Ajeet Kumar

Ajeet Kumar

Applied Mathematician with Specialization in Full Stack Machine Learning and Data Science

DDG — Advanced Discrete Differential Geometry Framework (Research-Grade)

Published:

A comprehensive, production-ready Discrete Exterior Calculus (DEC) / FEM implementation for triangle meshes with spectral geometry, curvature analysis, PDE solvers, and advanced vector field processing.

✅ ALL PHASES IMPLEMENTED (100% feature coverage)

🌟 Features Overview

  • Phase 1–2: Core DEC ✅
    • Half-edge mesh with adjacency queries
    • Exterior derivatives d₀, d₁ (topological matrices)
    • Hodge star operators *₀, *₁, *₂
    • Laplace–Beltrami operator
  • Phase 5A: Vector Operators ✅
    • gradient(u) — vertex scalar → edge values
    • divergence(v) — edge values → vertex scalar
    • curl(u) scalar and curl(v) vector forms
  • Phase 5B: Spectral + Shape ✅
    • Wave Kernel Signature (WKS) — advanced shape descriptor
    • Vertex normals, principal directions
    • Shape operator (Weingarten map)
  • Phase 5C: Advanced PDE ✅
    • Geodesic distance (heat method)
    • Hodge decomposition (curl-free + div-free + harmonic)
  • Phase 6: Visualization ✅
    • Polyscope integration (interactive 3D viewer)
    • Batch visualization API
  • Phase 7: I/O & Utilities ✅
    • OBJ, PLY, OFF file support
    • Auto-format detection

🚀 Quick Start

Installation

Install dependencies:

pip install -r requirements.txt
pip install polyscope  # For interactive 3D visualization (optional)

Run Demos

python examples/advanced_demo.py      # All features in one go
python examples/spectral_demo.py      # Eigenvalues + HKS
python examples/curvature_demo.py     # Curvature visualization
python examples/pde_demo.py           # PDE solvers

Run Tests

pytest tests/ -v

📚 Mathematical References

  • Crane et al. Discrete Differential Geometry: An Applied Introduction (2018)
  • Botsch et al. Polygon Mesh Processing (2010)
  • Meyer et al. Discrete differential-geometry operators for triangulated 2-manifolds (2003)
  • Crane et al. Geodesics in Heat (2013)

👥 Team Roster for ajeetkbhardwaj/discrete-differential-geometry

  • 👑 Team Leader:
    • ajeetkbhardwaj (Active Commits)
  • 👨‍💻 Team Members:
    • Open-Source Contributors (Active Commits)

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