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author | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2020-01-27 10:32:03 +0100 |
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committer | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2020-01-27 10:32:03 +0100 |
commit | 0ce82cdc262fe9c09a1df1f559e1c17abfbbea3d (patch) | |
tree | 56fcdcce7544a32899d0707c2274274df2c37d30 /src/Alpha_complex/doc/Intro_alpha_complex.h | |
parent | 7cd38c50d3843fd222d4210507bad948afe63912 (diff) | |
parent | 5d5f40493ce60f2a606793645bf713c60fb5284d (diff) |
Merge upstream and resolve conflict
Diffstat (limited to 'src/Alpha_complex/doc/Intro_alpha_complex.h')
-rw-r--r-- | src/Alpha_complex/doc/Intro_alpha_complex.h | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index 6931420a..60da7169 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -31,8 +31,8 @@ namespace alpha_complex { * 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. + * All simplices that have a filtration value \f$ > \alpha^2 \f$ are removed from the Delaunay complex + * when creating the simplicial complex if it is specified. * * \image html "alpha_complex_representation.png" "Alpha-complex representation" * @@ -46,8 +46,8 @@ namespace alpha_complex { * \cite cgal:s-gkd-19b from CGAL as template parameter. * * \remark - * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay - * complex with filtration values. The Delaunay complex without filtartion values is also available by passing + * - When the simplicial complex is constructed with an infinite value of \f$ \alpha^2 \f$, the complex is a Delaunay + * complex with special filtration values. The Delaunay complex without filtration values is also available by passing * `default_filtration_value=true` to `Alpha_complex::create_complex`. * - For people only interested in the topology of the \ref alpha_complex (for instance persistence), * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii. @@ -136,13 +136,13 @@ namespace alpha_complex { * * \subsubsection nondecreasing Non decreasing filtration values * - * As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not - * quite define a proper filtration (i.e. non-decreasing with respect to inclusion). + * As the squared radii computed by CGAL are an approximation, it might happen that these \f$ \alpha^2 \f$ 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. + * The simplex tree is pruned from the given maximum \f$ \alpha^2 \f$ value (cf. * `SimplicialComplexForAlpha::prune_above_filtration()`). * In the following example, the value is given by the user as argument of the program. * |