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docs: integrate publication analysis — Alexa, Bobenko, Springborn, Crane, Lutz

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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>
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Tarik Moussa
2026-05-25 23:51:26 +02:00
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@@ -27,6 +27,14 @@ Java reference implementation: [github.com/varylab/conformallab](https://github.
| **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 |
| **Desbrun, Kanso, Tong** — *Discrete Differential Forms for Computational Modeling*, SIGGRAPH Course Notes (2006) | Discrete exterior calculus background for Phase 10a |
| **Crane, Soliman, Ben-Chen, Schröder** — *Optimal Cone Singularities for Conformal Flattening*, ACM SIGGRAPH (2018). DOI: [10.1145/3197517.3201367](https://doi.org/10.1145/3197517.3201367) | L¹-optimal automatic cone placement — **Phase 9d.2** (non-Euclidean cone extensions). Provides the optimisation algorithm for choosing cone positions automatically; complements Bobenko-Lutz 2025 on non-Euclidean settings. |
| **Bobenko, Lutz** — *Decorated Discrete Conformal Equivalence in Non-Euclidean Geometries*, Discrete & Computational Geometry (2025). arXiv: [2310.17529](https://arxiv.org/abs/2310.17529) | **Phase 9d.2**: extends DCE to hyperbolic + spherical geometry with Penner-coordinate decorations; unifies cone singularities and hyperideal cusps in one algebraic framework. |
| **Bobenko, Lutz** — *Decorated Discrete Conformal Maps and Convex Polyhedral Cusps*, IMRN 2024(12), pp. 9505–9534. arXiv: [2305.10988](https://arxiv.org/abs/2305.10988) | **Phase 10b/10c**: discrete uniformization theorem for decorated piecewise Euclidean surfaces; connects Phase 2/3 hyperideal vertices (cusps at ∞) to the period matrix and fundamental domain. |
| **Lutz** — *Canonical Tessellations of Decorated Hyperbolic Surfaces*, Geometriae Dedicata 217 (2023). arXiv: [2206.13461](https://arxiv.org/abs/2206.13461) | **Phase 10c**: canonical Delaunay tessellations in Penner coordinates; unifies the decorated framework with the fundamental domain construction for genus g ≥ 2. |
| **Lutz** — *Decorated Discrete Conformal Equivalence, Canonical Tessellations, and Polyhedral Realization* (PhD thesis, TU Berlin, 2024). DOI: [10.14279/depositonce-20357](https://doi.org/10.14279/depositonce-20357) | Comprehensive single reference for Phases 9d.2, 10b, 10c — collects Bobenko-Lutz 2024/2025 and Lutz 2023 with complete proofs. |
| **Bowers, Bowers, Lutz** — *Rigidity of circle polyhedra and hyperideal polyhedra: the tangency case* (2026). arXiv: [2601.22903](https://arxiv.org/abs/2601.22903) | **Phase 9b-analytic + Phase 10c'** (KoebePolyhedron): theoretical uniqueness/rigidity for hyperideal polyhedra in the tangency case; supports correctness of the analytic Hessian and the KAT construction. |
| **Alexa, Wardetzky** — *Discrete Laplacians on General Polygonal Meshes*, ACM SIGGRAPH (2011). DOI: [10.1145/1964921.1964997](https://doi.org/10.1145/1964921.1964997) | **Phase 9f**: virtual-node polygon Laplacian extending Pinkall-Polthier to non-triangular meshes. Enables DCE on quad/Voronoi meshes without triangulation. |
| **Alexa** — *Discrete Laplacians on General Polygonal Meshes*, ACM TOG 39(6) (2020). DOI: [10.1145/3414685.3417840](https://doi.org/10.1145/3414685.3417840) | **Phase 9f** (extended journal version): error bounds, generalised polygon cotangent weights, convergence analysis. |
---
@@ -58,3 +66,5 @@ builds on this paper and augments it with Ptolemaic flips.
| **Farkas, Kra** — *Riemann Surfaces*, Springer GTM 71 | Siegel period matrix, Teichmüller theory |
| **Siegel** — *Topics in Complex Function Theory, Vol. 2*, Wiley | Siegel upper half-space H_g, Sp(2g,ℤ) reduction |
| **Bobenko, Mercat, Schmies** — *Period Matrices of Polyhedral Surfaces*, in: Computational Approach to Riemann Surfaces (2011) | Discrete period matrices on polyhedral surfaces |
| **Bobenko, Bücking** — *Conformal Structures and Period Matrices of Polyhedral Surfaces* (2009) | Phase 10b: explicit algorithm for computing the discrete Siegel period matrix Ωᵢⱼ on a polyhedral surface from cotangent-weighted integration. |
| **Rivin, Springborn** — *The Schläfli formula in Einstein manifolds with boundary*, Electron. Res. Announc. AMS 5 (1999) | Phase 9b-analytic: modern form of the Schläfli identity `2 dV = Σ aₑ dαₑ` for manifolds with boundary — the bilinear form used to derive the analytic HyperIdeal Hessian. |