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>
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References
Primary source
This library implements the algorithms from:
| 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 · CC BY-SA 4.0 |
Java reference implementation: github.com/varylab/conformallab
References by module
| Reference | Used in |
|---|---|
| Springborn — Ideal Hyperbolic Polyhedra and Discrete Uniformization, Discrete & Computational Geometry (2020) | hyper_ideal_geometry.hpp — ζ₁₃/ζ₁₄/ζ₁₅ functions; hyper_ideal_functional.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 — not yet ported, Phase 9a |
| 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 |
geometry-central cross-reference (optional comparison track)
These references relate to an alternative implementation of the same mathematical problem. They are not prerequisites for conformallab++, but are relevant for cross-validation and possible algorithmic adoptions (→ GC-1/2/3 in the phase roadmap, → Section 9 in
validation.md).
| Reference | Relevance |
|---|---|
| Gillespie, Springborn, Crane — Discrete Conformal Equivalence of Polyhedral Surfaces, ACM SIGGRAPH 2021. DOI: 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. |
| Sharp, Soliman, Crane — Navigating Intrinsic Triangulations, ACM SIGGRAPH 2019 | Algorithmic basis for SignpostIntrinsicTriangulation in geometry-central — relevant for GC-2 (optional pre-conditioning). |
Note on Springborn 2020:
The paper "Ideal Hyperbolic Polyhedra and Discrete Uniformization"
(Springborn, Discrete & Computational Geometry 2020) is already implemented in
conformallab++ — it is the direct reference for the HyperIdeal geometry mode
(hyper_ideal_geometry.hpp). The geometry-central implementation (Gillespie 2021)
builds on this paper and augments it with Ptolemaic flips.
Phase 10 references (future research)
| Reference | Relevant for |
|---|---|
| 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 |