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Diffstat (limited to 'src/python/doc/alpha_complex_user.rst')
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 19 |
1 files changed, 9 insertions, 10 deletions
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index b7e69e12..60319e84 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -16,7 +16,8 @@ Definition Remarks ^^^^^^^ -When an :math:`\alpha`-complex is constructed with an infinite value of :math:`\alpha`, the complex is a Delaunay complex (with special filtration values). +When an :math:`\alpha`-complex is constructed with an infinite value of :math:`\alpha^2`, +the complex is a Delaunay complex (with special filtration values). Example from points ------------------- @@ -137,19 +138,20 @@ sets the filtration value (0 in case of a vertex - propagation will have no effe 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). +As the squared radii computed by CGAL are an approximation, it might happen that these +:math:`\alpha^2` values do not quite define a proper filtration (i.e. non-decreasing with +respect to inclusion). 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. +The simplex tree is pruned from the given maximum :math:`\alpha^2` 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. +In the following example, a threshold of :math:`\alpha^2 = 32.0` is used. Example from OFF file @@ -166,7 +168,7 @@ Then, it is asked to display information about the alpha complex: import gudhi alpha_complex = gudhi.AlphaComplex(off_file=gudhi.__root_source_dir__ + \ '/data/points/alphacomplexdoc.off') - simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=59.0) + simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=32.0) result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ repr(simplex_tree.num_simplices()) + ' simplices - ' + \ repr(simplex_tree.num_vertices()) + ' vertices.' @@ -179,7 +181,7 @@ the program output is: .. testoutput:: - Alpha complex is of dimension 2 - 23 simplices - 7 vertices. + Alpha complex is of dimension 2 - 20 simplices - 7 vertices. [0] -> 0.00 [1] -> 0.00 [2] -> 0.00 @@ -200,9 +202,6 @@ the program output is: [4, 6] -> 22.74 [4, 5, 6] -> 22.74 [3, 6] -> 30.25 - [2, 6] -> 36.50 - [2, 3, 6] -> 36.50 - [2, 4, 6] -> 37.24 CGAL citations ============== |