diff options
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 3c32a1e6..a8b1a106 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. + * - When an \f$\alpha\f$-complex is constructed with an infinite value of \f$ \alpha^2 \f$, the complex is a Delaunay + * complex (with special filtration values). * - For people only interested in the topology of the \ref alpha_complex (for instance persistence), * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii. * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii. @@ -135,13 +135,13 @@ namespace alpha_complex { * * \subsubsection nondecreasing Non decreasing filtration values * - * As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not - * quite define a proper filtration (i.e. non-decreasing with respect to inclusion). + * As the squared radii computed by CGAL are an approximation, it might happen that these \f$ \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. * |