Chalc Documentation

Chalc is a Python package for computing chromatic Delaunay filtrations of labelled point clouds in Euclidean space, and their persistent homology. Chalc is named for chromatic alpha complexes, but it can also compute chromatic Delaunay–Čech and chromatic Delaunay–Rips filtrations. Chalc is written in C++ and relies on the Computational Geometry Algorithms Library (CGAL) for fast and accurate geometric computations, and Phimaker for persistent homology calculations.

Documentation index

• Installation
  • Using pip
  • Build from source
  • Building the Documentation
• Example Usage
• API Reference
  • chalc
• License
  • GNU General Public License (“GPL”) copyright permissions statement:

Citing this Software

If you want to use chalc in your work, please use the following citation:

Text

Abhinav Natarajan, Thomas Chaplin, Adam Brown, and Maria-Jose Jimenez. “Morse Theory for Chromatic Delaunay Triangulations”. May 30, 2024. arXiv: 2405.19303.

BibTex

@misc{natarajan2024morse,
   title={Morse Theory for Chromatic Delaunay Triangulations},
   author={Abhinav Natarajan and Thomas Chaplin and Adam Brown and Maria-Jose Jimenez},
   year={2024},
   eprint={2405.19303},
   archivePrefix={arXiv},
   primaryClass={math.AT}
}

See Also

The Python package chromatic-tda (written by the original authors of [1]) provides similar functionality, but is currently limited to points in two dimensions with upto three colours, although an alpha version with support for higher dimensions is available.

References

1. Sebastiano Cultrera di Montesano, Ondřej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes”. Feb. 7, 2024. arXiv: 2212.03128.