62b02f88b9
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>
74 lines
2.8 KiB
C++
74 lines
2.8 KiB
C++
#pragma once
|
||
// spherical_geometry.hpp
|
||
//
|
||
// Pure-math building blocks for the spherical discrete conformal map.
|
||
// Ported from de.varylab.discreteconformal.functional.SphericalFunctional
|
||
// (the geometry helpers embedded there).
|
||
//
|
||
// Notation:
|
||
// u_i – vertex conformal factor (DOF)
|
||
// λ°_e – base log-length of edge e (fixed initial value)
|
||
// λ_ij – effective log-length = λ°_ij + u_i + u_j
|
||
// l_ij – spherical arc length = 2·asin(min(exp(λ_ij/2), 1))
|
||
// α_k – interior angle of the spherical triangle at vertex k
|
||
|
||
#include "constants.hpp"
|
||
#include <cmath>
|
||
#include <algorithm>
|
||
|
||
namespace conformallab {
|
||
|
||
/// Backward-compatible alias — prefer conformallab::PI in new code.
|
||
constexpr double PI_SPHER = PI;
|
||
|
||
// ── Effective spherical arc length ────────────────────────────────────────────
|
||
|
||
/// Spherical arc length `l(λ) = 2·asin(min(exp(λ/2), 1))`.
|
||
/// Clamps `exp(λ/2)` to `[0, 1]` so `asin` stays in domain.
|
||
inline double spherical_l(double lambda)
|
||
{
|
||
double half = std::exp(lambda * 0.5);
|
||
if (half >= 1.0) half = 1.0 - 1e-15;
|
||
if (half <= 0.0) return 0.0;
|
||
return 2.0 * std::asin(half);
|
||
}
|
||
|
||
// ── Interior angles of a spherical triangle ──────────────────────────────────
|
||
|
||
/// Interior angles of a spherical triangle, plus a `valid` flag.
|
||
struct SphericalFaceAngles {
|
||
double alpha1; ///< Corner angle at vertex v₁.
|
||
double alpha2; ///< Corner angle at vertex v₂.
|
||
double alpha3; ///< Corner angle at vertex v₃.
|
||
bool valid; ///< `false` when the three lengths violate the spherical triangle inequality.
|
||
};
|
||
|
||
/// Compute the spherical-triangle corner angles `(α₁, α₂, α₃)` from
|
||
/// the three arc lengths `(l₁₂, l₂₃, l₃₁)` using the half-angle form
|
||
/// of the spherical law of cosines. Returns `valid = false` for
|
||
/// degenerate or out-of-range triangles.
|
||
inline SphericalFaceAngles spherical_angles(double l12, double l23, double l31)
|
||
{
|
||
double s = (l12 + l23 + l31) * 0.5;
|
||
double s12 = s - l12;
|
||
double s23 = s - l23;
|
||
double s31 = s - l31;
|
||
|
||
// Spherical triangle inequalities: all s-deficiencies > 0 and s < π.
|
||
if (s12 <= 0.0 || s23 <= 0.0 || s31 <= 0.0 || s >= PI_SPHER)
|
||
return {0.0, 0.0, 0.0, false};
|
||
|
||
const double ss = std::sin(s);
|
||
const double ss12 = std::sin(s12);
|
||
const double ss23 = std::sin(s23);
|
||
const double ss31 = std::sin(s31);
|
||
|
||
double a1 = 2.0 * std::atan2(std::sqrt(ss12 * ss31), std::sqrt(ss * ss23));
|
||
double a2 = 2.0 * std::atan2(std::sqrt(ss12 * ss23), std::sqrt(ss * ss31));
|
||
double a3 = 2.0 * std::atan2(std::sqrt(ss23 * ss31), std::sqrt(ss * ss12));
|
||
|
||
return {a1, a2, a3, true};
|
||
}
|
||
|
||
} // namespace conformallab
|