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authorThéo Lacombe <lacombe1993@gmail.com>2020-06-29 10:24:44 +0200
committerGitHub <noreply@github.com>2020-06-29 10:24:44 +0200
commit0b4de61a18bc30f66a7fb45cc246cff2f55ba1a1 (patch)
tree47527fd4d63632f3c39a6f2660ec141417f093b6 /src/python/doc/alpha_complex_sum.inc
parent6c65d29acc3b03d21beca653834340787bf0c65e (diff)
parentcec4a5d7df6d5ed43511e94f9db580489979105a (diff)
Merge branch 'master' into fix342
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@@ -3,15 +3,13 @@
+----------------------------------------------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------+
| .. 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 | | :Since: 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 | :License: MIT (`GPL v3 </licensing/>`_) |
- | | simplex is then said to be Gabriel), and as the minimum of the | |
- | | filtration values of the codimension 1 cofaces that make it not | :Requires: `Eigen <installation.html#eigen>`_ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`_ :math:`\geq` 4.11.0 |
- | | Gabriel otherwise. | |
+ | ../../doc/Alpha_complex/alpha_complex_representation.png | cells of a Delaunay Triangulation. It has the same persistent homology | |
+ | :alt: Alpha complex representation | as the Čech complex and is significantly smaller. | :Since: GUDHI 2.0.0 |
+ | :figclass: align-center | | |
+ | | | :License: MIT (`GPL v3 </licensing/>`_) |
+ | | | |
+ | | | :Requires: `Eigen <installation.html#eigen>`_ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`_ :math:`\geq` 4.11.0 |
| | | |
- | | For performances reasons, it is advised to use CGAL :math:`\geq` 5.0.0. | |
+----------------------------------------------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------+
| * :doc:`alpha_complex_user` | * :doc:`alpha_complex_ref` |
+----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+