triangulumancer 0.1.0

Construct triangulations of point configurations.

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 --recurse-submodules https://github.com/ariostas/triangulumancer.git
cd triangulumancer
pip install .
# You might need to set your LD_LIBRARY_PATH to include extern/topcom/external/lib.

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

License

All original triangulumancer code is distributed under the GNU General Public License version 3. The libraries it depends on, which can be found in the extern directory, are redistributed under their corresponding licenses.