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

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>
This commit is contained in:
Tarik Moussa
2026-05-25 23:59:47 +02:00
parent 068df474b1
commit ab07f90653
2 changed files with 20 additions and 0 deletions

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@@ -348,6 +348,12 @@ Phase 10 Global uniformization for genus g ≥ 2
10a Discrete holomorphic and harmonic 1-forms
→ Integrate basis 1-forms ωᵢ along b-cycles of the cut graph.
Mathematical reference: Bobenko-Springborn 2004 §6 + Mercat 2001.
Knöppel, Crane, Pinkall, Schröder 2015 "Stripe
Patterns on Surfaces" (ACM SIGGRAPH 2015) —
application of discrete holomorphic 1-forms to
direction field design; provides an independent
C++ reference implementation (geometry-central)
for cross-validating the Phase 10a computation.
Java sources (partial, port-with-research):
CanonicalBasisUtility.java 337 lines (homology basis)
HomologyUtility.java 122 lines
@@ -367,6 +373,10 @@ Phase 10 Global uniformization for genus g ≥ 2
Maps and Convex Polyhedral Cusps" — uniformization
theorem connecting cusps ↔ hyperideal vertices
(bridges Phase 2/3 HyperIdeal geometry to 10b).
Springborn 2019 "A discrete version of Liouville's
theorem on conformal maps" (arXiv:1911.00966) —
proves uniqueness/rigidity of the discrete conformal
structure; justifies that Ω is a conformal invariant.
Java partial reference: DiscreteRiemannUtility.java (186 lines).
Requires: 10a.
Effort: ~1 week net after 10a.
@@ -398,6 +408,12 @@ Phase 10 Global uniformization for genus g ≥ 2
Bobenko, Lutz 2024 IMRN (arXiv:2305.10988) —
discrete uniformization theorem for decorated
piecewise Euclidean surfaces.
Springborn, Veselov 2015 "Quasiconformal distortion
of projective transformations and discrete conformal
maps" (Int. Math. Res. Not.) — error estimates for
the discrete-to-smooth conformal approximation;
quantifies how well H²/Γ approximates the smooth
hyperbolic metric.
Java reference: NONE — Java has the polygon + period matrix
pieces but does not assemble them into
a Fuchsian-group representation.