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
| 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 |
Special functions
| Header |
Description |
clausen.hpp |
clausen_cl2(θ) (Clausen Cl₂), lobachevsky(θ) (Л), im_li2(θ) (ImLi₂ = imaginary part of dilogarithm) |
HyperIdeal geometry (H²)
| 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) |
Spherical geometry (S²)
| 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::* |
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