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-.. 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: 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: `Eigen3 <installation.html#eigen3>`__ 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` |
- +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+