068df474b1
Add phases 9d / 9e / 9f and literature citations derived from a systematic
review of the five authors' publication lists (Tier 1 / 2 / 3 analysis).
phases.md:
- Phase 9d: ConesUtility port (9d.1) + non-Euclidean cone extensions
(9d.2, RESEARCH) + StereographicUnwrapper (9d.3)
- Phase 9e: CirclePatternLayout + CirclePatternUtility (Java port)
- Phase 9f: Polygon Laplacian on non-triangular meshes (Alexa 2011/2020,
RESEARCH — no Java equivalent)
- Phase 9b-analytic: add Rivin-Springborn 1999 as Schläfli source
- Phase 10b: add Bobenko-Bücking 2009 + Bobenko-Lutz 2024 IMRN
- Phase 10c: add Lutz 2023 (canonical tessellations) + Bobenko-Lutz 2024
- Phase 10c' KoebePolyhedron: add Bowers-Bowers-Lutz 2026 rigidity result
references.md:
- Crane et al. 2018 Optimal Cone Singularities (Phase 9d.2)
- Bobenko-Lutz 2025 Discrete & Comput. Geom. (Phase 9d.2)
- Bobenko-Lutz 2024 IMRN (Phase 10b/c)
- Lutz 2023 Geom. Dedicata (Phase 10c)
- Lutz PhD thesis TU Berlin 2024 (Phases 9d.2, 10b, 10c)
- Bowers-Bowers-Lutz 2026 (Phase 9b-analytic + 10c')
- Alexa-Wardetzky 2011 + Alexa 2020 (Phase 9f)
- Bobenko-Bücking 2009 (Phase 10b)
- Rivin-Springborn 1999 (Phase 9b-analytic)
research-track.md:
- New entry: Phase 9d.2 non-Euclidean cone extensions (Bobenko-Lutz 2025
+ Crane 2018), with acceptance criteria
- New entry: Phase 9f polygon Laplacian (Alexa-Wardetzky 2011 / Alexa 2020),
with acceptance criteria
java-parity.md:
- Split cone-metrics row into Euclidean (9d.1 port) and non-Euclidean
(9d.2 research) with literature references
- Add ConesUtility to "utility classes not yet ported" table
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
187 lines
12 KiB
Markdown
187 lines
12 KiB
Markdown
# Java ConformalLab vs. conformallab++ — Feature Parity
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Reference: [github.com/varylab/conformallab](https://github.com/varylab/conformallab)
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Java package root: `de.varylab.discreteconformal`
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When porting a Java class, locate the original in the Java repository and use it
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as the reference implementation for expected behaviour, edge cases, and test cases.
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---
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## Algorithm parity
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| Mathematical layer | Java ConformalLab | conformallab++ | Notes |
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| Euclidean functional — energy, gradient | ✅ | ✅ | |
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| Spherical functional — energy, gradient, gauge-fix | ✅ | ✅ | |
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| HyperIdeal functional — energy, gradient | ✅ | ✅ | |
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| Inversive-distance functional (Luo 2004) | ❌ *(not in Java)* | ❌ Phase 9a.2 | **No Java source.** Implemented in C++ from Luo 2004 + Glickenstein 2011 + Bowers-Stephenson 2004 — **new research, not a port**. Verified: `find /Users/tarikmoussa/Desktop/conformallab -iname "*nversive*"` returns zero. |
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| CP-Euclidean functional (BPS 2010) | ✅ | ❌ Phase 9a.1 | `CPEuclideanFunctional.java` (260 lines) — face-based circle packing |
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| Euclidean Hessian — cotangent Laplacian | ✅ analytic | ✅ analytic | Pinkall–Polthier (1993) |
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| Spherical Hessian — ∂α/∂u via law of cosines | ✅ analytic | ✅ analytic | |
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| HyperIdeal Hessian — analytic via ζ → l → β/α | ❌ *(`hasHessian()==false`)* | ⚠️ FD (Phase 4a) → block-FD (Phase 9b) | **Java has NO Hessian for HyperIdeal** (verified: `HyperIdealFunctional.java:295-298` declares `hasHessian() { return false; }`). Both C++ Hessian variants are **new research beyond Java**; analytic Schläfli-based variant is Phase 9b-analytic. |
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| Newton solver | ✅ | ✅ | |
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| SparseQR fallback for gauge modes | unknown | ✅ | New in C++ |
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| Cone metrics — prescribed Θᵥ ≠ 2π (Euclidean) | ✅ fully | ❌ Phase 9d.1 (port) | Java Euclidean-only; `ConesUtility.java` ~200 lines |
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| Cone metrics — non-Euclidean (HyperIdeal / Spherical) | ❌ *(not in Java)* | ❌ Phase 9d.2 (research) | **No Java source.** Mathematical basis: Bobenko-Lutz 2025 (decorated DCE) + Crane et al. 2018 (optimal cone placement). |
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| Layout / embedding — ℝ² / H² / S² | ✅ | ✅ priority-BFS all three | |
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| Exact hyperbolic trilateration | ✅ Möbius | ✅ Möbius + law of cosines | |
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| halfedge_uv — seam-aware UV (texture atlas) | ✅ | ✅ | |
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| Gauss–Bonnet consistency check | ✅ | ✅ | |
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| Tree-cotree cut graph (2g edges) | ✅ | ✅ Erickson–Whittlesey (2005) | |
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| Holonomy — Euclidean (translations) | ✅ | ✅ | |
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| Holonomy — Hyperbolic (SU(1,1) Möbius maps) | ✅ | ✅ | |
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| Period matrix τ — genus 1, SL(2,ℤ)-reduced | ✅ | ✅ | |
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| Fundamental domain — genus 1 | ✅ | ✅ CCW parallelogram | |
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| 4g-polygon boundary walk — genus g > 1 | ✅ | ❌ Phase 9c | `FundamentalDomainUtility.java` |
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| Siegel period matrix Ω — genus g ≥ 2 | ✅ | ❌ Phase 10b | |
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| Global uniformization — genus g ≥ 2 | ✅ | ❌ Phase 10c | |
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| Clausen / Lobachevsky / ImLi₂ | ✅ | ✅ | |
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| Poincaré disk / Lorentz boost visualisation | ✅ | ✅ | |
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| Mesh I/O + serialisation | ✅ XML/CoHDS | ✅ OFF/OBJ/PLY + JSON/XML | |
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| Interactive viewer | ✅ jReality | ✅ libigl/GLFW | |
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---
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## Java utility classes not yet ported
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These exist in `de.varylab.discreteconformal.util` in the Java library.
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They are candidates for Phase 9 or Phase 10.
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| Java class | Description | Phase |
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| `ConesUtility` (~200 lines) | Prescribed cone angles Θᵥ ≠ 2π — Euclidean mode only | 9d.1 |
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| `CPEuclideanFunctional` | Face-based circle-packing energy (BPS 2010) | 9a.1 |
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| `FundamentalPolygonUtility` (698 lines) | Construction + canonicalisation of 4g-gons for genus-g | 9c |
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| `CanonicalFormUtility` (532 lines) | High-level wrapper for 9c — drives canonicalisation pipeline | 9c |
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| `CuttingUtility` + `SurgeryUtility` (~800 lines) | Mesh cuts and gluing operations needed for fundamental domains | 9c (foundation) |
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| `DiscreteHarmonicFormUtility` (657 lines) | Discrete harmonic 1-forms via cotangent Laplacian (Hodge theory) | 10a prerequisite |
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| `DiscreteHolomorphicFormUtility` (285 lines) | Holomorphic differentials via Mercat complex structure | 10a (Bobenko-Springborn 2004 §6) |
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| `CanonicalBasisUtility` (337 lines) | Symplectic homology basis with intersection-form normalisation | 10a prerequisite |
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| `DiscreteRiemannUtility` (186 lines) | Period matrix τ, Siegel reduction (genus g) | 10b |
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| `DualityUtility` (308 lines), `HomologyUtility` (122 lines) | Primal/dual cohomology, cycle generators | 10a support |
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| `HyperbolicCyclicFunctional` (530 lines) | Discrete hyperbolic conformal energy (analogue of Euclidean) — completes the geometry suite | 10b–c |
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| `QuasiisothermicUtility` + `SinConditionApplication` (~1200 lines) | Lawson-correspondence parametrisation, sin-condition functional | 10b |
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| `KoebePolyhedron` (321 lines) | Koebe–Andreev–Thurston circle-packing construction | 10c |
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| `StereographicUnwrapper` (266 lines) | Stereographic projection S²→ℂ + Möbius centring — converts the Spherical-DCE output into a 2-D atlas | 10b' (Sphere visualisation) |
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| `CircleDomainUnwrapper` (570 lines) | Conformal map of a multiply-connected planar region onto a disk-with-holes — classical complex-analysis use case | 11+ (new use-case class) |
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| `ElectrostaticSphereFunctional`, `MobiusCenteringFunctional` | Sphere-domain pre-processing functionals | 10c (optional) |
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Note: items marked as *new research* (e.g. Inversive Distance, HyperIdeal Hessian variants)
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are tracked separately in `doc/roadmap/research-track.md`.
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---
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## Java packages not yet in the roadmap — 2026 full-library scan
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A complete scan of the Java source tree (`de.varylab.discreteconformal`) revealed the
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following packages and classes not yet covered by Phases 1–9c or the Phase-10 plan.
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Organised by value / effort.
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### Functional package (`de.varylab.discreteconformal.functional`)
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| Java class | What it does | Proposed phase |
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| `ConesUtility` (in `unwrapper/`) | Cone singularity detection, BFS-path cutting from cone to boundary, auto-placement via conjugate gradient, quantization to π/2 / π/3 / π/6 — fills the "⚠️ data structure only" gap in the parity table | **9d** |
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| `MobiusCenteringFunctional` | Variational Möbius centering via Lorentz geometry: E = Σ log(−⟨x,p⟩/√(−⟨x,x⟩)). Supplies full gradient + Hessian — more principled than the iterative Fréchet mean in `normalise_hyperbolic()` | **9d** |
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| `ElectrostaticSphereFunctional` | Repulsive electrostatic energy on S² (E = Σ 0.5/d² + sphere constraint). Useful as initialization heuristic for spherical uniformization | **9d** (optional) |
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| `EuclideanCyclicFunctional` | Euclidean DCE functional reduced to a cyclic-symmetry quotient — reduces DOFs for surfaces with cyclic symmetry group | **10g** |
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| `HyperbolicCyclicFunctional` | Hyperbolic analogue of above | **10g** |
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### Circle pattern package (`de.varylab.discreteconformal.unwrapper.circlepattern`)
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| Java class | What it does | Proposed phase |
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| `CirclePatternUtility` | Computes circle pattern radii (ρ per face) via Newton trust-region on CPEuclidean energy — the solver side | **9e** |
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| `CirclePatternLayout` | Embeds a circle pattern in the plane from the ρ values — the layout side. Required complement to `cp_euclidean_functional.hpp` already ported in 9a.1 | **9e** |
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| `CPEuclideanRotation` | Rotation-invariant variant of the CP-Euclidean functional | **9e** |
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### Uniformization package (`de.varylab.discreteconformal.uniformization`)
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| Java class | What it does | Proposed phase |
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| `CutAndGlueUtility` | Mesh surgery beyond tree-cotree: arbitrary cut paths, gluing cut surfaces back together — needed for genus g > 1 canonical polygon construction | **9c** (add to existing plan) |
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| `VisualizationUtility` | Java/jReality specific — do not port | — |
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| `Uniformizer` | High-level pipeline driver — already covered by our CLI + pipeline API | — |
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### Unwrapper package — additional classes
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| Java class | What it does | Proposed phase |
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| `StereographicUnwrapper` | Stereographic projection S²→ℂ∪{∞} + Möbius centring — converts spherical DCE output to 2-D atlas for genus-0 | **9d** |
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| `SphereUtility` | Sphere-specific utilities (area centroid, antipodal, normalization helpers) | **9d** |
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| `CircleDomainUnwrapper` | Conformal map of multiply-connected planar region onto disk-with-holes (Koebe-Andreev-Thurston) | **10d** |
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### Quasi-isothermic package (`de.varylab.discreteconformal.unwrapper.quasiisothermic`)
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Quasi-isothermic maps generalize conformal maps to meshes where exact conformality is impossible.
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Entirely absent from the current roadmap.
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| Java class | What it does | Proposed phase |
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| `QuasiisothermicDelaunay` | Delaunay-conformal triangulation as QI preprocessing | **10e** |
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| `QuasiisothermicLayout` | Embedding from quasi-isothermic DOFs | **10e** |
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| `QuasiisothermicUtility` | Lawson-correspondence parameterization (~800 lines) | **10e** |
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| `DBFSolution` | Discrete Beltrami field solution | **10e** |
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| `SinConditionApplication` | Sin-condition functional for QI maps | **10e** |
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| `ConformalStructureUtility` | Conformal structure extraction from QI solution | **10e** |
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### Koebe package (`de.varylab.discreteconformal.unwrapper.koebe`)
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| Java class | What it does | Proposed phase |
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| `KoebePolyhedron` | Koebe–Andreev–Thurston theorem: realization of every 3-connected planar graph as a convex polyhedron with edges tangent to the unit sphere (321 lines) | **10f** |
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### Util package — additional classes not yet in roadmap
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| Java class | What it does | Proposed phase |
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| `DualityUtility` | Hodge-star operator + dual cycles via cotangent weights — **prerequisite for Phase 10a** (discrete holomorphic forms need the dual mesh) | **10a prerequisite** (consider 9c) |
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| `HyperellipticUtility` | Hyperelliptic surfaces (genus g ≥ 2 with Z₂ symmetry) — period matrix has block-diagonal structure | **10b** |
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| `HyperIdealHyperellipticUtility` | HyperIdeal variant for hyperelliptic surfaces | **10b** |
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| `PathUtility` | Mesh path operations — supporting infrastructure for Phase 9c homology basis | **9c** |
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| `LaplaceUtility` | Discrete Laplace operators (cotangent + combinatorial) | **9 / infrastructure** |
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| `EdgeUtility` | Edge orientation and classification helpers | **infrastructure** |
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| `StitchingUtility` | Seam stitching after cut-and-glue | **9c** |
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### Do not port — Java-specific or superseded
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| Java class | Reason |
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|---|---|
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| `ColtIterationReporterImpl` | Colt sparse matrix library — replaced by Eigen |
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| `NodeIndexComparator` | Java Comparator — replaced by `std::less` |
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| `SimpleMatrixPrintUtility` | Debug print — Eigen `.format()` is sufficient |
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| `EuclideanUnwrapperPETSc` / `SphericalNormalizerPETSc` | PETSc solver binding — replaced by Eigen |
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| `Search` | CoHDS-specific graph search — replaced by CGAL halfedge iteration |
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| `SparseUtility` | Colt sparse matrix utils — replaced by Eigen |
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---
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## HyperIdeal Hessian — correction of an earlier mis-claim
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> **2026-05-21 audit:** A previous version of this document claimed
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> "the Java library computes the HyperIdeal Hessian analytically through the
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> chain (bᵢ, aₑ) → lᵢⱼ → ζ₁₃/ζ₁₄/ζ₁₅ → αᵢⱼ/βᵢ". **This is incorrect.**
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> The Java source file `HyperIdealFunctional.java` line 295-298 declares
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> ```java
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> @Override
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> public boolean hasHessian() {
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> return false;
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> }
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> ```
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> i.e. the upstream Java implementation supplies **no** HyperIdeal Hessian at
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> all — neither analytic nor numerical. The chain rule above is the
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> *mathematical formulation* (from Springborn 2020 §4 + Schläfli 1858), not
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> something the Java code implements.
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### Actual state of HyperIdeal Hessian in conformallab++
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| Variant | Status | Notes |
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| Phase 4a — full FD `H[i,j] = (G(x+εeⱼ)[i] − G(x−εeⱼ)[i]) / (2ε)` | ✅ implemented | O(n·F) cost; PSD by Springborn 2020 strict convexity |
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| Phase 9b — block-FD (per-face 6×6 local block, scatter to global) | ✅ implemented (PR #9) | O(F·36) cost; ~96× speed-up over Phase 4a measured on V=200 mesh |
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| Phase 9b-analytic — Schläfli identity + chain rule through ζ₁₃/ζ₁₄/ζ₁₅ | 🔲 planned (research) | See `doc/roadmap/research-track.md` for the formal plan and citations |
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All three are **new research beyond the Java port**. Java parity for
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HyperIdeal stops at the gradient.
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