ConformalLabpp/doc/reviewer/questions.md

Questions for the external reviewer

Please skim this before the meeting. Each question is scoped so that "do A" / "do B" / "either is fine" is a sufficient answer; deeper dives are welcome but not required.

These are the five decisions that would benefit most from a second opinion. Items 1-3 affect the porting roadmap directly; 4-5 affect the long-term goal (CGAL submission).

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Q1 — Phase 9c (4g-polygon canonical form): port-literal vs re-derive?

The Java original has two utility classes:

• FundamentalPolygonUtility (~600 lines)
• CanonicalFormUtility (~900 lines)

that together compute the canonical 4g-polygon for a higher-genus surface from its cut graph.

We can either:

• (A) Port literally (~2 weeks). Faithful, predictable, fixes the Java algorithm in C++. Down-side: we inherit the Java code's ad-hoc style and edge-case handling.
• (B) Re-derive from Springborn 2020 §5 (~3 weeks). Uses our existing cut_graph.hpp + holonomy infrastructure cleanly. Down-side: longer; potential for new bugs not seen by the Java original's test cases.

Question: which route do you prefer, and is there a reference implementation (Mathematica notebook, paper appendix, other research codebase) we should cross-validate against?

Context: doc/roadmap/phases.md §Phase 9c, doc/roadmap/porting-status.md.

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Q2 — Phase 9b-analytic Hessian: implement now or later?

We have:

• Done: per-face block-FD Hessian (96× faster than naive full-FD).
• Derived but not implemented: analytic Hessian via the Schläfli identity, expected ~6× further speedup over block-FD.
• Derivation document: doc/math/hyperideal-hessian-derivation.md (805 lines, all sign pitfalls covered, references Schläfli 1858, Milnor 1982, Vinberg 1993, Cho-Kim 1999, Glickenstein 2011, Springborn 2020).

Question:

• At what mesh size does the ~6× become user-visible enough to justify ~2 weeks of implementation work?
• Are you aware of subtleties in the Schläfli-based derivation our document might be missing?

If the answer is "implement", we'd target Phase 9b-analytic right after the meeting.

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Q3 — output_uv_map for CP-Euclidean: build now or defer?

For CP-Euclidean (face-based DOFs, BPS 2010) the natural output is a per-face circle packing in ℝ² — not a per-vertex Point_2 map the way the other four DCE entries produce.

Today the entry throws std::runtime_error with a helpful pointer if the caller passes output_uv_map(...). A faithful layout would be ~150 lines implementing BPS-2010 §6.

Question: do your CP-Euclidean use cases need a UV-like output, or are the face circle radii themselves the deliverable? The answer shapes whether Phase 9c gets it now or later.

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Q4 — CGAL submission strategy: one package or five?

For the long-term CGAL submission:

• (A) One package "Discrete_conformal_map" — single entry header, five solver functions, one set of named parameters. Easier for users to find; harder to compartmentalise reviews.
• (B) Five packages "Discrete_*" — each DCE model is its own CGAL package with its own concept + reference manual. More ceremony for users; more familiar review surface for CGAL editors.

Today the code is structured per-functional (Strategy C — see locked-vs-flexible.md §7). Either submission packaging is achievable from this base.

Question: what's the CGAL editor convention for related-but-distinct algorithms — Polygon_mesh_processing as one example (one package, many algorithms), vs Triangulation_2/Triangulation_3/Periodic_/Hyperbolic_ as another (multiple packages for related algorithms)?

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Q5 — geometry-central cross-validation (GC-1)

Two libraries solve the DCE problem from opposite algorithmic directions:

• conformallab++: Newton on the fixed mesh (no intrinsic flips).
• geometry-central: Ptolemy flips on an intrinsic triangulation.

An automated comparison on common meshes would be:

• A nice paper (the disagreement modes are interesting in their own right).
• A confidence-building tool for both libraries (we benefit from catching corner-case bugs, they benefit from cross-validation against a Newton baseline).
• ~3 days of plumbing (CMake-fetch geometry-central, write 5 common test meshes, compare u_per_vertex to a tolerance).

Question: would you be interested in co-authoring such a comparison note (with us doing the implementation)? Or do you know someone in the Crane group who would?

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Things you do not need to comment on (unless you want)

• C++ style choices captured in .clang-format + .clang-tidy.
• Test framework choice (GTest).
• License (MIT, with vendored deps catalogued in code/deps/THIRD-PARTY-LICENSES.md).
• Build system (CMake ≥ 3.20, header-only consumer + optional CLI/Viewer).

These are conscious decisions matched to CGAL conventions and aren't load-bearing in the sense that revisiting them later is cheap.

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What I'm hoping you'll say "no" to

This is a deliberately blunt question because positive feedback is nice but negative feedback is rarer and more valuable:

Looking at any of the 12 architecture decisions in locked-vs-flexible.md, is there one where you think "no, that's the wrong call, here's why"?

The 🔴 load-bearing decisions are the most consequential to revisit, because waiting longer makes them more expensive. No is the most useful answer.