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fix+test: Euclidean holonomy/τ end-to-end + spherical edge-DOF oracle (2026-05-29 audit)
Bundles the 2026-05-29 Java↔C++ math-correctness audit (doc/reviewer/
java-port-audit.md, 11 findings) with two follow-up fixes.

Audit code changes:
- Finding 3 (spherical_functional): edge-DOF replacement parameterization via
  spher_eff_lambda; edge gradient α_opp⁺+α_opp⁻−θ_e (drops additive −(S⁺+S⁻)/2)
- Finding 4 (spherical_hessian): always-compiled edge-DOF throw guard
- Finding 6 (period_matrix): faithful normalizeModulus (0≤Re≤½, Im≥0, |τ|≥1)
- Finding 9 (inversive_distance): degenerate-face limiting angles, no skip
- Findings 1/2 (euclidean): degenerate gradient limiting angles + Hessian guard

Euclidean holonomy/τ fix: develop the cut surface across the dual spanning tree
only (cut_graph now exposes is_dual_tree), so genus-1 cut edges yield
non-degenerate lattice generators. Previously τ came out 0 / NaN / 1e13 on the
bundled tori; now matches the analytic revolution modulus i·√(R²−r²)/r. Re-enabled
τ reporting in the Euclidean CLI; rewrote validation.md §3/§4 accordingly.

Tests (240 CGAL, 0 skipped):
- HolonomyEndToEnd ×3 — tori of revolution (4×4, hex 6×6, 8×8) vs analytic modulus
- SphericalFunctional.EdgeGradient_RegularTetClosedForm — independent closed-form
  π/3 oracle locking the Finding-3 edge formula (the path-integral FD check cannot
  detect a wrong-but-conservative gradient)

Also documents the latent spherical/hyperbolic holonomy-extraction bug (same
single-development pattern, dead code today) in research-track.md (Phase 9c/10),
and adds favour/normalisations to the codespell ignore list.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
2026-05-29 12:50:16 +02:00

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# conformallab++
[![CI](https://git.eulernest.eu/conformallab/ConformalLabpp/actions/workflows/cpp-tests.yml/badge.svg)](https://git.eulernest.eu/conformallab/ConformalLabpp/actions)
[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](LICENSE)
[![DOI](https://img.shields.io/badge/doi-Sechelmann%202016-blue)](https://depositonce.tu-berlin.de/items/8e2988b2-d991-45b5-aad5-9fb7988f3b2f)
[![API docs](https://img.shields.io/badge/API%20docs-Doxygen-orange)](https://tmoussa.codeberg.page/ConformalLabpp/)
C++17 reimplementation of [ConformalLab](https://github.com/varylab/conformallab) —
Stefan Sechelmann's Java research library for discrete conformal geometry (TU Berlin).
The long-term goal is a **CGAL package** for discrete conformal maps.
Algorithmic foundation:
> Stefan Sechelmann — *Variational Methods for Discrete Surface Parameterization: Applications and Implementation*, TU Berlin 2016.
> DOI: [10.14279/depositonce-5415](https://depositonce.tu-berlin.de/items/8e2988b2-d991-45b5-aad5-9fb7988f3b2f) · CC BY-SA 4.0 ·
> [Java original](https://github.com/varylab/conformallab) · [sechel.de](https://sechel.de/)
**Status:** v0.9.0 — Phases 19a complete, Phase 8b-Lite CGAL API surface. Newton solvers for **five** DCE models (Euclidean / Spherical / HyperIdeal / CP-Euclidean / Inversive-Distance), priority-BFS layout in ℝ²/S²/Poincaré disk, GaussBonnet, tree-cotree cut graph, Möbius holonomy, period matrix (genus 1), fundamental domain, halfedge_uv texture atlas, JSON/XML serialisation, CLI app. Full test suite passing, 0 skipped — see [`doc/api/tests.md`](doc/api/tests.md) for the per-suite breakdown.
---
## Quick start
```bash
git clone https://codeberg.org/TMoussa/ConformalLabpp && cd ConformalLabpp
# Fast tests — no system dependencies
cmake -S code -B build && cmake --build build --target conformallab_tests -j$(nproc)
ctest --test-dir build --output-on-failure
# CGAL tests headless (apt install libboost-dev / brew install boost)
cmake -S code -B build -DWITH_CGAL_TESTS=ON
cmake --build build --target conformallab_cgal_tests -j$(nproc)
ctest --test-dir build -R "^cgal\." --output-on-failure
# Full build with CLI + viewer (requires Wayland/X11 dev headers)
cmake -S code -B build -DWITH_CGAL=ON && cmake --build build -j$(nproc)
# Conformal flattening (Θ_v = 2π target). Closed meshes pin one vertex +
# enforce Gauss-Bonnet; open meshes pin the boundary and flatten the interior.
./bin/conformallab_core -i code/data/off/torus_8x8.off -g euclidean -v \
-o layout.off -j result.json
# topology: closed, free DOFs=63, genus=1
# Euclidean: converged=yes iter=3 |grad|_inf≈5e-15
./bin/conformallab_core -i code/data/obj/cathead.obj -g euclidean -v -o cat.off
# topology: open (boundary pinned), free DOFs=119
# Euclidean: converged=yes iter=4
# API documentation (requires doxygen: brew/apt install doxygen)
cmake --build build --target doc
open doc/doxygen/html/index.html
```
### Compile-time workflow modes
The default build (PCH + Unity Build + Dense→Core trims) takes ~47 s
clean for the full CGAL test target. Five opt-in modes cover other
iteration scenarios:
```bash
# Configure-only, no compile. ~1 s configure, 0 s build — emits
# compile_commands.json for IDE / clangd; skips the GTest fetch.
cmake -S code -B build -DBUILD_TESTING=OFF
# Header smoke check: per-public-header isolated compile. ~12 s full,
# ~0.1 s after touching one header. "Does my refactor still parse?"
cmake -S code -B build -DBUILD_TESTING=OFF -DCONFORMALLAB_HEADERS_CHECK=ON
cmake --build build --target headers_check
# Dev iteration: PCH on, Unity off. Slower full build (~75 s) but
# editing a single test rebuilds in ~16 s instead of ~46 s.
cmake -S code -B build -DWITH_CGAL_TESTS=ON -DCONFORMALLAB_DEV_BUILD=ON
# Fast CI tests: -O0 -g for the test executables only (library /
# install targets keep -O3). Linux + g++ typically ~40 % faster
# build at the cost of 515× slower test RUN. Neutral on macOS.
cmake -S code -B build -DWITH_CGAL_TESTS=ON -DCONFORMALLAB_FAST_TEST_BUILD=ON
# Pristine measurement: disable both performance levers, e.g. for
# scripts/quality/coverage.sh that needs every TU compiled fresh.
cmake -S code -B build -DWITH_CGAL_TESTS=ON \
-DCONFORMALLAB_USE_PCH=OFF -DCMAKE_UNITY_BUILD=OFF
```
ccache is detected automatically when present on `PATH`; disable with
`-DCONFORMALLAB_USE_CCACHE=OFF`. Full mode matrix + measurements in
[`doc/architecture/compile-time.md`](doc/architecture/compile-time.md).
---
## Minimal usage
```cpp
#include "conformal_mesh.hpp"
#include "mesh_io.hpp"
#include "euclidean_functional.hpp"
#include "gauss_bonnet.hpp"
#include "newton_solver.hpp"
#include "layout.hpp"
using namespace conformallab;
ConformalMesh mesh = load_mesh("input.off");
EuclideanMaps maps = setup_euclidean_maps(mesh);
compute_euclidean_lambda0_from_mesh(mesh, maps);
// Assign DOFs — pin first vertex (gauge fix)
auto vit = mesh.vertices().begin();
maps.v_idx[*vit++] = -1;
int idx = 0;
for (; vit != mesh.vertices().end(); ++vit) maps.v_idx[*vit] = idx++;
// Natural equilibrium target: x* = 0 by construction
std::vector<double> x0(idx, 0.0);
auto G0 = euclidean_gradient(mesh, x0, maps);
for (auto v : mesh.vertices())
if (maps.v_idx[v] >= 0) maps.theta_v[v] -= G0[maps.v_idx[v]];
check_gauss_bonnet(mesh, maps);
NewtonResult res = newton_euclidean(mesh, x0, maps);
Layout2D layout = euclidean_layout(mesh, res.x, maps);
```
---
## Documentation
| | |
|---|---|
| **API reference (Doxygen HTML)** — every public class, function and named-parameter helper | https://tmoussa.codeberg.page/ConformalLabpp/ |
| **Getting started** — build modes, single-test invocation, CLI, Docker | [doc/getting-started.md](doc/getting-started.md) |
| **Pipeline API** — all three geometries, holonomy, serialisation | [doc/api/pipeline.md](doc/api/pipeline.md) |
| **Public headers** — all public headers with descriptions | [doc/api/headers.md](doc/api/headers.md) |
| **Test suites** — per-suite breakdown and counts (single source of truth) | [doc/api/tests.md](doc/api/tests.md) |
| **Extending** — new functionals, geometry modes, porting from Java | [doc/api/extending.md](doc/api/extending.md) |
| **Processing unit contracts** — preconditions / provides table | [doc/api/contracts.md](doc/api/contracts.md) |
| **CGAL package design** — Phase 8 target, YAML pipeline | [doc/api/cgal-package.md](doc/api/cgal-package.md) |
| **Architecture & pipeline diagram** | [doc/architecture/overall_pipeline.md](doc/architecture/overall_pipeline.md) |
| **geometry-central comparison** — shared core, demarcation, adoption candidates, scientific added value | [doc/architecture/geometry-central-comparison.md](doc/architecture/geometry-central-comparison.md) |
| **Design decisions** — key architectural choices + rationale | [doc/architecture/design-decisions.md](doc/architecture/design-decisions.md) |
| **Project structure** — directory tree + build targets | [doc/architecture/project-structure.md](doc/architecture/project-structure.md) |
| **Discrete conformal theory** — mathematical background for collaborators | [doc/math/discrete-conformal-theory.md](doc/math/discrete-conformal-theory.md) |
| **Validation** — known analytic results + how to verify them | [doc/math/validation.md](doc/math/validation.md) |
| **Validation protocol** — concrete commands with expected outputs | [doc/math/validation-protocol.md](doc/math/validation-protocol.md) |
| **Tutorial: add a new functional** — step-by-step Inversive-Distance port | [doc/tutorials/add-inversive-distance.md](doc/tutorials/add-inversive-distance.md) |
| **Declarative YAML pipeline** — concept, token vocabulary, 5 examples | [doc/concepts/declarative-pipeline.md](doc/concepts/declarative-pipeline.md) |
| **Geometry modes** — Euclidean / Spherical / HyperIdeal comparison | [doc/math/geometry-modes.md](doc/math/geometry-modes.md) |
| **References** — all papers by module | [doc/math/references.md](doc/math/references.md) |
| **Software landscape** — how conformallab++ relates to libigl, CGAL, geometry-central | [doc/math/software-landscape.md](doc/math/software-landscape.md) |
| **Novelty statement** — unique features, target audience, what this is not | [doc/math/novelty-statement.md](doc/math/novelty-statement.md) |
| **Complexity & scalability** — O() analysis, measured timings on real meshes, HyperIdeal bottleneck | [doc/math/complexity.md](doc/math/complexity.md) |
| **Roadmap** — Phases 110 | [doc/roadmap/phases.md](doc/roadmap/phases.md) |
| **Java parity table** — what is ported, what is planned | [doc/roadmap/java-parity.md](doc/roadmap/java-parity.md) |
| **Contributing** — language policy, test standards, release flow | [doc/contributing.md](doc/contributing.md) |
| **Claude Code context** | [CLAUDE.md](CLAUDE.md) |
---
## Citing
If you use conformallab++ in your research, please cite it using the metadata
in [`CITATION.cff`](CITATION.cff). GitHub and Codeberg show a "Cite this repository"
button that generates BibTeX and APA automatically.
The primary algorithmic source is:
> Stefan Sechelmann — *Variational Methods for Discrete Surface Parameterization:
> Applications and Implementation*, TU Berlin 2016.
> DOI: [10.14279/depositonce-5415](https://depositonce.tu-berlin.de/items/8e2988b2-d991-45b5-aad5-9fb7988f3b2f)
---
## Bugs & questions
- **Bug reports / feature requests:** [Gitea Issues](https://git.eulernest.eu/conformallab/ConformalLabpp/issues)
- **Code mirror (read-only):** [Codeberg](https://codeberg.org/TMoussa/ConformalLabpp)
- **Contact:** Tarik Moussa · Tarik.moussa95@gmail.com
---
## License
conformallab++ is released under the MIT License (see [LICENSE](LICENSE)).
Copyright © 20242026 Tarik Moussa.
The dissertation (Sechelmann 2016) is CC BY-SA 4.0.