Triangulumancer

This project provides tools to construct $n$-dimensional triangulations of point configurations. It uses CGAL's dD Triangulations package to construct Delaunay and regular triangulations with given heights/weights, and it uses TOPCOM to find pulling/pushing triangulations, to find the list of available bistellar flips, and to find the complete list of triangulations of a point configuration.

The functionality and documentation of this project are currently fairly limited. If there is enough interest, I will continue to expand on both functionality and documentation. Please open an issue to ask for more functionality, or even better, make a pull request!

Installation

Triangulumancer can be installed in most cases simply by running

pip install triangulumancer

If you want to tweak compilation parameters or anything else, you can clone the repository and build the wheel yourself.

git clone https://github.com/ariostas/triangulumancer.git
cd triangulumancer
pip install .
# If you need to install the dependencies yourself, you can do so with
# conda install -c conda-forge c-compiler cxx-compiler eigen cgal gmp libboost cddlib cmake

Usage

Here is a basic example that shows the available functionality.

>>> from triangulumancer import PointConfiguration
>>>
>>> p = PointConfiguration(
...     [[0, 0], [1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]
... )
>>> p
A 2-dimensional point configuration with 9 points
>>> t_delaunay = p.delaunay_triangulation()
>>> t_delaunay
A triangulation with 8 simplices of a point configuration with 9 points
>>> t_heights = p.triangulate_with_heights([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> t_heights
A triangulation with 8 simplices of a point configuration with 9 points
>>> t_weights = p.triangulate_with_weights([1, 2, 3, 4, 5, 6, 7, 8, 9])
A triangulation with 5 simplices of a point configuration with 9 points
>>> t_placing = p.placing_triangulation()
A triangulation with 8 simplices of a point configuration with 9 points
>>> t_placing_neighbors = t_placing.neighbors()
>>> len(t_placing_neighbors)
6
>>> list_t_connected = p.all_connected_triangulations()
>>> len(list_t_connected)
>>> 387
>>> list_t_connected_fine = p.all_connected_triangulations(only_fine=True)
>>> len(list_t_connected_fine)
64
>>> list_t_all = p.all_triangulations()
>>> len(list_t_all)
387
>>> list_t_all_fine = p.all_triangulations(only_fine=True)
>>> len(list_t_all_fine)
64

There is equivalent functionality for vector configurations, but it is not fully complete and has not been tested as much, so we have not included it in the example above.

Please open an issue if have any issues or want to see more functionality. Pull requests are also welcome!

License

All original triangulumancer code is distributed under the GNU General Public License version 3. It directly depends on CGAL and TOPCOM. Since packaged versions of triangulumancer include CGAL and TOPCOM, the license of those packages also applies. Please refer to the CGAL and TOPCOM websites for more information.