DDG Course Companion

Companion implementations and notes for Keenan Crane's Discrete Differential Geometry course.

Current state: educational and improving, not production-complete.

Status Snapshot

Area	Status	Notes
C++ core mesh + DDG algorithms	Partial	Boundary-safe topology, symmetric cotan operators, constrained solves; Hodge bases remain experimental
C# core mesh + DDG algorithms	Partial	Boundary-safe parity for topology, curvature, Laplacian, Heat divergence, and boundary mapping
Python tooling	Supported utility	Dependency-free OBJ topology inspector plus optional visualizer
Web companion	Interactive reference	Responsive workbench with a JS reference engine and optional WASM acceleration
Test coverage	Partial	Closed/open topology and Gauss–Bonnet coverage; broader parity datasets remain future work

See docs/status/IMPLEMENTATION_AUDIT.md for the detailed audit.

Implemented Algorithms by Language

Algorithm	C++	C#	Maturity
Cotan Laplacian	✅	✅	Partial (C# currently relies on simplified edge cotan path)
Mean Curvature Flow	✅	✅	Partial
Discrete Gaussian Curvature	✅	✅	Partial
Conformal Parameterization	✅	✅	Partial/Experimental
Heat Method	✅	✅	Partial/Experimental
Hodge Decomposition	✅	✅	Experimental

Legend: Complete = solidly validated and robust, Partial = implemented with known gaps, Experimental = scaffold/initial implementation, Planned = not yet implemented.

Quick Start

C++

cd src/cpp
cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j4
cd build
ctest --output-on-failure

C#

cd src/csharp
dotnet restore
dotnet build --configuration Release
cd Tests
dotnet test --configuration Release

WebAssembly

WASM bindings and demos live under src/wasm/. Open web/index.html for the interactive workbench; it falls back honestly to the JavaScript reference engine when compiled WASM artifacts are absent.

Repository Layout

src/cpp/        C++ core mesh, algorithms, tests, examples
src/csharp/     C# core mesh, algorithms, tests, CLI examples
src/wasm/       Emscripten bindings and wasm build config
docs/           Chapters, formulas, assignments, tutorials, status docs
examples/       Example usage notes and Python helper script
web/            Interactive scientific workbench and legacy WASM pages

Documentation

• docs/README.md
• docs/algorithms/README.md
• docs/formulas/index.md
• docs/assignments/README.md
• docs/tutorials/README.md
• docs/status/IMPLEMENTATION_AUDIT.md
• docs/status/NEXT_RELEASE_PLAN.md

Roadmap (Realistic)

1.2.0 release candidate

• Explicit boundary halfedges and topology validation in C++ and C#
• Symmetric cotan assembly and constrained Poisson infrastructure
• Boundary-aware curvature, Heat divergence, and harmonic disk mapping
• Dependency-free Python inspection and an interactive web workbench

Later

• True LSCM assembly, harmonic basis generation, and ARAP deformation
• Cross-language parity datasets and larger numerical regression suites

Contributing

See CONTRIBUTING.md for build/test workflow, contribution expectations, and documentation standards.

License

MIT (LICENSE).