docs: integrate publication analysis — Alexa, Bobenko, Springborn, Crane, Lutz
Add phases 9d / 9e / 9f and literature citations derived from a systematic
review of the five authors' publication lists (Tier 1 / 2 / 3 analysis).
phases.md:
- Phase 9d: ConesUtility port (9d.1) + non-Euclidean cone extensions
(9d.2, RESEARCH) + StereographicUnwrapper (9d.3)
- Phase 9e: CirclePatternLayout + CirclePatternUtility (Java port)
- Phase 9f: Polygon Laplacian on non-triangular meshes (Alexa 2011/2020,
RESEARCH — no Java equivalent)
- Phase 9b-analytic: add Rivin-Springborn 1999 as Schläfli source
- Phase 10b: add Bobenko-Bücking 2009 + Bobenko-Lutz 2024 IMRN
- Phase 10c: add Lutz 2023 (canonical tessellations) + Bobenko-Lutz 2024
- Phase 10c' KoebePolyhedron: add Bowers-Bowers-Lutz 2026 rigidity result
references.md:
- Crane et al. 2018 Optimal Cone Singularities (Phase 9d.2)
- Bobenko-Lutz 2025 Discrete & Comput. Geom. (Phase 9d.2)
- Bobenko-Lutz 2024 IMRN (Phase 10b/c)
- Lutz 2023 Geom. Dedicata (Phase 10c)
- Lutz PhD thesis TU Berlin 2024 (Phases 9d.2, 10b, 10c)
- Bowers-Bowers-Lutz 2026 (Phase 9b-analytic + 10c')
- Alexa-Wardetzky 2011 + Alexa 2020 (Phase 9f)
- Bobenko-Bücking 2009 (Phase 10b)
- Rivin-Springborn 1999 (Phase 9b-analytic)
research-track.md:
- New entry: Phase 9d.2 non-Euclidean cone extensions (Bobenko-Lutz 2025
+ Crane 2018), with acceptance criteria
- New entry: Phase 9f polygon Laplacian (Alexa-Wardetzky 2011 / Alexa 2020),
with acceptance criteria
java-parity.md:
- Split cone-metrics row into Euclidean (9d.1 port) and non-Euclidean
(9d.2 research) with literature references
- Add ConesUtility to "utility classes not yet ported" table
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
Tarik Moussa
@@ -109,6 +109,8 @@ mesh type.
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9b-analytic Full analytic HyperIdeal Hessian via Schläfli identity
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→ planned, see research-track.md
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Mathematical source: Springborn 2020 §4 + Schläfli 1858/60
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+ Rivin, Springborn 1999 "The Schläfli formula in
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Einstein manifolds with boundary" (ERA-AMS 5)
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+ Cho-Kim 1999 + Glickenstein 2011 §4
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Algorithm: explicit chain rule through (bᵢ,aₑ) → ℓᵢⱼ → ζ₁₃/ζ₁₄/ζ₁₅ → αᵢⱼ/βᵢ
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Includes: short LaTeX correctness note in doc/math/.
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@@ -127,6 +129,69 @@ mesh type.
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+ holonomy infrastructure.
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Effort: ~2 weeks for fundamental polygon, +2 weeks for surgery
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layer, +1 week integration.
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9d — Cone singularities + sphere atlas (Java port + research extension)
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────────────────────────────────────────────────────────────────────────
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9d.1 ConesUtility (Java port — Euclidean only)
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→ cones_utility.hpp
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Java source: ConesUtility.java (~200 lines)
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Mathematical reference: Troyanov 1991 + Springborn 2020 §3
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Port scope: prescribed cone angles Θᵥ ≠ 2π in Euclidean mode.
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Status: 🔲 planned
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9d.2 Non-Euclidean cone extensions (RESEARCH, not in Java)
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→ extend ConesUtility to HyperIdeal + Spherical modes
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Java source: NONE — Java ConesUtility is Euclidean-only.
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Mathematical reference:
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Bobenko, Lutz 2025 "Decorated Discrete Conformal Equivalence in
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Non-Euclidean Geometries" (Discrete & Comput. Geom. 2025,
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arXiv:2310.17529) §3 — decorated DCE framework unifying cone
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singularities and cusps in hyperbolic + spherical geometry.
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Crane, Soliman, Ben-Chen, Schröder 2018 "Optimal Cone Singularities
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for Conformal Flattening" (ACM SIGGRAPH 2018) — L¹-optimal
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automatic cone placement; directly applicable to 9d.2 algorithm.
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Status: 🔲 planned
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9d.3 StereographicUnwrapper (Java port)
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→ stereo_unwrapper.hpp
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Java source: StereographicUnwrapper.java (266 lines)
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Converts spherical DCE output (Point_3 on S²) to a 2-D atlas
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via stereographic projection + Möbius centring.
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Closes the visualisation gap from discrete_conformal_map_spherical().
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Effort: small (~3 days).
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Status: 🔲 planned
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9e — CirclePatternLayout (Java port)
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─────────────────────────────────────
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9e CirclePatternLayout + CirclePatternUtility (Java port)
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→ circle_pattern_layout.hpp
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Java sources: CirclePatternLayout.java + CirclePatternUtility.java
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+ CPEuclideanRotation.java
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Mathematical reference: Bobenko-Springborn 2004 variational principle
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+ Bobenko-Hoffmann-Springborn 2006 "Minimal
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surfaces from circle patterns" (Discrete &
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Comput. Geom. 35, 2006).
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Status: 🔲 planned
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9f — Polygon Laplacian (RESEARCH — no Java equivalent)
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──────────────────────────────────────────────────────
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9f Discrete Laplacian on general polygonal meshes
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→ polygon_laplacian.hpp
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Java source: NONE
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Mathematical reference:
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Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
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Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
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polygon cotangent weights extending the Pinkall-Polthier formula.
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Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
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(ACM TOG 39, 2020) — extended journal treatment, error bounds.
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Enables: DCE energy evaluation on quad-dominant / Voronoi /
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polygon meshes without forced triangulation.
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Replaces euclidean_hessian.hpp for non-triangular inputs.
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Status: 🔲 planned (pure research, no Java source)
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Effort: medium (~2 weeks core + tests; +1 week Newton integration).
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```
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9d — Cone metrics + sphere utilities (Java port — 2026 library scan)
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@@ -295,6 +360,13 @@ Phase 10 Global uniformization for genus g ≥ 2
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→ Ωᵢⱼ = ∫_{bⱼ} ωᵢ
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→ Reduction to Siegel fundamental domain via Sp(2g,ℤ).
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Mathematical reference: Bobenko-Springborn 2004 + Gottschling 1959.
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Bobenko, Bücking 2009 "Conformal Structures and
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Period Matrices of Polyhedral Surfaces" — discrete
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period matrix Ωᵢⱼ on polyhedral surfaces.
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Bobenko, Lutz 2024 IMRN "Decorated Discrete Conformal
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Maps and Convex Polyhedral Cusps" — uniformization
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theorem connecting cusps ↔ hyperideal vertices
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(bridges Phase 2/3 HyperIdeal geometry to 10b).
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Java partial reference: DiscreteRiemannUtility.java (186 lines).
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Requires: 10a.
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Effort: ~1 week net after 10a.
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@@ -318,6 +390,14 @@ Phase 10 Global uniformization for genus g ≥ 2
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→ Embedding as H²/Γ with Γ ⊂ PSL(2,ℝ) a Fuchsian group.
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Mathematical reference: Sechelmann 2016 §6 (discrete instance);
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Bers 1960 (continuous theory).
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Lutz 2023 "Canonical Tessellations of Decorated
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Hyperbolic Surfaces" (Geom. Dedicata 217,
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arXiv:2206.13461) — canonical Delaunay tessellations
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in Penner coordinates; unifies the decorated
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framework with the fundamental domain construction.
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Bobenko, Lutz 2024 IMRN (arXiv:2305.10988) —
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discrete uniformization theorem for decorated
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piecewise Euclidean surfaces.
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Java reference: NONE — Java has the polygon + period matrix
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pieces but does not assemble them into
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a Fuchsian-group representation.
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@@ -327,6 +407,9 @@ Phase 10 Global uniformization for genus g ≥ 2
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10c' Optional Java-port additions (low priority)
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→ KoebePolyhedron.java (321 lines) — Koebe-Andreev-Thurston
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circle packings. Adds a fifth DCE method.
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Rigidity: Bowers, Bowers, Lutz 2026 "Rigidity of circle polyhedra
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and hyperideal polyhedra: the tangency case" (arXiv:2601.22903)
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— theoretical uniqueness backing the KAT construction.
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→ ElectrostaticSphereFunctional (127 lines) — sphere
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distribution baseline.
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→ CirclePatternLayout / CirclePatternUtility — face-circle
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