diff --git a/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Data_structure.h b/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Data_structure.h
index 4dda920a5f0..b1d30735608 100644
--- a/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Data_structure.h
+++ b/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Data_structure.h
@@ -1459,6 +1459,8 @@ public:
     CGAL_assertion(pvertices[idx] == null_pvertex());
     pvertices[idx] = propagated;
 
+    CGAL_assertion(is_correctly_oriented(
+      propagated.first, future_direction, ivertex, iedge));
     // CGAL_assertion_msg(false, "TODO: CREATE NEW PVERTEX!");
   }
 
@@ -2349,8 +2351,16 @@ public:
   **    CHECKING PROPERTIES     **
   ********************************/
 
-  bool belongs_to_iedge(const PVertex& /*pvertex*/, const IEdge& /*iedge*/) const {
-    return true; // TODO: finish this using dot products and orientations!
+  bool is_correctly_oriented(
+    const std::size_t sp_idx, const Vector_2& direction,
+    const IVertex& ivertex, const IEdge& iedge) const {
+
+    CGAL_assertion(direction.squared_length() != FT(0));
+    const auto overtex = opposite(iedge, ivertex);
+    const Vector_2 ref_direction(
+      point_2(sp_idx, ivertex), point_2(sp_idx, overtex));
+    const FT vec_dot = direction * ref_direction;
+    return (vec_dot >= FT(0));
   }
 
   template<typename Pair>
diff --git a/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Propagation.h b/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Propagation.h
index 3bac50bba02..bb263e2ac16 100644
--- a/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Propagation.h
+++ b/Kinetic_shape_reconstruction/include/CGAL/KSR_3/Propagation.h
@@ -1716,7 +1716,8 @@ private:
       m_data.direction(cropped) = future_direction;
       if (m_verbose) std::cout << "- cropped: " <<
         m_data.str(cropped) << ", " << m_data.point_3(cropped) << std::endl;
-      // CGAL_assertion(m_data.belongs_to_iedge(cropped, iedge_0)); // Can we do it more precise?
+      CGAL_assertion(m_data.is_correctly_oriented(
+        cropped.first, future_direction, ivertex, iedge_0));
     }
 
     // Create new pfaces if any.
@@ -1921,6 +1922,8 @@ private:
       m_data.direction(cropped) = future_direction;
       if (m_verbose) std::cout << "- cropped: " <<
         m_data.str(cropped) << ", " << m_data.point_3(cropped) << std::endl;
+      CGAL_assertion(m_data.is_correctly_oriented(
+        cropped.first, future_direction, ivertex, iedge_0));
     }
 
     // Create new pfaces if any.
@@ -2266,6 +2269,8 @@ private:
       m_data.direction(cropped) = future_directions.front();
       if (m_verbose) std::cout << "- cropped 1: " <<
         m_data.str(cropped) << ", " << m_data.point_3(cropped) << std::endl;
+      CGAL_assertion(m_data.is_correctly_oriented(
+        cropped.first, future_directions.front(), ivertex, crossed_iedges.front().first));
     }
 
     { // second crop
@@ -2299,6 +2304,8 @@ private:
       m_data.direction(cropped) = future_directions.back();
       if (m_verbose) std::cout << "- cropped 2: " <<
         m_data.str(cropped) << ", " << m_data.point_3(cropped) << std::endl;
+      CGAL_assertion(m_data.is_correctly_oriented(
+        cropped.first, future_directions.back(), ivertex, crossed_iedges.back().first));
     }
 
     // Create new pfaces if any.