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Diffstat (limited to 'src/Alpha_complex/doc/Intro_alpha_complex.h')
| -rw-r--r-- | src/Alpha_complex/doc/Intro_alpha_complex.h | 15 |
1 files changed, 8 insertions, 7 deletions
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index a8b1a106..60da7169 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -46,16 +46,17 @@ namespace alpha_complex { * \cite cgal:s-gkd-19b from CGAL as template parameter. * * \remark - * - When an \f$\alpha\f$-complex is constructed with an infinite value of \f$ \alpha^2 \f$, the complex is a Delaunay - * complex (with special filtration values). + * - When the simplicial complex is constructed with an infinite value of \f$ \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. * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii. - * - 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"> + * - Using the default `CGAL::Epeck_d` makes the construction safe. If you pass `exact=true` to + * `Alpha_complex::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 |