From 1b05ce304b4036a7a84b6108215e3516d2117e62 Mon Sep 17 00:00:00 2001 From: Simon Giraudot Date: Tue, 10 Oct 2017 11:35:02 +0200 Subject: [PATCH] Add a note on Wasserstein distance to make it clear it is not Hausdorff --- .../include/CGAL/Optimal_transportation_reconstruction_2.h | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h b/Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h index d9a552d5510..42d913a8ef0 100644 --- a/Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h +++ b/Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h @@ -1565,6 +1565,13 @@ public: collapse operators on the output simplex until the user-defined tolerance is reached. + \note The tolerance is given in the sense of the Wasserstein + distance. It is _not_ a Hausdorff tolerance: it does not mean that + the distance between the input samples and the output polyline is + guaranteed to be less than `tolerance`. It means that the square + root of transport cost per mass (homogeneous to a distance) is at + most `tolerance`. + \param tolerance Tolerance on the Wasserstein distance. */ void run_under_wasserstein_tolerance (const FT tolerance) {