diff --git a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/pwsrec.ui b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/pwsrec.ui
index 229957863c0..4a2a9b0eda4 100644
--- a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/pwsrec.ui
+++ b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/pwsrec.ui
@@ -42,7 +42,7 @@
      <x>0</x>
      <y>0</y>
      <width>680</width>
-     <height>21</height>
+     <height>22</height>
     </rect>
    </property>
    <widget class="QMenu" name="menuFile">
@@ -97,6 +97,7 @@
     <addaction name="actionReconstruction_100_steps"/>
     <addaction name="actionReconstruction_1000_steps"/>
     <addaction name="actionReconstruction_until"/>
+    <addaction name="actionReconstruction_Wasserstein_tolerance"/>
     <addaction name="separator"/>
     <addaction name="actionRelocate_vertices"/>
     <addaction name="actionReconstruction_reinit"/>
@@ -596,6 +597,14 @@
     <string>Output to console</string>
    </property>
   </action>
+  <action name="actionReconstruction_Wasserstein_tolerance">
+   <property name="text">
+    <string>Run under Wasserstein tolerance...</string>
+   </property>
+   <property name="shortcut">
+    <string>W</string>
+   </property>
+  </action>
  </widget>
  <customwidgets>
   <customwidget>
diff --git a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/scene.h b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/scene.h
index 587f22ca60f..cd8c84b6bfd 100644
--- a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/scene.h
+++ b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/scene.h
@@ -227,9 +227,14 @@ public:
 
   void load(const QString& filename, QWidget* qw) {
 
-    if (filename.contains(".xy", Qt::CaseInsensitive)) {
+    if (filename.contains(".xyz", Qt::CaseInsensitive)) {
+      load_xyz_file(filename);
+      //      normalize_points();
+      return;
+    }
+    else if (filename.contains(".xy", Qt::CaseInsensitive)) {
       load_xy_file(filename);
-      normalize_points();
+      //      normalize_points();
       return;
     }
 
@@ -279,6 +284,25 @@ public:
     ifs.close();
   }
 
+  void load_xyz_file(const QString& fileName) {
+
+    std::cout << "filename: " << fileName.toUtf8().constData() << std::endl;
+    std::ifstream ifs(qPrintable(fileName));
+    std::cerr << "reading xyz...";
+    unsigned int nb = 0;
+    std::string str;
+    while (getline (ifs, str)) {
+      std::istringstream iss (str);
+      double x = 0., y = 0.;
+      iss >> x >> y;
+      str.clear();
+      add_sample(Point (x, y), 1.0);
+      nb++;
+    }
+    std::cerr << "done (" << nb << " points)" << std::endl;
+    ifs.close();
+  }
+
 
 #ifdef CGAL_USE_CIMG
   void load_image(const QString& fileName) {
@@ -486,6 +510,13 @@ public:
     m_pwsrec->run_until(nv);
   }
 
+  void reconstruct_wasserstein_tolerance (const double tolerance) {
+    std::cout << "reconstruct_wasserstein_tolerance" << std::endl;
+    if (!m_init_done)
+      init_reconstruction(m_percentage);
+    m_pwsrec->run_under_wasserstein_tolerance (tolerance);
+  }
+
   void reconstruct(const unsigned int steps) {
     std::cout << "reconstruct" << std::endl;
     if (!m_init_done)
diff --git a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.cpp b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.cpp
index 31dbfff7da3..def2d275888 100644
--- a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.cpp
+++ b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.cpp
@@ -527,6 +527,22 @@ void MainWindow::on_actionReconstruction_until_triggered()
   update();
 }
 
+void MainWindow::on_actionReconstruction_Wasserstein_tolerance_triggered()
+{
+  bool ok;
+  double tolerance = QInputDialog::getDouble(
+      this, tr("Wasserstein tolerance"), tr("Tolerance:"), 0.1, 0., 1000000., 2, &ok);
+  if (!ok) return;
+
+  set_scene_options();
+
+  QApplication::setOverrideCursor(Qt::WaitCursor);
+  m_scene->reconstruct_wasserstein_tolerance (tolerance);
+  QApplication::restoreOverrideCursor();
+
+  update();
+}
+
 void MainWindow::on_actionRelocate_vertices_triggered()
 {
   QApplication::setOverrideCursor(Qt::WaitCursor);
diff --git a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.h b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.h
index 07a80ac05b9..5913807cb4e 100644
--- a/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.h
+++ b/Optimal_transportation_reconstruction_2/demo/Optimal_transportation_reconstruction_2/window.h
@@ -95,6 +95,7 @@ public:
   void on_actionReconstruction_100_steps_triggered();
   void on_actionReconstruction_1000_steps_triggered();
   void on_actionReconstruction_until_triggered();
+  void on_actionReconstruction_Wasserstein_tolerance_triggered();
   void on_actionRelocate_vertices_triggered();
   void on_actionReconstruction_reinit_triggered();
   void on_actionOutput_console_triggered();