src/cython/doc/alpha_complex_sum.inc


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   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
   | .. 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 simplex  | :Copyright: MIT (`GPL v3 </licensing/>`_)                                                                                   |
   |                                                                | is then said to be Gabriel), and as the minimum of the filtration      |                                                                                                                             |
   |                                                                | values of the codimension 1 cofaces that make it not Gabriel           | :Requires: `Eigen <installation.html#eigen>`__ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 |
   |                                                                | otherwise. All simplices that have a filtration value strictly         |                                                                                                                             |
   |                                                                | greater than a given alpha squared value are not inserted into the     |                                                                                                                             |
   |                                                                | complex.                                                               |                                                                                                                             |
   |                                                                |                                                                        |                                                                                                                             |
   |                                                                | This package requires having CGAL version 4.7 or higher (4.8.1 is      |                                                                                                                             |
   |                                                                | advised for better performance).                                       |                                                                                                                             |
   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
   | * :doc:`alpha_complex_user`                                    | * :doc:`alpha_complex_ref`                                                                                                                                                                           |
   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+