src/python/doc/alpha_complex_sum.inc


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

.. table::
   :widths: 30 50 20

   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
   | .. figure::                                                    | Alpha complex is a simplicial complex constructed from the finite      | :Author: Vincent Rouvreau                                                                                                   |
   |      ../../doc/Alpha_complex/alpha_complex_representation.png  | cells of a Delaunay Triangulation.                                     |                                                                                                                             |
   |      :alt: Alpha complex representation                        |                                                                        | :Introduced in: GUDHI 2.0.0                                                                                                 |
   |      :figclass: align-center                                   | The filtration value of each simplex is computed as the **square** of  |                                                                                                                             |
   |                                                                | the circumradius of the simplex if the circumsphere is empty (the      | :Copyright: MIT (`GPL v3 </licensing/>`_)                                                                                   |
   |                                                                | simplex is then said to be Gabriel), and as the minimum of the         |                                                                                                                             |
   |                                                                | filtration values of the codimension 1 cofaces that make it not        | :Requires: `Eigen <installation.html#eigen>`__ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 |
   |                                                                | Gabriel otherwise.                                                     |                                                                                                                             |
   |                                                                |                                                                        |                                                                                                                             |
   |                                                                | For performances reasons, it is advised to use CGAL ≥ 5.0.0.           |                                                                                                                             |
   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
   | * :doc:`alpha_complex_user`                                    | * :doc:`alpha_complex_ref`                                                                                                                                                                           |
   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+