From 7865ef2cc4abd972b2ba1eb50790912820fa2ee2 Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Tue, 25 Sep 2018 16:05:33 +0000 Subject: clang-format all files Add safe version alpha complex 3d persistence utility git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alpha_complex_3d_module_vincent@3907 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 54b2d0de9231511864df9fa637b60b7ccf34f50f --- src/Alpha_complex/doc/Intro_alpha_complex.h | 76 ++++++++++++++--------------- 1 file changed, 38 insertions(+), 38 deletions(-) (limited to 'src/Alpha_complex/doc/Intro_alpha_complex.h') diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index 82aee275..648fb6d6 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -29,34 +29,34 @@ namespace Gudhi { namespace alpha_complex { /** \defgroup alpha_complex Alpha complex - * + * * \author Vincent Rouvreau * * @{ - * + * * \section definition Definition - * + * * Alpha_complex is a simplicial complex * constructed from the finite cells of a Delaunay Triangulation. - * + * * The filtration value of each simplex is computed as the square of the circumradius of the simplex if the * circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration * values of the codimension 1 cofaces that make it not Gabriel otherwise. - * + * * All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into * the complex. - * + * * \image html "alpha_complex_representation.png" "Alpha-complex representation" - * + * * Alpha_complex is constructing a Delaunay Triangulation * \cite cgal:hdj-t-15b from CGAL (the Computational Geometry * Algorithms Library \cite cgal:eb-15b) and is able to create a `SimplicialComplexForAlpha`. - * + * * The complex is a template class requiring an Epick_d dD Geometry Kernel * \cite cgal:s-gkd-15b from CGAL as template parameter. - * + * * \remark * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay * complex. @@ -65,30 +65,30 @@ namespace alpha_complex { * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii. * * \section pointsexample Example from points - * + * * This example builds the Delaunay triangulation from the given points in a 2D static kernel, and creates a * `Simplex_tree` with it. - * + * * Then, it is asked to display information about the simplicial complex. - * + * * \include Alpha_complex/Alpha_complex_from_points.cpp - * + * * When launching: - * + * * \code $> ./Alpha_complex_example_from_points * \endcode * * the program output is: - * + * * \include Alpha_complex/alphaoffreader_for_doc_60.txt - * + * * \section createcomplexalgorithm Create complex algorithm - * + * * \subsection datastructure Data structure - * + * * In order to create the simplicial complex, first, it is built from the cells of the Delaunay Triangulation. * The filtration values are set to NaN, which stands for unknown value. - * + * * In example, : * \image html "alpha_complex_doc.png" "Simplicial complex structure construction example" * @@ -118,53 +118,53 @@ namespace alpha_complex { * \f$ * * \subsubsection dimension2 Dimension 2 - * + * * From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...), * computes the filtration value of the triangle, and then propagates the filtration value as described * here : * \image html "alpha_complex_doc_420.png" "Filtration value propagation example" - * + * * \subsubsection dimension1 Dimension 1 - * + * * Then, the algorithm looks into each edge ([0,1], [0,2], [1,2], ...), * computes the filtration value of the edge (in this case, propagation will have no effect). - * + * * \subsubsection dimension0 Dimension 0 - * + * * Finally, the algorithm looks into each vertex ([0], [1], [2], [3], [4], [5] and [6]) and * sets the filtration value (0 in case of a vertex - propagation will have no effect). - * + * * \subsubsection nondecreasing 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 `SimplicialComplexForAlpha::make_filtration_non_decreasing()`. - * + * * \subsubsection pruneabove Prune above given filtration value - * + * * The simplex tree is pruned from the given maximum alpha squared value (cf. * `SimplicialComplexForAlpha::prune_above_filtration()`). * In the following example, the value is given by the user as argument of the program. - * - * + * + * * \section offexample Example from OFF file - * + * * This example builds the Delaunay triangulation in a dynamic kernel, and initializes the alpha complex with it. - * - * + * + * * Then, it is asked to display information about the alpha complex. - * + * * \include Alpha_complex/Alpha_complex_from_off.cpp - * + * * When launching: - * + * * \code $> ./Alpha_complex_example_from_off ../../data/points/alphacomplexdoc.off 32.0 * \endcode * * the program output is: - * + * * \include Alpha_complex/alphaoffreader_for_doc_32.txt - * + * * * \section weighted3dexample 3d specific example * -- cgit v1.2.3