diff options
-rw-r--r-- | src/Alpha_complex/include/gudhi/Alpha_complex.h | 15 |
1 files changed, 13 insertions, 2 deletions
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h index b3d1e6ea..0c2569c8 100644 --- a/src/Alpha_complex/include/gudhi/Alpha_complex.h +++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h @@ -77,8 +77,19 @@ template<typename D> struct Is_Epeck_D<CGAL::Epeck_d<D>> { static const bool val * < <a target="_blank" href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dynamic__dimension__tag.html"> * CGAL::Dynamic_dimension_tag </a> > * - * \remark When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. - * + * \remark + * - When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. + * - Using the default `CGAL::Epeck_d` makes the construction safe. If you pass exact=true to create_complex, the + * filtration values are the exact ones converted to the filtration value type of the simplicial complex. This can be + * very slow. If you pass exact=false (the default), the filtration values are only guaranteed to have a small + * multiplicative error compared to the exact value, see <code><a class="el" target="_blank" + * href="https://doc.cgal.org/latest/Number_types/classCGAL_1_1Lazy__exact__nt.html"> + * CGAL::Lazy_exact_nt<NT>::set_relative_precision_of_to_double</a></code> for details. A drawback, when computing + * persistence, is that an empty exact interval [10^12,10^12] may become a non-empty approximate interval + * [10^12,10^12+10^6]. Using `CGAL::Epick_d` makes the computations slightly faster, and the combinatorics are still + * exact, but the computation of filtration values can exceptionally be arbitrarily bad. In all cases, we still + * guarantee that the output is a valid filtration (faces have a filtration value no larger than their cofaces). + * - For performances reasons, it is advised to use `Alpha_complex` with \ref cgal ≥ 5.0.0. */ template<class Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>> class Alpha_complex { |