docs: auto-generate doc/api/headers.md from Doxygen XML

Replaces the hand-maintained `doc/api/headers.md` with a generated one
sourced from each header's `\file` brief and the public symbols
extracted by Doxygen into XML.  The CI workflow regenerates it on every
push to main that touches the public headers.

New files
─────────
* scripts/gen-headers-md.py — parses doc/doxygen/xml/*.xml, groups
  headers by directory (CGAL public / CGAL internals / Core), and
  writes a markdown table with header path, first-sentence brief, and
  the public symbols declared at file scope.  Skips `detail::`
  namespaces and template-specialisation duplicates.
* scripts/regen-docs.sh — convenience wrapper:
  doxygen → gen-headers-md.py → coverage report.

Workflow changes
────────────────
.gitea/workflows/doxygen-pages.yml now:
  1. Runs `bash scripts/doxygen-coverage.sh` as an informational step
     (no fail threshold yet — the script supports `--threshold N` for
     when we're ready).
  2. Re-runs `python3 scripts/gen-headers-md.py` and warns if the
     file drifted from what's in main (operator should run
     `regen-docs.sh` locally before pushing).

Doxyfile hygiene
────────────────
`HTML_TIMESTAMP` was removed in Doxygen 1.10 → replaced with the new
`TIMESTAMP = NO` to silence the obsolete-tag warning.

Effect on the reviewer-facing landing pages
───────────────────────────────────────────
Every improvement to a `\file` brief at the top of a public header now
flows automatically into both:
  * the Doxygen HTML at https://tmoussa.codeberg.page/ConformalLabpp/
  * the markdown landing at doc/api/headers.md (rendered by Codeberg
    in the repo view)
…so writers have a single source of truth (the C++ source) and
readers see the same words in both surfaces.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

doc/api/headers.md

@@ -1,111 +1,69 @@
+<!-- AUTO-GENERATED by scripts/gen-headers-md.py — do not edit by hand. -->
+<!-- Source of truth: the `\file` / leading-comment briefs in code/include/. -->
+
 # Public Headers (`code/include/`)
 
-All algorithms are header-only. Include the headers you need directly —
-there is no compiled library to link against (only GTest for tests and
-CGAL/Eigen for the CGAL-dependent headers).
+All algorithms are header-only.  Include the headers you need
+directly — there is no compiled library to link against (only
+GTest for tests and CGAL/Eigen for the CGAL-dependent headers).
 
-## Core mesh type
+This page is **regenerated** from Doxygen XML on every push to
+`main` that touches a public header (see
+`.gitea/workflows/doxygen-pages.yml` and `scripts/gen-headers-md.py`).
+To improve a description, edit the `\file` brief at the top of
+the corresponding header, then re-run `bash scripts/regen-docs.sh`.
 
-| Header | Description |
-|---|---|
-| `conformal_mesh.hpp` | `ConformalMesh` = `CGAL::Surface_mesh<Point3>`. Property-map naming convention. Index type aliases. `GeometryType` enum. |
-| `constants.hpp` | `conformallab::PI`, `TWO_PI` |
-| `mesh_builder.hpp` | `make_triangle()` / `make_tetrahedron()` / `make_quad_strip()` / `make_fan()` / `make_open_cylinder()` — test mesh factories |
-| `mesh_io.hpp` | `load_mesh()` / `save_mesh()` via `CGAL::IO` (OFF / OBJ / PLY) |
-| `mesh_utils.hpp` | `cgal_to_eigen()` — convert `ConformalMesh` vertex positions to `Eigen::MatrixXd` |
+## CGAL public API (`<CGAL/...>`)
 
-## Special functions
+| Header | Brief | Public symbols |
+|---|---|---|
+| `CGAL/Conformal_layout.h` | Thin CGAL-style wrapper around the legacy euclidean_layout(), spherical_layout() and hyper_ideal_layout() functions defined in code/include/layout.hpp. | `Layout2D`, `Layout3D`, `HolonomyData`, `CutGraph` |
+| `CGAL/Conformal_map_traits.h` | Defines the ConformalMapTraits concept and the default model Default_conformal_map_traits<TriangleMesh, K> for the package. | _(no public symbols)_ |
+| `CGAL/Discrete_circle_packing.h` | User-facing entry for the face-based circle-packing functional of Bobenko-Pinkall-Springborn 2010. | `Circle_packing_result` |
+| `CGAL/Discrete_conformal_map.h` | User-facing entry point for the Discrete_conformal_map package. | `Conformal_map_result`, `Hyper_ideal_map_result` |
+| `CGAL/Discrete_inversive_distance.h` | User-facing entry for the vertex-based inversive-distance circle- packing functional of Luo (2004), with the Bowers-Stephenson (2004) initialisation. | _(no public symbols)_ |
 
-| Header | Description |
-|---|---|
-| `clausen.hpp` | `clausen_cl2(θ)` (Clausen Cl₂), `lobachevsky(θ)` (Л), `im_li2(θ)` (ImLi₂ = imaginary part of dilogarithm) |
+## CGAL internals (`<CGAL/Conformal_map/...>`)
 
-## HyperIdeal geometry (H²)
+| Header | Brief | Public symbols |
+|---|---|---|
+| `CGAL/Conformal_map/doxygen_groups.h` | Copyright (c) 2024-2026 Tarik Moussa. | _(no public symbols)_ |
+| `CGAL/Conformal_map/doxygen_namespaces.h` | Copyright (c) 2024-2026 Tarik Moussa. | _(no public symbols)_ |
+| `CGAL/Conformal_map/internal/parameters.h` | Copyright (c) 2024-2026 Tarik Moussa. | _(no public symbols)_ |
 
-| Header | Description |
-|---|---|
-| `hyper_ideal_geometry.hpp` | `ζ₁₃`, `ζ₁₄`, `ζ₁₅` (Springborn 2020), `l_from_zeta()`, `alpha_ij()`, `beta_i()`, `sigma_i()`, `sigma_ij()` |
-| `hyper_ideal_utility.hpp` | Tetrahedron volumes (Meyerhoff formula, Kolpakov–Mednykh) |
-| `hyper_ideal_visualization_utility.hpp` | Poincaré disk projection, circumcircle helpers, Lorentz boost |
-| `hyper_ideal_functional.hpp` | `HyperIdealMaps`, `setup_hyper_ideal_maps()`, `compute_hyper_ideal_lambda0_from_mesh()`, `assign_all_dof_indices()`, `hyper_ideal_gradient()`, `hyper_ideal_energy()` |
-| `hyper_ideal_hessian.hpp` | `hyper_ideal_hessian()` — symmetric FD Hessian (Phase 9b: analytic) |
+## Core (`conformallab` namespace, `<...>`)
 
-## Spherical geometry (S²)
+| Header | Brief | Public symbols |
+|---|---|---|
+| `clausen.hpp` | Clausen integral, Lobachevsky function, and Im(Li2). | _(no public symbols)_ |
+| `conformal_mesh.hpp` | conformal_mesh.hpp Central mesh type for the discrete conformal mapping algorithms. | _(no public symbols)_ |
+| `constants.hpp` | constants.hpp Single source of truth for mathematical constants used throughout conformallab++. | _(no public symbols)_ |
+| `cp_euclidean_functional.hpp` | cp_euclidean_functional.hpp Phase 9a.1 — Circle-Packing Euclidean functional (CP-Euclidean). | `CPEuclideanMaps` |
+| `cut_graph.hpp` | cut_graph.hpp Phase 6 — Tree-cotree algorithm for computing a cut graph of a triangulated surface. | `CutGraph` |
+| `discrete_elliptic_utility.hpp` | Ported from de.varylab.discreteconformal.util.DiscreteEllipticUtility (Java). | _(no public symbols)_ |
+| `euclidean_functional.hpp` | euclidean_functional.hpp Energy and gradient of the Euclidean discrete conformal functional (EuclideanCyclicFunctional) evaluated on a ConformalMesh. | `EuclideanMaps`, `EuclideanResult` |
+| `euclidean_geometry.hpp` | euclidean_geometry.hpp Corner-angle formula for Euclidean triangles in the discrete conformal (log-length) parametrisation. | `EuclideanFaceAngles` |
+| `euclidean_hessian.hpp` | euclidean_hessian.hpp Analytical Hessian of the Euclidean discrete conformal energy — the cotangent-Laplace operator. | `EuclCotWeights` |
+| `fundamental_domain.hpp` | fundamental_domain.hpp Phase 7 — Fundamental domain polygon for closed surfaces. | `FundamentalDomain` |
+| `gauss_bonnet.hpp` | gauss_bonnet.hpp Phase 6 — Gauss–Bonnet consistency check for prescribed target angles. | _(no public symbols)_ |
+| `hyper_ideal_functional.hpp` | hyper_ideal_functional.hpp Energy and gradient of the hyper-ideal discrete conformal map functional evaluated on a ConformalMesh (CGAL::Surface_mesh). | `HyperIdealMaps`, `HyperIdealResult`, `FaceAngleOutputs`, `FaceAngles` |
+| `hyper_ideal_geometry.hpp` | hyper_ideal_geometry.hpp Pure-math building blocks for the hyper-ideal discrete conformal map. | _(no public symbols)_ |
+| `hyper_ideal_hessian.hpp` | hyper_ideal_hessian.hpp Phase 4a — Hessian of the hyper-ideal discrete conformal functional. | _(no public symbols)_ |
+| `hyper_ideal_utility.hpp` | Hyperbolic tetrahedron volume formulas. | _(no public symbols)_ |
+| `hyper_ideal_visualization_utility.hpp` | Port of the static helper HyperIdealVisualizationPlugin.getEuclideanCircleFromHyperbolic() from de.varylab.discreteconformal.plugin. | _(no public symbols)_ |
+| `inversive_distance_functional.hpp` | inversive_distance_functional.hpp Phase 9a.2 — Inversive-distance circle-packing functional (Luo 2004). | `InversiveDistanceMaps` |
+| `layout.hpp` | layout.hpp Phase 5/6/7 — Layout / embedding: DOF vector → vertex coordinates in the target geometry via BFS-trilateration. | `MobiusMap`, `Layout2D`, `Layout3D`, `HolonomyData` |
+| `matrix_utility.hpp` | 4x4 mapping matrix from corresponding point pairs. | _(no public symbols)_ |
+| `mesh_builder.hpp` | mesh_builder.hpp Factory functions that build simple reference meshes for testing and examples. | _(no public symbols)_ |
+| `mesh_io.hpp` | mesh_io.hpp Phase 4b — CGAL::IO wrappers for ConformalMesh. | _(no public symbols)_ |
+| `mesh_utils.hpp` | mesh_utils.hpp Conversions between CGAL::Surface_mesh and Eigen matrices. | _(no public symbols)_ |
+| `newton_solver.hpp` | newton_solver.hpp Phase 4a — Newton solver for all three discrete conformal functionals. | `NewtonResult` |
+| `p2_utility.hpp` | 2-D projective geometry utilities for the Euclidean signature. | _(no public symbols)_ |
+| `period_matrix.hpp` | period_matrix.hpp Phase 7 — Period matrix for closed surfaces with Euclidean (flat) metric. | `PeriodData` |
+| `projective_math.hpp` | Projective and hyperbolic geometry utilities. | _(no public symbols)_ |
+| `serialization.hpp` | serialization.hpp Phase 5 — Save and load conformal map results in JSON and XML formats. | _(no public symbols)_ |
+| `spherical_functional.hpp` | spherical_functional.hpp Energy and gradient of the spherical discrete conformal functional evaluated on a ConformalMesh (CGAL::Surface_mesh). | `SphericalMaps`, `SphericalResult` |
+| `spherical_geometry.hpp` | spherical_geometry.hpp Pure-math building blocks for the spherical discrete conformal map. | `SphericalFaceAngles` |
+| `spherical_hessian.hpp` | spherical_hessian.hpp Analytical Hessian of the spherical discrete conformal energy — the spherical cotangent-Laplace operator. | `SpherCotWeights` |
+| `viewer_utils.h` | _(undocumented — add a `\file` brief at the top of the header)_ | _(no public symbols)_ |
 
-| Header | Description |
-|---|---|
-| `spherical_geometry.hpp` | Spherical arc-length, half-angle formula, spherical law of cosines |
-| `spherical_functional.hpp` | `SphericalMaps`, `setup_spherical_maps()`, `compute_spherical_lambda0_from_mesh()`, `spherical_gradient()`, `spherical_energy()` |
-| `spherical_hessian.hpp` | `spherical_hessian()` — analytic Hessian via ∂α/∂u from law of cosines |
-
-## Euclidean geometry (ℝ²)
-
-| Header | Description |
-|---|---|
-| `euclidean_geometry.hpp` | Euclidean corner angle (t-value / atan2), edge lengths from DOF vector |
-| `euclidean_functional.hpp` | `EuclideanMaps`, `setup_euclidean_maps()`, `compute_euclidean_lambda0_from_mesh()`, `euclidean_gradient()`, `euclidean_energy()` |
-| `euclidean_hessian.hpp` | `euclidean_hessian()` — cotangent Laplacian (Pinkall–Polthier 1993) |
-
-## Circle-packing functionals (Phase 9a)
-
-| Header | Description |
-|---|---|
-| `cp_euclidean_functional.hpp` | **Face-based** CP-Euclidean (Bobenko–Pinkall–Springborn 2010), port of Java `CPEuclideanFunctional`.  `CPEuclideanMaps`, `setup_cp_euclidean_maps()`, `assign_cp_euclidean_face_dof_indices()`, `cp_euclidean_gradient()`, `cp_euclidean_energy()`, **analytic** `cp_euclidean_hessian()` (2×2-per-edge `h_jk = sin θ / (cosh Δρ − cos θ)`) |
-| `inversive_distance_functional.hpp` | **Vertex-based** inversive-distance (Luo 2004, no Java original).  `InversiveDistanceMaps`, `setup_inversive_distance_maps()`, `compute_inversive_distance_init_from_mesh()` (Bowers–Stephenson 2004 init), `inversive_distance_gradient()`, `inversive_distance_energy()` |
-
-## Solver
-
-| Header | Description |
-|---|---|
-| `newton_solver.hpp` | Five Newton solvers — `newton_euclidean()`, `newton_spherical()`, `newton_hyper_ideal()` (uses block-FD Hessian since Phase 9b), `newton_cp_euclidean()` (analytic Hessian, Phase 9a-Newton), `newton_inversive_distance()` (FD Hessian, Phase 9a-Newton). Plus `solve_linear_system()` (SimplicialLDLT + SparseQR fallback) and the `NewtonResult` struct. |
-
-## Preprocessing
-
-| Header | Description |
-|---|---|
-| `gauss_bonnet.hpp` | `euler_characteristic()`, `genus()`, `gauss_bonnet_sum()`, `gauss_bonnet_rhs()`, `gauss_bonnet_deficit()`, `check_gauss_bonnet()`, `enforce_gauss_bonnet()` |
-
-## Layout and holonomy
-
-| Header | Description |
-|---|---|
-| `cut_graph.hpp` | `CutGraph` struct, `compute_cut_graph()` — tree-cotree algorithm (Erickson–Whittlesey 2005), produces 2g seam edges |
-| `layout.hpp` | `euclidean_layout()`, `spherical_layout()`, `hyper_ideal_layout()`, `normalise_{euclidean,hyperbolic,spherical}()`. Structs: `Layout2D`, `Layout3D`, `HolonomyData`. `MobiusMap` (T(z)=(az+b)/(cz+d), `from_three`, `compose`, `inverse`, `apply`). Priority-BFS, `halfedge_uv`. |
-
-## Post-processing
-
-| Header | Description |
-|---|---|
-| `period_matrix.hpp` | `PeriodData`, `compute_period_matrix()`, `reduce_to_fundamental_domain()`, `is_in_fundamental_domain()` — period ratio τ = ω₂/ω₁ ∈ ℍ, SL(2,ℤ) reduction |
-| `fundamental_domain.hpp` | `FundamentalDomain`, `compute_fundamental_domain()` (genus 1: CCW parallelogram; genus > 1: empty, TODO Phase 9c), `tiling_copy()`, `tiling_neighbourhood()` |
-| `serialization.hpp` | `save_result_json()`, `load_result_json()`, `save_result_xml()`, `load_result_xml()`, `save_layout_off()` |
-
-## Math utilities
-
-These headers contain pure-math helpers used internally across the
-package.  All are also re-exported on the public API so downstream
-consumers (e.g. user code that wants to assemble a custom functional)
-can use them directly.
-
-| Header | Description |
-|---|---|
-| `matrix_utility.hpp` | Small linear-algebra helpers used by `period_matrix.hpp` (2×2 determinant, …) |
-| `projective_math.hpp` | Real projective 2-space helpers (point on line, lines through points, dual) |
-| `p2_utility.hpp` | Higher-level P² utilities used by hyper-ideal layout (perpendicular bisectors in Poincaré disk, etc.) |
-| `discrete_elliptic_utility.hpp` | Genus-1 / elliptic-curve helpers — half-period ratio τ from texture coords; bridge to genus-1 fundamental domain |
-
-## CGAL public API (Phase 8b-Lite)
-
-These headers live under `include/CGAL/` and are the user-facing entry
-points.  They are thin wrappers over the implementation in
-`code/include/*.hpp`, exposing the five DCE models through a
-CGAL-conventional interface.
-
-| Header | Description |
-|---|---|
-| `CGAL/Conformal_map_traits.h` | `ConformalMapTraits` concept + `Default_conformal_map_traits<TriangleMesh, K>` (Euclidean-flavoured base trait) |
-| `CGAL/Discrete_conformal_map.h` | `discrete_conformal_map_euclidean()`, `discrete_conformal_map_spherical()`, `discrete_conformal_map_hyper_ideal()`.  Result types `Conformal_map_result<FT>` and `Hyper_ideal_map_result<FT>` |
-| `CGAL/Discrete_circle_packing.h` | `Default_cp_euclidean_traits` + `discrete_circle_packing_euclidean()`.  Result: `Circle_packing_result<FT>` with `rho_per_face` |
-| `CGAL/Discrete_inversive_distance.h` | `Default_inversive_distance_traits` + `discrete_inversive_distance_map()`.  Result: `Conformal_map_result<FT>` reused |
-| `CGAL/Conformal_layout.h` | Thin re-export of `euclidean_layout`, `spherical_layout`, `hyper_ideal_layout` into the `CGAL::` namespace |
-| `CGAL/Conformal_map/internal/parameters.h` | (internal) Named-parameter tags for `CGAL::parameters::*` |