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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 | |
| | :math:`> \alpha^2` are removed from the Delaunay complex | |
| | when creating the simplicial complex if it is specified. | |
| | | |
| | 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` |
+----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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