docs: fix cherry-pick duplicate 9d/9e sections — merge into unified structure
Auto-merge from cherry-pick concatenated both branch versions of Phase 9d
and 9e. This commit resolves the duplication:
- 9d now has 4 sub-items (9d.1–9d.4) combining both branches:
9d.1 ConesUtility (detailed: BFS, auto-placement, quantization)
+ Troyanov/Springborn refs (from literature analysis)
9d.2 Non-Euclidean cone extensions (RESEARCH)
+ Bobenko-Lutz 2025 + Crane 2018 (from literature analysis)
9d.3 StereographicUnwrapper + SphereUtility
9d.4 MobiusCenteringFunctional
- 9e keeps the detailed reviewer/meeting-prep version
+ adds mathematical references (Bobenko-Hoffmann-Springborn 2006)
- 9f (Polygon Laplacian, Alexa 2011/2020) retained as standalone section
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
Tarik Moussa
@@ -129,16 +129,22 @@ mesh type.
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+ holonomy infrastructure.
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Effort: ~2 weeks for fundamental polygon, +2 weeks for surgery
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layer, +1 week integration.
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```
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9d — Cone singularities + sphere atlas (Java port + research extension)
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────────────────────────────────────────────────────────────────────────
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9d — Cone metrics + sphere utilities (Java port + research extension)
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────────────────────────────────────────────────────────────────────
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9d.1 ConesUtility (Java port — Euclidean only)
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→ cones_utility.hpp
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Java source: ConesUtility.java (~200 lines)
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```
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9d.1 ConesUtility (Java port: unwrapper/ConesUtility.java)
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→ cone_singularities.hpp
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Fills the "⚠️ data structure only" gap in java-parity.md:
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- Detect interior cone vertices (angle deficit ≠ 0)
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- BFS path from cone to mesh boundary → cut edge set
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- Auto-placement: conjugate gradient on Θ-gradient magnitude
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- Quantization: snap cone angles to π/2, π/3, π/6 for
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quad / triangle / hexagonal atlas targets
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Java reference: unwrapper/ConesUtility.java
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Mathematical reference: Troyanov 1991 + Springborn 2020 §3
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Port scope: prescribed cone angles Θᵥ ≠ 2π in Euclidean mode.
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Status: 🔲 planned
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9d.2 Non-Euclidean cone extensions (RESEARCH, not in Java)
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→ extend ConesUtility to HyperIdeal + Spherical modes
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@@ -153,68 +159,13 @@ mesh type.
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automatic cone placement; directly applicable to 9d.2 algorithm.
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Status: 🔲 planned
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9d.3 StereographicUnwrapper (Java port)
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→ stereo_unwrapper.hpp
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Java source: StereographicUnwrapper.java (266 lines)
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Converts spherical DCE output (Point_3 on S²) to a 2-D atlas
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via stereographic projection + Möbius centring.
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Closes the visualisation gap from discrete_conformal_map_spherical().
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Effort: small (~3 days).
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Status: 🔲 planned
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9e — CirclePatternLayout (Java port)
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─────────────────────────────────────
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9e CirclePatternLayout + CirclePatternUtility (Java port)
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→ circle_pattern_layout.hpp
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Java sources: CirclePatternLayout.java + CirclePatternUtility.java
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+ CPEuclideanRotation.java
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Mathematical reference: Bobenko-Springborn 2004 variational principle
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+ Bobenko-Hoffmann-Springborn 2006 "Minimal
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surfaces from circle patterns" (Discrete &
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Comput. Geom. 35, 2006).
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Status: 🔲 planned
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9f — Polygon Laplacian (RESEARCH — no Java equivalent)
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──────────────────────────────────────────────────────
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9f Discrete Laplacian on general polygonal meshes
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→ polygon_laplacian.hpp
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Java source: NONE
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Mathematical reference:
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Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
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Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
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polygon cotangent weights extending the Pinkall-Polthier formula.
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Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
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(ACM TOG 39, 2020) — extended journal treatment, error bounds.
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Enables: DCE energy evaluation on quad-dominant / Voronoi /
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polygon meshes without forced triangulation.
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Replaces euclidean_hessian.hpp for non-triangular inputs.
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Status: 🔲 planned (pure research, no Java source)
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Effort: medium (~2 weeks core + tests; +1 week Newton integration).
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```
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9d — Cone metrics + sphere utilities (Java port — 2026 library scan)
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────────────────────────────────────────────────────────────────────
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```
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9d.1 ConesUtility (Java port: unwrapper/ConesUtility.java)
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→ cone_singularities.hpp
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Fills the "⚠️ data structure only" gap in java-parity.md:
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- Detect interior cone vertices (angle deficit ≠ 0)
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- BFS path from cone to mesh boundary → cut edge set
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- Auto-placement: conjugate gradient on Θ-gradient magnitude
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- Quantization: snap cone angles to π/2, π/3, π/6 for
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quad / triangle / hexagonal atlas targets
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Java reference: unwrapper/ConesUtility.java
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9d.2 StereographicUnwrapper + SphereUtility (Java port)
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9d.3 StereographicUnwrapper + SphereUtility (Java port)
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→ stereographic_layout.hpp
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Stereographic projection S²→ℂ∪{∞} + Möbius centering for
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genus-0 surfaces. Converts spherical DCE output to a flat 2-D atlas.
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Java reference: unwrapper/StereographicUnwrapper.java (266 lines)
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9d.3 MobiusCenteringFunctional (Java port, optional upgrade)
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9d.4 MobiusCenteringFunctional (Java port, optional upgrade)
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→ integrate into layout.hpp normalise_hyperbolic()
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Variational Möbius centering via Lorentz geometry:
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E = Σ log(-⟨x,p⟩/√(-⟨x,x⟩))
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@@ -235,6 +186,30 @@ mesh type.
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- CPEuclideanRotation: rotation-invariant CP functional variant
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Java references: unwrapper/circlepattern/CirclePattern{Layout,Utility}.java
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unwrapper/circlepattern/CPEuclideanRotation.java
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Mathematical reference: Bobenko-Springborn 2004 variational principle
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+ Bobenko-Hoffmann-Springborn 2006 "Minimal
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surfaces from circle patterns" (Discrete &
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Comput. Geom. 35, 2006).
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```
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9f — Polygon Laplacian (RESEARCH — no Java equivalent)
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──────────────────────────────────────────────────────
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```
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9f Discrete Laplacian on general polygonal meshes
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→ polygon_laplacian.hpp
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Java source: NONE
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Mathematical reference:
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Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
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Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
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polygon cotangent weights extending the Pinkall-Polthier formula.
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Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
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(ACM TOG 39, 2020) — extended journal treatment, error bounds.
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Enables: DCE energy evaluation on quad-dominant / Voronoi /
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polygon meshes without forced triangulation.
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Replaces euclidean_hessian.hpp for non-triangular inputs.
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Status: 🔲 planned (pure research, no Java source)
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Effort: medium (~2 weeks core + tests; +1 week Newton integration).
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```
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---
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