ConformalLabpp/doc/architecture/locked-vs-flexible.md

Locked-in vs flexible architecture decisions

Purpose. External collaborators (especially mathematicians evaluating whether to extend the library) need to know which design choices are load-bearing (changing them is expensive across the whole codebase) and which are opportunistic (made on first principles and easy to revisit).

Why this matters now. A v0.9.0 + Springborn-Bobenko-alumnus external review (May 2026) is the right moment to surface these decisions before they ossify further. If any of the locked decisions need revisiting, this is the cheapest moment in the project's life to do so.

Three tiers:

🔴 LOAD-BEARING         changing requires repo-wide refactoring
🟡 SEMI-FIXED           changing affects multiple subsystems; possible but not casual
🟢 OPPORTUNISTIC        changing is one-PR work

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1. Mesh data structure → CGAL::Surface_mesh<P>

Status	🔴 load-bearing
Locked since	Phase 3 (2025)
Alternative considered	OpenMesh / pmp-library / custom halfedge / Java CoHDS literal port
Why locked	Every header code/include/*.hpp uses ConformalMesh = CGAL::Surface_mesh<Point3> and CGAL property maps explicitly. Phase 8a Traits provide a concept abstraction but the Default model is Surface_mesh-only.
Cost to change	~3 weeks: rewrite traits, every functional, every test mesh factory. Touched in ~30 headers + ~25 test files.
Mitigation	Traits-based design (Phase 8a) means user-supplied mesh types CAN be added as Default-traits specialisations without touching algorithms — Phase 8a.2 plan documents this. But the Default model is Surface_mesh.
When to revisit	If a major user wants Polyhedron_3 or OpenMesh as default. Currently no concrete request → keep.

Recommended posture for an external contributor: use the existing Surface_mesh-based API for any new functional. Adding generic-FaceGraph support is a single architectural step that doesn't need to be repeated per functional — wait for one user to need it.

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2. Floating-point kernel → CGAL::Simple_cartesian<double>

Status	🟡 semi-fixed
Locked since	Phase 3 (deliberate decision: conformal geometry doesn't need exact predicates)
Cost to change	Per-functional template parameterisation. The Phase 8 MVP wrapper already deduces the kernel from the mesh point type, so user code can specify any CGAL kernel — but the legacy code/include/*.hpp headers are hardcoded.
When to revisit	If a user reports floating-point catastrophic cancellation in the half-tangent angle formula on extreme meshes. Hasn't happened in 250 tests over 9 phases.

Recommended posture: stay with Simple_cartesian<double>. If a specific algorithm needs Exact_predicates_inexact_constructions_kernel for robustness, parameterise that one algorithm — don't refactor the whole codebase.

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3. Header-only, no compiled library

Status	🔴 load-bearing
Locked since	Phase 1
Cost to change	Significant: would need to introduce .cpp files, link order, ABI compatibility decisions. But everything in code/include/*.hpp is inline or template, so a header-only-to-compiled migration is mechanical.
Why locked	CGAL package convention is also header-only. Forking would break that goal.
When to revisit	If compilation times become prohibitive (currently < 30 s clean build with all 5 functionals). Or if a future cyclic dependency between functionals forces it. Neither is on the horizon.

Recommended posture: stay header-only. This is also the de-facto norm for CGAL packages of comparable scope.

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4. Five DCE models on the same mesh

Status	🟡 semi-fixed
Locked since	Phase 9a (2026-05) — when CP-Euclidean introduced face-DOFs
Why semi-fixed	Each model has its own *Maps bundle with its own property-map name prefix (ev:, sv:, v:, cf:/ce:, iv:/ie:) so all five can coexist on the same CGAL::Surface_mesh. Adding a sixth model means picking a new prefix + writing a new *Maps struct + Default trait.
Cost to add a sixth model	~1 week (CP-Euclidean took ~3 days, Inversive-Distance ~3 days, Hessian + Newton + CGAL entry add another ~3 days).
When to revisit	If a unified base-Maps abstraction would actually win something (currently it would not — the property-map sets differ in kind, not just in name).

Recommended posture for adding a new functional:

1. Pick a 2-letter prefix not in {ev, sv, v, cf, ce, iv, ie}.
2. Define your *Maps struct with that prefix.
3. Define your Default_*_traits<Surface_mesh, K> class in a new header code/include/CGAL/Discrete_*.h.
4. Wire it into newton_solver.hpp (template-copy from newton_inversive_distance is the closest pattern for vertex-DOFs; newton_cp_euclidean for face-DOFs).
5. Add a CGAL entry in the new header.
6. Add tests following add-inversive-distance.md.

This recipe has been validated three times now (CP-Euclidean, Inversive Distance, and the four Phase-8b-Lite wrappers).

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5. Newton solver with line search + SparseQR fallback

Status	🟡 semi-fixed
Locked since	Phase 4
Cost to change	Each newton_* function is ~50-80 lines; replacing the solver across all five is ~2 days.
When to revisit	If a future functional needs trust-region or BFGS. None of the five currently does — Newton converges quadratically near the optimum and the line search handles bad initial points.

Recommended posture: Newton with line search is enough for any strictly-convex variational problem. For non-convex variants, consider adding a newton_with_trust_region() helper alongside, not replacing.

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6. Eigen as the linear-algebra back-end

Status	🔴 load-bearing
Locked since	Phase 4
Alternative considered	PETSc/Tao (Java original) / Boost.uBLAS / Blaze
Why locked	Eigen is header-only (no external dependency at build time), bundled as a CGAL dependency, fast, and offers SimplicialLDLT + SparseQR which the gauge-singular-mesh case needs.
Cost to change	Significant — every Hessian header (*_hessian.hpp) and every Newton solver uses Eigen::SparseMatrix and Eigen::VectorXd directly. ~2 weeks repo-wide.
When to revisit	If a sparse-solver feature (e.g. parallel Cholesky) is needed that Eigen doesn't offer.

Recommended posture: stay with Eigen.

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7. CGAL public-API surface layout

Status	🟡 semi-fixed (Phase 8a-MVP design decision, 2026-05-19)
Locked since	PR #6 (v0.9.0)
Strategy chosen	"Strategy C" — functional-specific Default traits, one entry function per functional, no fat unified trait.
Cost to change to unified trait	~1 week — refactor Default_*_traits<> into a single Default_conformal_map_traits<> with all property-map fields. Existing 8 tests would need updating.
When to revisit	When the first cross-functional algorithm (e.g. a hybrid functional that uses both face and vertex DOFs) lands. Speculation today.

Recommended posture: stay with Strategy C. CGAL's own Polygon_mesh_processing package follows the same convention — one default trait per algorithm family.

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8. Named-parameter mechanism

Status	🟢 opportunistic
Locked since	Phase 8 MVP (2026-05-19)
Current state	Six tags: vertex_curvature_map, fixed_vertex_map, gradient_tolerance, max_iterations, output_uv_map, normalise_layout. Pipe-operator `
Cost to extend with .member() chaining	~2 days IF CGAL upstream is forked / patched; otherwise the pipe-operator workaround is the maintainable path.
When to revisit	At any time; this is the lowest-risk change in the codebase. Tutorials add-output-uv-map.md §4 explains the mechanism.

Recommended posture: the pipe-operator | is already shipped and sufficient. Add .member() chaining only if a concrete user pushes for the CGAL-canonical syntax AND we are willing to fork CGAL upstream.

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9. Property-map name conventions

Status	🟢 opportunistic
Locked since	Phase 3 + 9a (prefix ev:/sv:/v:/cf:/ce:/iv:/ie: set when each functional was introduced)
Cost to change	One sed-replace + recompile. No user-visible effect because the names are an internal convention; the CGAL public API never exposes them.
When to revisit	If a future functional reuses an existing letter prefix. Already discussed in locked-vs-flexible.md.

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10. Tests: GTest, not CGAL's own test format

Status	🟡 semi-fixed
Locked since	Phase 1
Cost to change	~1 week — rewrite test harnesses to CGAL's test/Conformal_map/ convention. This is Phase 8d (planned for CGAL submission).
Why GTest now	Faster development cycle, IDE-friendly (Xcode / VSCode / CLion all have native GTest support). No CGAL submission is in progress yet.
When to revisit	When committing to CGAL submission (Phase 8c-d, decided to be a future commitment, see release-policy.md).

Recommended posture: keep GTest as primary. When/if CGAL submission happens, add a test/Conformal_map/ shim that calls into the GTest suite — both formats can coexist.

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11. License: MIT

Status	🔴 load-bearing
Locked since	Project inception
Cost to change	High organisational cost (requires consent of all contributors); ~no code cost.
Why locked	MIT was chosen for academic friendliness (citing, modifying, embedding). CGAL upstream requires LGPL for submitted packages.
Trade-off	Submitting to CGAL upstream is not possible without re-licensing. The codebase architecture is "CGAL-style" but the project would publish independently.
When to revisit	If/when a concrete CGAL upstream submission is decided. See release-policy.md for the formal policy.

Recommended posture: stay with MIT. Build the "CGAL-style package for external distribution" as the primary deliverable. Re-license only when the CGAL editorial board commits to accepting the submission.

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12. Documentation pattern: Markdown + Doxygen

Status	🟢 opportunistic
Locked since	Phase 7.5 (2026-05)
Current state	code/include/*.hpp carry Doxygen-style /// comments (87% coverage); doc/*.md for prose; Doxyfile generates HTML in doc/doxygen/.
Cost to add more	Per-file basis; ~1 hour per header for full Doxygen.
When to revisit	When chasing CGAL-submission readiness (need PackageDescription.txt + User_manual.md).

Recommended posture: keep adding /// comments incrementally with each new public function.

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Summary table

Decision	Tier	Cost to change
1. CGAL::Surface_mesh as default mesh	🔴 load-bearing	~3 weeks
2. Simple_cartesian kernel	🟡 semi-fixed	per-functional
3. Header-only architecture	🔴 load-bearing	medium (mechanical)
4. Five DCE models, separate Maps	🟡 semi-fixed	~1 week per new model
5. Newton + line search + SparseQR	🟡 semi-fixed	~2 days
6. Eigen back-end	🔴 load-bearing	~2 weeks
7. Strategy C (per-functional traits)	🟡 semi-fixed	~1 week
8. Named-parameter mechanism	🟢 opportunistic	pipe ✅; .member() ~2 days
9. Property-map name conventions	🟢 opportunistic	~1 hour
10. GTest, not CGAL test format	🟡 semi-fixed	~1 week
11. MIT license	🔴 load-bearing	organisational
12. Markdown + Doxygen	🟢 opportunistic	per-file

Key insight: the load-bearing decisions are all good in 2026. Surface_mesh + Eigen + header-only + MIT are the right defaults for a research-quality CGAL-style package. The semi-fixed decisions are all behind one concrete blocker (single user request, CGAL submission commitment, etc.). The opportunistic decisions are cheap to revisit any time.

The architecture is in a good place for the v0.9.0 → v0.10.0 transition. No "expensive corner" has been painted into; every locked decision matches the project's three-goal hierarchy in research-track.md.

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Open questions for the external reviewer

Items where the project would benefit from a second opinion:

1. Phase 9c (4g-polygon) algorithm choice. Two routes:

   • Port the Java FundamentalPolygonUtility + CanonicalFormUtility literally (~2 weeks).
   • Or: re-derive from Springborn 2020 §5 using the existing cut_graph.hpp + holonomy infrastructure (~3 weeks, cleaner architecture). Which is preferred? See phases.md §Phase 9c.

2. Phase 10a (forms) priorities. Three sub-items (DiscreteHarmonicFormUtility, DiscreteHolomorphicFormUtility, CanonicalBasisUtility) interlock. Which to start with?

3. Analytic Hessian payoff. The Schläfli-based analytic HyperIdeal Hessian (Phase 9b-analytic — derivation already written: hyperideal-hessian-derivation.md) would add another ~6× over block-FD. Is that worth ~2 weeks of implementation effort for a working-mesh size on which?

4. CGAL upstream vs independent distribution. Does the reviewer know a CGAL editor / has personal opinion on the LGPL-vs-MIT trade-off?

5. geometry-central cross-validation (GC-1). Two libraries solve the same DCE problem from different algorithmic directions (Newton-on-mesh vs Ptolemaic-flips-on-intrinsic-triangulation). An independent comparison would be a nice paper. Interested?