diff --git a/code/include/CGAL/Discrete_circle_packing.h b/code/include/CGAL/Discrete_circle_packing.h index 3942e76..e774262 100644 --- a/code/include/CGAL/Discrete_circle_packing.h +++ b/code/include/CGAL/Discrete_circle_packing.h @@ -8,7 +8,7 @@ \ingroup PkgConformalMapRef User-facing entry for the **face-based** circle-packing functional of -Bobenko-Pinkall-Springborn 2010. See `cp_euclidean_functional.hpp` +Bobenko-Pinkall-Springborn 2015. See `cp_euclidean_functional.hpp` for the underlying algorithm and `doc/architecture/phase-9a-validation.md` for the line-by-line mapping to the Java original `CPEuclideanFunctional.java`. @@ -44,7 +44,7 @@ namespace CGAL { \ingroup PkgConformalMapConcepts \brief Traits class for `discrete_circle_packing_euclidean()` — declares the kernel, mesh and property-map types used by the -BPS-2010 face-based circle-packing functional. +BPS-2015 face-based circle-packing functional. Primary template; specialise it for non-`Surface_mesh` triangle meshes. */ @@ -115,7 +115,7 @@ struct Circle_packing_result /*! \ingroup PkgConformalMapRef -Compute the BPS-2010 face-based circle-packing of `mesh`. +Compute the BPS-2015 face-based circle-packing of `mesh`. \tparam TriangleMesh A `CGAL::Surface_mesh

`. \tparam NamedParameters Optional CGAL named-parameter pack. @@ -132,7 +132,7 @@ Compute the BPS-2010 face-based circle-packing of `mesh`. \returns A `Circle_packing_result` with `ρ_f` per face. \pre `mesh` is a triangle mesh. -\pre `φ_f` and `θ_e` satisfy the BPS-2010 admissibility conditions +\pre `φ_f` and `θ_e` satisfy the BPS-2015 admissibility conditions (Σ_f φ_f = 2π·χ + Σ_e (π − θ_e), see paper §6). */ template /*! \ingroup PkgConformalMapRef -Compute the Luo-2004 vertex-based inversive-distance circle packing of `mesh`. +Compute the Luo 2004 vertex-based inversive-distance circle packing of `mesh`. The per-edge constant `I_ij` is computed once at the start from the input 3-D geometry via the Bowers-Stephenson identity diff --git a/code/include/cp_euclidean_functional.hpp b/code/include/cp_euclidean_functional.hpp index 8267591..f39998f 100644 --- a/code/include/cp_euclidean_functional.hpp +++ b/code/include/cp_euclidean_functional.hpp @@ -19,7 +19,7 @@ // │ The variable is ρ_f = log R_f. │ // │ Adjacent face-circles intersect at a prescribed angle θ_e per edge. │ // │ │ -// │ This is the FACE-DUAL of the classical vertex-based Luo (2004) │ +// │ This is the FACE-DUAL of the classical vertex-based Luo 2004 │ // │ inversive-distance circle packing implemented in │ // │ inversive_distance_functional.hpp (Phase 9a.2). The relation │ // │ I_ij = cos θ_e │ @@ -33,7 +33,7 @@ // │ θ_e per edge intersection angle of the two face-circles │ // │ φ_f per face target sum of corner-angles inside the face │ // │ │ -// │ Energy (BPS-2010 §6) │ +// │ Energy (BPS-2015 §6) │ // │ E(ρ) = Σ_f φ_f · ρ_f │ // │ + Σ_{(h,f=face(h)): │ // │ [ if opposite face exists ] │ @@ -52,7 +52,7 @@ // │ Per interior hf: −(p + θ*) added to G[face(h)] │ // │ Per boundary hf: −2 θ* added to G[face(h)] │ // │ │ -// │ Hessian (analytic, BPS-2010 eq. 6.8; Java getHessian lines 127-166) │ +// │ Hessian (analytic, BPS-2015 eq. 6.8; Java getHessian lines 127-166) │ // │ Per interior undirected edge e (connecting faces j and k): │ // │ h_jk = sin θ / (cosh Δρ − cos θ) │ // │ H[j,j] += h_jk, H[k,k] += h_jk, H[j,k] −= h_jk, H[k,j] −= h_jk │ @@ -90,7 +90,7 @@ using CPEMapD = ConformalMesh::Property_map; // ── Persistent map bundle ───────────────────────────────────────────────────── /// Bundle of the three property maps consumed by the CP-Euclidean -/// (Bobenko-Pinkall-Springborn 2010) circle-packing functional. +/// (Bobenko-Pinkall-Springborn 2015) circle-packing functional. struct CPEuclideanMaps { CPFMapI f_idx; ///< DOF index per face (−1 = pinned) CPEMapD theta_e; ///< intersection angle per edge (default π/2 = orthogonal) diff --git a/code/include/newton_solver.hpp b/code/include/newton_solver.hpp index 6252586..da2efe3 100644 --- a/code/include/newton_solver.hpp +++ b/code/include/newton_solver.hpp @@ -465,7 +465,7 @@ inline NewtonResult newton_hyper_ideal( /// Solve the CP-Euclidean circle-packing problem: find ρ ∈ ℝ^F such that the /// per-face angle sums match φ_f at every free face. /// -/// The CP-Euclidean energy (Bobenko-Pinkall-Springborn 2010 §6) is strictly +/// The CP-Euclidean energy (Bobenko-Pinkall-Springborn 2015 §6) is strictly /// convex on its open domain of validity, so the Hessian H is PSD and the /// solution is unique up to the gauge mode pinned by `f_idx == −1`. /// `cp_euclidean_hessian` provides the analytic 2×2-per-edge formula @@ -483,7 +483,7 @@ inline NewtonResult newton_hyper_ideal( /// \note Unlike the Euclidean solver, the CP-Euclidean Hessian is exact /// (analytic), so the SparseQR fallback only triggers in genuine /// gauge-singular situations (no pinned face). -/// \see doc/architecture/phase-9a-validation.md §1 for the BPS-2010 mapping. +/// \see doc/architecture/phase-9a-validation.md §1 for the BPS-2015 mapping. inline NewtonResult newton_cp_euclidean( ConformalMesh& mesh, std::vector x0, diff --git a/doc/math/references.md b/doc/math/references.md index 8ca8e0b..ce90980 100644 --- a/doc/math/references.md +++ b/doc/math/references.md @@ -29,12 +29,14 @@ Java reference implementation: [github.com/varylab/conformallab](https://github. | Reference | Used in | |---|---| | ✅ **Springborn** — *Ideal Hyperbolic Polyhedra and Discrete Uniformization*, Discrete & Computational Geometry **64** (2020), pp. 63–108. DOI: [10.1007/s00454-019-00132-8](https://doi.org/10.1007/s00454-019-00132-8) | `hyper_ideal_geometry.hpp` — ζ₁₃/ζ₁₄/ζ₁₅ functions; `hyper_ideal_functional.hpp` | +| ✅ **Kolpakov, Mednykh** — *A Formula for the Volume of a Hyperbolic Tetrahedron*, arXiv: [math/0603097](https://arxiv.org/abs/math/0603097) (2006) | Tetrahedron volume with one ideal vertex: `calculateTetrahedronVolumeWithIdealVertexAtGamma` in `hyper_ideal_utility.hpp` (Phase 9b analytic Hessian) | +| ✅ **Meyerhoff, Ushijima** — *A Note on the Dirichlet Domain*, in: The Epstein Birthday Schrift (2006) | Tetrahedron volume with three ideal vertices: `calculateTetrahedronVolumeFullyIdeal` in `hyper_ideal_utility.hpp` | | **Pinkall, Polthier** — *Computing Discrete Minimal Surfaces and Their Conjugates*, Experimental Mathematics (1993) | `euclidean_hessian.hpp` — cotangent Laplacian | | **Bobenko, Springborn** — *Variational Principles for Circle Patterns and Koebe's Theorem*, Transactions AMS (2004) | Variational angle-sum framework underlying all three functionals | | **Luo** — *Combinatorial Yamabe Flow on Surfaces*, Communications in Contemporary Mathematics (2004) | Inversive-distance functional — **new research** in Phase 9a.2 (no Java original; implemented from this paper + Glickenstein 2011 + Bowers-Stephenson 2004) | | **Bowers, Stephenson** — *Uniformizing dessins and Belyĭ maps via circle packing*, Memoirs of the AMS 170(805) (2004) | Introduces **inversive-distance circle packings** (used in Phase 9a.2). *Hinweis:* die zur Initialisierung benutzte Formel I_ij = (ℓ²−r_i²−r_j²)/(2 r_i r_j) ist die **klassische** inversive Distanz (vgl. Glickenstein §5.2: ℓ²=r_i²+r_j²+2r_ir_jη), nicht eine eigene „Bowers-Stephenson-Identität" — B–S liefern die Packungstheorie, nicht diese Formel. | | **Glickenstein** — *Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds*, J. Differential Geometry **87**(2) (2011), pp. 201–238 | Analytic Hessian of the inversive-distance functional. ⚠️ *Korrektur:* die Arbeit nummeriert Gleichungen **nicht** im Format „(4.6)" — der Verweis ist durch die **§5.2**-Parametrisierung ℓ²_ij = r²_i + r²_j + 2 r_i r_j η_ij zu ersetzen. Cross-correspondence: η_ij ist die inversive Distanz und entspricht dem Kosinus des **Supplements** des Schnittwinkels (Schnitt bei arccos(−η_ij)) — also I_ij = cos θ_e **nur bis aufs Vorzeichen/Supplement**, nicht wörtlich. | -| **Bobenko, Pinkall, Springborn** — *Discrete conformal maps and ideal hyperbolic polyhedra*, Geometry & Topology **19**(4) (2015), pp. 2155–2215. arXiv: [1005.2698](https://arxiv.org/abs/1005.2698) | Face-based circle-packing functional (`CPEuclideanFunctional.java` → `cp_euclidean_functional.hpp`, Phase 9a.1) | +| ✅ **Bobenko, Pinkall, Springborn** — *Discrete conformal maps and ideal hyperbolic polyhedra*, Geometry & Topology **19**(4) (2015), pp. 2155–2215. arXiv: [1005.2698](https://arxiv.org/abs/1005.2698) (first posted 2010) | Face-based circle-packing functional (`CPEuclideanFunctional.java` → `cp_euclidean_functional.hpp`, Phase 9a.1) | | **Schläfli** — *On the multiple integral ∫dx dy …*, Quarterly Journal of Pure and Applied Mathematics (1858/60) | Klassische Schläfli-Differentialformel (dV = −½ Σ_e ℓ_e dθ_e). ⚠️ *Hinweis:* die in Phase 9b-analytic benutzte **Randterm-Form** `2 dV = Σ_e aₑ dαₑ + Σ_v bᵥ dβᵥ` steht **nicht** bei Schläfli 1858, sondern ist die verallgemeinerte Fassung für Mannigfaltigkeiten mit Rand → korrekter Beleg: **Rivin–Schlenker 1999** (Phase-10-Liste). Schläfli 1858 nur als historischer Ursprung zitieren. | | **Erickson, Whittlesey** — *Greedy Optimal Homotopy and Homology Generators*, SODA (2005) | `cut_graph.hpp` — tree-cotree algorithm | | **Bobenko, Springborn** — *A Discrete Laplace–Beltrami Operator for Simplicial Surfaces*, Discrete & Computational Geometry (2007) | Background for cotangent weights |