From e56c6dbeb1b4a0139e3d329e4d29a71c65f28ba9 Mon Sep 17 00:00:00 2001 From: ROUVREAU Vincent Date: Wed, 4 Dec 2019 09:35:51 +0100 Subject: Delaunay triangulation for alpha complex in dD --- src/Alpha_complex/doc/Intro_alpha_complex.h | 13 +++++++------ 1 file changed, 7 insertions(+), 6 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 3c32a1e6..6931420a 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -47,15 +47,16 @@ namespace alpha_complex { * * \remark * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay - * complex. + * complex with filtration values. The Delaunay complex without filtartion 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 + * - 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 + * * CGAL::Lazy_exact_nt::set_relative_precision_of_to_double 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 -- cgit v1.2.3