d25f3cafe6
- phases.md: neue Sektion "Optional/Hypothetisch — geometry-central Cross-Comparison" mit GC-1 (Output-Vergleich, sofort möglich), GC-2 (Intrinsic Delaunay Pre-Conditioning, nach Phase 8) und GC-3 (Ptolemäischer Flip-Solver, hypothetisch Phase 10+) - validation.md: neuer Abschnitt 9 mit Vergleichstabelle, Normalisierungs- abgleich, Zeitplan und Springborn-2020-Einordnung - references.md: Gillespie–Springborn–Crane SIGGRAPH 2021 + Sharp 2019 als geometry-central-Referenzen eingetragen; Klarstellung zu Springborn 2020 - validation.md: Testzähler 170→173 / 11 skips→1 skip korrigiert Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
57 lines
3.8 KiB
Markdown
57 lines
3.8 KiB
Markdown
# References
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## Primary source
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This library implements the algorithms from:
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| **Sechelmann** — *Variational Methods for Discrete Surface Parameterization: Applications and Implementation*, Doctoral thesis, TU Berlin 2016 | The complete mathematical foundation: discrete conformal equivalence, variational angle-sum functionals, Newton solver, uniformization, period matrices, holonomy. DOI: [10.14279/depositonce-5415](https://depositonce.tu-berlin.de/items/8e2988b2-d991-45b5-aad5-9fb7988f3b2f) · CC BY-SA 4.0 |
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Java reference implementation: [github.com/varylab/conformallab](https://github.com/varylab/conformallab)
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---
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## References by module
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| Reference | Used in |
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| **Springborn** — *Ideal Hyperbolic Polyhedra and Discrete Uniformization*, Discrete & Computational Geometry (2020) | `hyper_ideal_geometry.hpp` — ζ₁₃/ζ₁₄/ζ₁₅ functions; `hyper_ideal_functional.hpp` |
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| **Pinkall, Polthier** — *Computing Discrete Minimal Surfaces and Their Conjugates*, Experimental Mathematics (1993) | `euclidean_hessian.hpp` — cotangent Laplacian |
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| **Bobenko, Springborn** — *Variational Principles for Circle Patterns and Koebe's Theorem*, Transactions AMS (2004) | Variational angle-sum framework underlying all three functionals |
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| **Luo** — *Combinatorial Yamabe Flow on Surfaces*, Communications in Contemporary Mathematics (2004) | Inversive-distance functional — **not yet ported**, Phase 9a |
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| **Erickson, Whittlesey** — *Greedy Optimal Homotopy and Homology Generators*, SODA (2005) | `cut_graph.hpp` — tree-cotree algorithm |
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| **Bobenko, Springborn** — *A Discrete Laplace–Beltrami Operator for Simplicial Surfaces*, Discrete & Computational Geometry (2007) | Background for cotangent weights |
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| **Desbrun, Kanso, Tong** — *Discrete Differential Forms for Computational Modeling*, SIGGRAPH Course Notes (2006) | Discrete exterior calculus background for Phase 10a |
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---
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## geometry-central cross-reference *(optional comparison track)*
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> Diese Referenzen beziehen sich auf eine alternative Implementierung desselben
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> mathematischen Problems. Sie sind keine Voraussetzung für conformallab++,
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> aber relevant für Kreuz-Validierung und mögliche algorithmische Adoptionen
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> (→ GC-1/2/3 im Phasen-Roadmap, → Abschnitt 9 in `validation.md`).
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| Reference | Relevanz |
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| **Gillespie, Springborn, Crane** — *Discrete Conformal Equivalence of Polyhedral Surfaces*, ACM SIGGRAPH 2021. DOI: [10.1145/3450626.3459763](https://doi.org/10.1145/3450626.3459763) | Implementiert in **geometry-central**. Erweitert Springborn 2020 um intrinsische Triangulierungen und Ptolemäische Flips. Löst dasselbe DCE-Problem wie conformallab++, aber mit anderem Algorithmus. |
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| **Sharp, Soliman, Crane** — *Navigating Intrinsic Triangulations*, ACM SIGGRAPH 2019 | Algorithmische Grundlage für `SignpostIntrinsicTriangulation` in geometry-central — relevant für GC-2 (optionales Pre-Conditioning). |
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**Hinweis zu Springborn 2020:**
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Das Papier *"Ideal Hyperbolic Polyhedra and Discrete Uniformization"*
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(Springborn, Discrete & Computational Geometry 2020) ist **in conformallab++
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bereits implementiert** — es ist die direkte Referenz für den HyperIdeal-Geometriemodus
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(`hyper_ideal_geometry.hpp`). Die geometry-central Implementierung (Gillespie 2021)
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baut auf diesem Papier auf und ergänzt es um Ptolemäische Flips.
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---
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## Phase 10 references (future research)
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| Reference | Relevant for |
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| **Farkas, Kra** — *Riemann Surfaces*, Springer GTM 71 | Siegel period matrix, Teichmüller theory |
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| **Siegel** — *Topics in Complex Function Theory, Vol. 2*, Wiley | Siegel upper half-space H_g, Sp(2g,ℤ) reduction |
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| **Bobenko, Mercat, Schmies** — *Period Matrices of Polyhedral Surfaces*, in: Computational Approach to Riemann Surfaces (2011) | Discrete period matrices on polyhedral surfaces |
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