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Add a note on Wasserstein distance to make it clear it is not Hausdorff

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Simon Giraudot 2017-10-10 11:35:02 +02:00
parent 7b8186a05b
commit 1b05ce304b
1 changed files with 7 additions and 0 deletions
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7
Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h
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@ -1565,6 +1565,13 @@ public:
collapse operators on the output simplex until the user-defined collapse operators on the output simplex until the user-defined
tolerance is reached. 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. \param tolerance Tolerance on the Wasserstein distance.
*/ */
void run_under_wasserstein_tolerance (const FT tolerance) { void run_under_wasserstein_tolerance (const FT tolerance) {