.. 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 `_) | | | 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 `__ :math:`\geq` 3.1.0 and `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` | +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+