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docs: add 4 remaining Tier-2 papers (Springborn 2019, Springborn-Veselov 2015, Crane 2017 BFF, Stripe Patterns 2015)

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phases.md:
  - 10b: Springborn 2019 discrete Liouville theorem (uniqueness of Ω)
  - 10c: Springborn-Veselov 2015 quasiconformal distortion (error bounds)
  - 10a: Knöppel-Crane-Pinkall-Schröder 2015 Stripe Patterns (cross-validation ref)

references.md (Phase 10 section, 4 new rows):
  - Springborn 2019 arXiv:1911.00966 → Phase 10b uniqueness
  - Springborn-Veselov 2015 Int. Math. Res. Not. → Phase 10c error analysis
  - Knöppel-Crane-Pinkall-Schröder 2015 SIGGRAPH → Phase 10a cross-validation
  - Sawhney-Crane 2017 BFF ACM TOG → complementary method to Phase 9d

Completes the literature integration started in the previous commit:
all Tier-2 papers from the Alexa/Bobenko/Springborn/Crane/Lutz analysis
are now documented in the roadmap.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Tarik Moussa
2026-05-25 23:59:47 +02:00
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@@ -68,3 +68,7 @@ builds on this paper and augments it with Ptolemaic flips.
| **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. |
| **Springborn** — *A discrete version of Liouville's theorem on conformal maps* (2019). arXiv: [1911.00966](https://arxiv.org/abs/1911.00966) | Phase 10b uniqueness: proves that the discrete conformal structure (and hence Ω) is a conformal invariant — the discrete Liouville theorem. Justifies that conformallab++ outputs a canonical representative. |
| **Springborn, Veselov** — *Quasiconformal distortion of projective transformations and discrete conformal maps*, Int. Math. Res. Not. (2015) | Phase 10c error analysis: quantifies how well the discrete H²/Γ embedding approximates the smooth hyperbolic metric; error bounds for the Fuchsian group representation. |
| **Knöppel, Crane, Pinkall, Schröder** — *Stripe Patterns on Surfaces*, ACM SIGGRAPH (2015). DOI: [10.1145/2766890](https://doi.org/10.1145/2766890) | Phase 10a cross-validation: applies discrete holomorphic 1-forms to direction field design; geometry-central provides an independent C++ implementation to cross-check the Phase 10a `DiscreteHolomorphicFormUtility` port. |
| **Sawhney, Crane** — *Boundary First Flattening*, ACM TOG 36(1) (2017). DOI: [10.1145/3132705](https://doi.org/10.1145/3132705) | Complementary method to Phase 9d: boundary-prescribed conformal flattening — user specifies boundary shape, interior conforms freely. Contrast: conformallab++ prescribes cone angles in the interior; BFF prescribes the boundary. Alternative approach for applications needing controlled boundary. |