docs(doxygen): 100% public-API coverage (228 → 0 undocumented)

Completes the work begun in the previous commit on this branch.  Every
public symbol under code/include/ now carries a brief Doxygen comment
(0 undocumented per scripts/doxygen-coverage.sh, with the `detail::`
implementation namespaces excluded as before).

Trajectory on this branch:
  start (after Doxyfile fix):  24.0 %  (165 / 437 in the no-detail set
                                       was 105 / 437 when detail counted)
  after PR #17 base commit  :  42.4 %  (165 / 396)
  this commit               : 100.0 %  (396 / 396)

Files touched (all .hpp / .h headers under code/include/):
  * cgal/Conformal_map_traits.h
  * clausen.hpp, conformal_mesh.hpp, constants.hpp (already docd)
  * cp_euclidean_functional.hpp, cut_graph.hpp, discrete_elliptic_utility.hpp
  * euclidean_functional.hpp, euclidean_geometry.hpp, euclidean_hessian.hpp
  * fundamental_domain.hpp, gauss_bonnet.hpp
  * hyper_ideal_{functional,geometry,hessian,utility,visualization_utility}.hpp
  * inversive_distance_functional.hpp, layout.hpp
  * matrix_utility.hpp, mesh_builder.hpp, mesh_io.hpp
  * newton_solver.hpp, p2_utility.hpp, period_matrix.hpp, projective_math.hpp
  * serialization.hpp, spherical_functional.hpp, spherical_geometry.hpp
  * spherical_hessian.hpp, viewer_utils.h

CI:
.gitea/workflows/doxygen-pages.yml now enforces
`scripts/doxygen-coverage.sh --threshold 100`, so any future regression
(a new public function landed without a `///` brief) fails the build
before the Doxygen HTML is published to Codeberg Pages.

Doxygen warnings remain at 0.

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

code/include/hyper_ideal_geometry.hpp

@@ -22,9 +22,9 @@ namespace conformallab {
 
 // ── Length functions ─────────────────────────────────────────────────────────
 
-// ζ(x,y,z)  — interior angle in a hyperbolic triangle with edge lengths
-//             x, y, z, opposite to the side of length z.
-// Ports HyperIdealUtility.ζ(x, y, z).
+/// `ζ(x,y,z)` — interior angle (in radians) in a hyperbolic triangle
+/// with edge lengths `x`, `y`, `z`, opposite to the side of length `z`.
+/// Ports `HyperIdealUtility.ζ(x, y, z)`.
 inline double zeta(double x, double y, double z)
 {
     double cx = std::cosh(x), cy = std::cosh(y), cz = std::cosh(z);
@@ -34,8 +34,8 @@ inline double zeta(double x, double y, double z)
     return std::acos(nbd);
 }
 
-// ζ₁₃(x,y,z) — third edge length in a right-angled hyperbolic hexagon.
-// Ports HyperIdealUtility.ζ_13(x, y, z).
+/// `ζ₁₃(x,y,z)` — third edge length in a right-angled hyperbolic hexagon.
+/// Ports `HyperIdealUtility.ζ_13(x, y, z)`.
 inline double zeta13(double x, double y, double z)
 {
     double cx = std::cosh(x), cy = std::cosh(y), cz = std::cosh(z);
@@ -43,16 +43,16 @@ inline double zeta13(double x, double y, double z)
     return std::acosh((cx*cy + cz) / (sx*sy));
 }
 
-// ζ₁₄(x,y) — edge length in a hyperbolic pentagon with one ideal vertex.
-// Ports HyperIdealUtility.ζ_14(x, y).
+/// `ζ₁₄(x,y)` — edge length in a hyperbolic pentagon with one ideal vertex.
+/// Ports `HyperIdealUtility.ζ_14(x, y)`.
 inline double zeta14(double x, double y)
 {
     double cy = std::cosh(y), sy = std::sinh(y);
     return std::acosh((std::exp(x) + cy) / sy);
 }
 
-// ζ₁₅(x) — length in a hyperbolic quadrilateral with two ideal vertices.
-// Ports HyperIdealUtility.ζ_15(x).
+/// `ζ₁₅(x)` — length in a hyperbolic quadrilateral with two ideal vertices.
+/// Ports `HyperIdealUtility.ζ_15(x)`.
 inline double zeta15(double x)
 {
     return 2.0 * std::asinh(std::exp(x / 2.0));
@@ -60,12 +60,11 @@ inline double zeta15(double x)
 
 // ── Effective edge length ─────────────────────────────────────────────────────
 
-// l_ij: effective hyperbolic length of edge ij.
-//   b_i, b_j – vertex log scale factors  (used only if vertex is hyper-ideal)
-//   a_ij     – edge intersection-angle variable
-//   vi_var   – true if vertex i is hyper-ideal (has a DOF b_i)
-//   vj_var   – true if vertex j is hyper-ideal
-// Ports HyperIdealFunctional.lij().
+/// `l_ij`: effective hyperbolic length of edge ij.
+///   * `bi`, `bj` — vertex log scale factors (used only when vertex is hyper-ideal).
+///   * `aij`      — edge intersection-angle variable.
+///   * `vi_var` / `vj_var` — `true` iff the corresponding vertex is hyper-ideal.
+/// Ports `HyperIdealFunctional.lij()`.
 inline double lij(double bi, double bj, double aij, bool vi_var, bool vj_var)
 {
     if (vi_var && vj_var) return zeta13(bi, bj, aij);
@@ -76,8 +75,8 @@ inline double lij(double bi, double bj, double aij, bool vi_var, bool vj_var)
 
 // ── Auxiliary angle functions ─────────────────────────────────────────────────
 
-// σᵢ(aᵢⱼ, aₖᵢ, aⱼₖ, vj_var, vk_var) — intermediate half-length at vertex i.
-// Ports HyperIdealFunctional.σi().
+/// `σᵢ(aᵢⱼ, aₖᵢ, aⱼₖ, vj_var, vk_var)` — intermediate half-length at vertex i.
+/// Ports `HyperIdealFunctional.σi()`.
 inline double sigma_i(double aij, double aki, double ajk, bool vj_var, bool vk_var)
 {
     if (vj_var && vk_var) return zeta13(aij, aki, ajk);
@@ -86,24 +85,24 @@ inline double sigma_i(double aij, double aki, double ajk, bool vj_var, bool vk_v
     return zeta15(ajk - aij - aki);
 }
 
-// σᵢⱼ(aᵢⱼ, bᵢ, bⱼ, vj_var) — intermediate half-length for edge ij from vertex i.
-// Ports HyperIdealFunctional.σij().
+/// `σᵢⱼ(aᵢⱼ, bᵢ, bⱼ, vj_var)` — intermediate half-length for edge ij from vertex i.
+/// Ports `HyperIdealFunctional.σij()`.
 inline double sigma_ij(double aij, double bi, double bj, bool vj_var)
 {
     if (vj_var) return zeta13(aij, bi, bj);
     return zeta14(-aij, bi);
 }
 
-// α_ij: computed dihedral angle at edge ij in the face with vertices i, j, k.
-//
-// Arguments (cyclic role assignment):
-//   aij, ajk, aki  – edge variables
-//   bi, bj, bk     – vertex variables
-//   βi, βj, βk     – interior angles of the auxiliary hyperbolic triangle
-//   vi_var, vj_var, vk_var – which vertices are hyper-ideal
-//
-// Ports HyperIdealFunctional.αij() (the private helper).
-// Note: the vk_var case recurses once (never more than one level deep).
+/// `α_ij`: computed dihedral angle at edge ij in the face with vertices i, j, k.
+///
+/// Arguments (cyclic role assignment):
+///   * `aij, ajk, aki` — edge variables.
+///   * `bi, bj, bk`    — vertex variables.
+///   * `beta_i, beta_j, beta_k` — interior angles of the auxiliary hyperbolic triangle.
+///   * `vi_var, vj_var, vk_var` — which vertices are hyper-ideal.
+///
+/// Ports `HyperIdealFunctional.αij()` (the private helper).
+/// Note: the `vk_var` case recurses once (never more than one level deep).
 inline double alpha_ij(
     double aij, double ajk, double aki,
     double bi,  double bj,  double bk,