diff --git a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
index 7ea9e73a8ad..4720d337470 100644
--- a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
+++ b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
@@ -270,6 +270,10 @@ namespace CGAL
           origin = boost::make_optional(interior.inside_point());
         }
 
+        // make sure the origin is on the negative side of all the planes
+        CGAL_assertion_code(for(PlaneIterator pit=begin;pit!=end;++pit))
+          CGAL_assertion(pit->has_on_negative_side(*origin));
+
         // compute the intersection of the half-space using the dual formulation
         Hull_traits_dual_3 dual_traits(*origin);
         Polyhedron_dual_3 dual_convex_hull;
diff --git a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_with_constructions_3.h b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_with_constructions_3.h
index 8fbd6384f50..99b72c759a1 100644
--- a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_with_constructions_3.h
+++ b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_with_constructions_3.h
@@ -146,6 +146,9 @@ namespace CGAL
             // construct dual points to apply the convex hull
             std::vector<Point> dual_points;
             for (PlaneIterator p = pbegin; p != pend; ++p) {
+                // make sure the origin is on the negative side of all the planes
+                CGAL_assertion(p->has_on_negative_side(p_origin));
+
                 // translate plane
                 Plane translated_p(p->a(),
                                    p->b(),