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Diffstat (limited to 'src/python/doc/alpha_complex_user.rst')
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 15 |
1 files changed, 8 insertions, 7 deletions
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index f9662a6d..950db3cd 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -9,19 +9,19 @@ Definition .. include:: alpha_complex_sum.inc -Alpha_complex is constructing a :doc:`Simplex_tree <simplex_tree_ref>` using +`AlphaComplex` is constructing a :doc:`SimplexTree <simplex_tree_ref>` using `Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ :cite:`cgal:hdj-t-15b` from `CGAL <http://www.cgal.org/>`_ (the Computational Geometry Algorithms Library :cite:`cgal:eb-15b`). Remarks ^^^^^^^ -When Alpha_complex is constructed with an infinite value of :math:`\alpha`, the complex is a Delaunay complex. +When an :math:`\alpha`-complex is constructed with an infinite value of :math:`\alpha`, the complex is a Delaunay complex (with special filtration values). Example from points ------------------- -This example builds the Delaunay triangulation from the given points, and initializes the alpha complex with it: +This example builds the alpha-complex from the given points: .. testcode:: @@ -139,15 +139,16 @@ Non decreasing filtration values As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not quite define a proper filtration (i.e. non-decreasing with respect to inclusion). -We fix that up by calling `Simplex_tree::make_filtration_non_decreasing()` (cf. +We fix that up by calling :func:`~gudhi.SimplexTree.make_filtration_non_decreasing` (cf. `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). Prune above given filtration value ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -The simplex tree is pruned from the given maximum alpha squared value (cf. `Simplex_tree::prune_above_filtration()` -in the `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). Note that this does not provide any kind -of speed-up, since we always first build the full filtered complex, so it is recommended not to use `max_alpha_square`. +The simplex tree is pruned from the given maximum alpha squared value (cf. +:func:`~gudhi.SimplexTree.prune_above_filtration`). Note that this does not provide any kind +of speed-up, since we always first build the full filtered complex, so it is recommended not to use +:paramref:`~gudhi.AlphaComplex.create_simplex_tree.max_alpha_square`. In the following example, a threshold of 59 is used. |