e958afbd19
Unified the codebase language to English throughout. German text appeared in code comments, test file headers, CI step names, and several markdown documents. All natural-language text is now English; proper nouns (Institut für Mathematik, Technische Universität Berlin) are unchanged. Files changed: - .gitea/workflows/cpp-tests.yml — CI step names and job comments - code/include/mesh_utils.hpp — inline comment - code/tests/cgal/CMakeLists.txt — section comment block - code/tests/cgal/test_geometry_utils.cpp — full file header + all test comments - doc/math/references.md — geometry-central section - doc/math/validation.md — Section 9 (geometry-central cross-validation) - doc/roadmap/phases.md — Optional geometry-central track (GC-1/2/3) 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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> These references relate to an alternative implementation of the same
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> mathematical problem. They are not prerequisites for conformallab++,
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> but are relevant for cross-validation and possible algorithmic adoptions
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> (→ GC-1/2/3 in the phase roadmap, → Section 9 in `validation.md`).
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| Reference | Relevance |
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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) | Implemented in **geometry-central**. Extends Springborn 2020 with intrinsic triangulations and Ptolemaic flips. Solves the same DCE problem as conformallab++, but with a different algorithm. |
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| **Sharp, Soliman, Crane** — *Navigating Intrinsic Triangulations*, ACM SIGGRAPH 2019 | Algorithmic basis for `SignpostIntrinsicTriangulation` in geometry-central — relevant for GC-2 (optional pre-conditioning). |
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**Note on Springborn 2020:**
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The paper *"Ideal Hyperbolic Polyhedra and Discrete Uniformization"*
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(Springborn, Discrete & Computational Geometry 2020) is **already implemented in
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conformallab++** — it is the direct reference for the HyperIdeal geometry mode
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(`hyper_ideal_geometry.hpp`). The geometry-central implementation (Gillespie 2021)
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builds on this paper and augments it with Ptolemaic 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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