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Wires the two Phase-9a functionals into the Newton-solver layer so
they are operational end-to-end. CGAL test count: 212 → 219 (+7).
Solvers
───────
* newton_cp_euclidean(mesh, x0, m, tol, max_iter)
- Uses cp_euclidean_hessian — analytic 2×2-per-edge BPS-2010
formula h_jk = sin θ / (cosh Δρ − cos θ).
- SparseQR fallback handles the gauge-singular case when no face
is pinned (caller error, but we recover gracefully).
- Strictly-convex energy ⇒ quadratic convergence near optimum.
* newton_inversive_distance(mesh, x0, m, tol, max_iter, hess_eps)
- Uses an inline FD Hessian (n × gradient evaluations per step) —
mirrors the Phase 4a HyperIdeal solver in spirit.
- Analytic alternative via Glickenstein 2011 eq. (4.6) is tracked
in doc/roadmap/research-track.md as Phase 9a.2-analytic.
- Sensitive to initial point; the test suite always starts from
a natural-theta setup (u = 0 is the equilibrium when
compute_inversive_distance_init_from_mesh was called).
Tests (test_newton_phase9a.cpp, 7 cases)
────────────────────────────────────────
* CPEuclidean_NaturalPhi_ClosedTetrahedron_ConvergesInZeroIterations
* CPEuclidean_PerturbedStart_ConvergesBackToEquilibrium
* CPEuclidean_OpenTetrahedron_NaturalPhi_Converges
* InversiveDistance_NaturalTheta_Triangle_ConvergesInZero
* InversiveDistance_PerturbedQuadStrip_Converges
* InversiveDistance_PerturbedTetrahedron_Converges
* CPEuclidean_UsesAnalyticHessian
Regression guard: 3-DOF problem converges in ≤ 10 iterations even
with strong perturbation, confirming the analytic Hessian path is
actually used.
All seven tests pass. Full CGAL suite: 219/219 PASSED, 0 SKIPPED.
Roadmap additions (`doc/roadmap/phases.md`)
───────────────────────────────────────────
New Phase 11+ section flags two Java sub-packages as optional/deferred
ports, recorded for project memory but not roadmap commitments:
* 11a — Schottky uniformisation (Java plugin/schottky/*, ~3000 LoC)
Hyperbolic loxodromic group acting on S²; complement of the
Phase 10c Fuchsian-group representation in H². Requires
Phase 10b period matrix + Möbius-group machinery from Phase 7.
Effort: very large (4-6 weeks).
* 11b — Riemann maps (Java plugin/riemannmap/*, ~1500 LoC)
Discrete Riemann mapping theorem; texture mapping of bounded
planar regions, classical conformal mapping for engineering.
Requires Phase 10b' quasi-isothermic or Phase 9a.1 CP-Euclidean.
Effort: large (3-4 weeks).
Both are explicitly NOT roadmap commitments — they live in the doc so
they aren't re-discovered.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
conformallab++
C++17 reimplementation of 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 · CC BY-SA 4.0 · Java original · sechel.de
Status: Phase 7 complete. Newton solver for all three geometries (Euclidean / Spherical / HyperIdeal), priority-BFS layout in ℝ²/S²/Poincaré disk, Gauss–Bonnet, tree-cotree cut graph, Möbius holonomy, period matrix (genus 1), fundamental domain, halfedge_uv texture atlas, JSON/XML serialisation, CLI app. 176 CGAL tests + 36 non-CGAL tests.
Quick start
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)
./bin/conformallab_core -i input.off -g euclidean -o layout.off -j result.json
# API documentation (requires doxygen: brew/apt install doxygen)
cmake --build build --target doc
open doc/doxygen/html/index.html
Minimal usage
#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
| Getting started — build modes, single-test invocation, CLI, Docker | doc/getting-started.md |
| Pipeline API — all three geometries, holonomy, serialisation | doc/api/pipeline.md |
| Public headers — all 24 headers with descriptions | doc/api/headers.md |
| Test suites — 35 suites, 176+36 tests, individual counts | doc/api/tests.md |
| Extending — new functionals, geometry modes, porting from Java | doc/api/extending.md |
| Processing unit contracts — preconditions / provides table | doc/api/contracts.md |
| CGAL package design — Phase 8 target, YAML pipeline | doc/api/cgal-package.md |
| Architecture & pipeline diagram | doc/architecture/overall_pipeline.md |
| geometry-central comparison — shared core, demarcation, adoption candidates, scientific added value | doc/architecture/geometry-central-comparison.md |
| Design decisions — key architectural choices + rationale | doc/architecture/design-decisions.md |
| Project structure — directory tree + build targets | doc/architecture/project-structure.md |
| Discrete conformal theory — mathematical background for collaborators | doc/math/discrete-conformal-theory.md |
| Validation — known analytic results + how to verify them | doc/math/validation.md |
| Validation protocol — concrete commands with expected outputs | doc/math/validation-protocol.md |
| Tutorial: add a new functional — step-by-step Inversive-Distance port | doc/tutorials/add-inversive-distance.md |
| Declarative YAML pipeline — concept, token vocabulary, 5 examples | doc/concepts/declarative-pipeline.md |
| Geometry modes — Euclidean / Spherical / HyperIdeal comparison | doc/math/geometry-modes.md |
| References — all papers by module | doc/math/references.md |
| Software landscape — how conformallab++ relates to libigl, CGAL, geometry-central | doc/math/software-landscape.md |
| Novelty statement — unique features, target audience, what this is not | doc/math/novelty-statement.md |
| Complexity & scalability — O() analysis, measured timings on real meshes, HyperIdeal bottleneck | doc/math/complexity.md |
| Roadmap — Phases 1–10 | doc/roadmap/phases.md |
| Java parity table — what is ported, what is planned | doc/roadmap/java-parity.md |
| Contributing — language policy, test standards, release flow | doc/contributing.md |
| Claude Code context | CLAUDE.md |
Citing
If you use conformallab++ in your research, please cite it using the metadata
in 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
Bugs & questions
- Bug reports / feature requests: Gitea Issues
- Code mirror (read-only): Codeberg
- Contact: Tarik Moussa · Tarik.moussa95@gmail.com
License
conformallab++ is released under the MIT License (see LICENSE).
Copyright © 2024–2026 Tarik Moussa.
The dissertation (Sechelmann 2016) is CC BY-SA 4.0.