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<!-- 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).

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`.

## CGAL public API (`<CGAL/...>`)

| 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)_ |

## CGAL internals (`<CGAL/Conformal_map/...>`)

| 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)_ |

## Core (`conformallab` namespace, `<...>`)

| 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)_ |

