML pipeline) are deferred to on-demand status —
no speculative architecture for an uncertain submission.

Root-level files added at v0.7.0:
- `CITATION.cff` — machine-readable citation (Sechelmann 2016, Springborn 2020, Bobenko–Springborn 2004)
- `CONTRIBUTING.md` — short root-level pointer to `doc/contributing.md`
- `scripts/try_it.sh` — one-script quickstart: build → 209 tests → example run
- CMake install target: `cmake --install build --prefix /usr/local` → headers land in `include/conformallab/`

## Port-vs-research maintenance rule (2026-05-21 audit)

Before claiming something "ports X from Java", **verify empirically**:

```bash
find /Users/tarikmoussa/Desktop/conformallab -iname "*X*"
grep -r "ClassName" /Users/tarikmoussa/Desktop/conformallab/src
```

If zero matches, the work is **new research** — add it to
`doc/roadmap/research-track.md` with primary literature citations,
**not** to `doc/roadmap/java-parity.md`.

The 2026-05-21 audit found four pre-existing mis-labels:

| Item | Wrong claim | Reality |
|---|---|---|
| `InversiveDistanceFunctional` | "Java port (Luo 2004)" | No such Java class exists |
| HyperIdeal Hessian (FD) | "Phase 4a" | Research — Java has `hasHessian()==false` |
| HyperIdeal Hessian (analytic) | "Phase 9b port" | Research — derivation via Schläfli 1858 |
| Tutorial framing | "ports `InversiveDistanceFunctional.java`" | Implementation from Luo 2004 + Glickenstein 2011 |

All four are corrected as of this commit.  Future contributors must
follow the empirical verification rule above before any new claim.

## Documentation map

24 documents across 6 categories. Read the relevant one before reasoning from scratch
— do not hallucinate content that is already written down.

### Mathematics & theory

| Question | Document |
|---|---|
| What problem does this library solve mathematically? | `doc/math/discrete-conformal-theory.md` |
| How do the three geometry modes differ (Euclidean/Spherical/HyperIdeal)? | `doc/math/geometry-modes.md` |
| What analytic invariants can be used to validate correctness? | `doc/math/validation.md` |
| What are the exact ctest commands with expected terminal output? | `doc/math/validation-protocol.md` |
| What is the O() complexity and how does it scale with mesh size? | `doc/math/complexity.md` |
| Which papers are referenced by which header? | `doc/math/references.md` |
| How does conformallab++ compare to libigl, CGAL, geometry-central, pmp-library? | `doc/math/software-landscape.md` |
| What is unique about conformallab++ (novelty, target audience)? | `doc/math/novelty-statement.md` |

### Architecture & design

| Question | Document |
|---|---|
| Full pipeline diagram and data-flow overview | `doc/architecture/overall_pipeline.md` |
| Directory tree, build targets, file organisation | `doc/architecture/project-structure.md` |
| Key architectural decisions and their rationale | `doc/architecture/design-decisions.md` |
| Detailed comparison with geometry-central (CMU): overlap, adoption, scientific value | `doc/architecture/geometry-central-comparison.md` |
| Phase 9a validation report (CP-Euclidean port + Luo-inversive-distance literature check) | `doc/architecture/phase-9a-validation.md` |

### API & extension

| Question | Document |
|---|---|
| All 24 public headers with descriptions | `doc/api/headers.md` |
| Full pipeline API for all three geometries | `doc/api/pipeline.md` |
| What does each processing unit require/provide (contracts)? | `doc/api/contracts.md` |
| How to add a new functional / geometry mode / port from Java | `doc/api/extending.md` |
| Per-suite breakdown and counts (single source of truth) | `doc/api/tests.md` |
| Phase 8 CGAL package design + Declarative YAML pipeline spec | `doc/api/cgal-package.md` |

### Concepts & specs

| Question | Document |
|---|---|
| Declarative YAML pipeline: token vocabulary, 5 examples, validation algorithm | `doc/concepts/declarative-pipeline.md` |

### Roadmap & porting

| Question | Document |
|---|---|
| Phases 1–10 with status and sub-tasks | `doc/roadmap/phases.md` |
| Which Java classes are ported, which are planned, which are skipped? | `doc/roadmap/java-parity.md` |
| New research items (beyond Java) — citations, acceptance criteria | `doc/roadmap/research-track.md` |

### Tutorials & onboarding

| Question | Document |
|---|---|
| Build modes, single-test invocation, CLI, Docker image rebuild | `doc/getting-started.md` |
| Step-by-step: port the Inversive Distance functional (Phase 9a template) | `doc/tutorials/add-inversive-distance.md` |
| Language policy, test standards, release flow | `doc/contributing.md` |
| Versioning rules + release process + single-source-of-truth list | `doc/release-policy.md` |

### geometry-central context

**geometry-central** (Keenan Crane, CMU) implements the same discrete conformal
equivalence problem (Gillespie, Springborn & Crane, SIGGRAPH 2021) but uses
Ptolemaic flips on intrinsic triangulations instead of Newton on the original mesh.
It has no period matrix, holonomy, or spherical geometry mode.
The shared mathematical core (Springborn 2020) means cross-validation is meaningful.
Full analysis: `doc/architecture/geometry-central-comparison.md`.
Optional adoption roadmap (GC-1/2/3): `doc/roadmap/phases.md` (Optional section).

## Known quirks

- **No GTEST_SKIP stubs remain** (since v0.9.0): the three stale HDS-port stub files were removed because the CGAL test suite covers the same functionality with real tests.  The pure-math `conformallab_tests` target now only contains active tests.
- **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.
