src/cython/doc/alpha_complex_sum.inc


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

.. 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 simplex  | :Copyright: GPL v3                            |
   |                                                                | 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: Eigen3 and CGAL :math:`\geq` 4.7.0 |
   |                                                                | 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`                                                                                             |
   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+