diff --git a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ConstructBoundingBox.cpp b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ConstructBoundingBox.cpp
index 7644372bfe6..480780d91fa 100644
--- a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ConstructBoundingBox.cpp
+++ b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ConstructBoundingBox.cpp
@@ -24,7 +24,35 @@ struct ConstructBoundingBox_impl
   CGAL::Bbox_2
   operator()(const X_monotone_curve_2& curve)
   {
-    return curve.bbox();
+    using Zero_resultant_exception = CGAL::internal::Zero_resultant_exception<
+      typename demo_types::Alg_seg_traits::Polynomial_2>;
+
+    CGAL::Bbox_2 bbox;
+    try
+    {
+      bbox= curve.bbox();
+    }
+    // algebraic traits sometimes when calling bbox
+    // example: xy=0
+    catch (std::exception& ex)
+    {
+      std::cerr << ex.what() << '\n';
+      std::cerr << __FILE__ << ':' << __LINE__ << '\n';
+      bbox = inf_bbox;
+    }
+    catch (Zero_resultant_exception& ex)
+    {
+      std::cerr << "Exception thrown of type \"Zero_resultant_exception\"\n";
+      std::cerr << __FILE__ << ':' << __LINE__ << '\n';
+      bbox = inf_bbox;
+    }
+    catch (...)
+    {
+      std::cerr << "Exception thrown of unknown type!\n";
+      std::cerr << __FILE__ << ':' << __LINE__ << '\n';
+      bbox = inf_bbox;
+    }
+    return bbox;
   }
 
   CGAL::Bbox_2
diff --git a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/EnvelopeCallback.cpp b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/EnvelopeCallback.cpp
index 10806249f35..25e6c602852 100644
--- a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/EnvelopeCallback.cpp
+++ b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/EnvelopeCallback.cpp
@@ -136,12 +136,13 @@ void EnvelopeCallback< Arr_>::updateEnvelope( bool lower )
   }
   catch (const std::exception& ex)
   {
-      std::cerr << ex.what() << '\n';
-      if (lower)
-        this->showLowerEnvelope(false);
-      else
-        this->showUpperEnvelope(false);
-      return;
+    std::cerr << ex.what() << '\n';
+    std::cerr << __FILE__ << ':' << __LINE__ << '\n';
+    if (lower)
+      this->showLowerEnvelope(false);
+    else
+      this->showUpperEnvelope(false);
+    return;
   }
 
   envelopeToUpdate->clear( );
diff --git a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/SplitEdgeCallback.cpp b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/SplitEdgeCallback.cpp
index 409befd82d1..8cec2d258c8 100644
--- a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/SplitEdgeCallback.cpp
+++ b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/SplitEdgeCallback.cpp
@@ -80,6 +80,7 @@ void SplitEdgeCallback<Arr_>::curveInputDoneEvent(
   catch (const std::exception& ex)
   {
     std::cerr << ex.what() << '\n';
+    std::cerr << __FILE__ << ':' << __LINE__ << '\n';
     return;
   }
 }
diff --git a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.cpp b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.cpp
index b01f9fec43d..fc61ccc5b26 100644
--- a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.cpp
+++ b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.cpp
@@ -384,7 +384,8 @@ Construct_x_monotone_subcurve_2<ArrTraits>::Construct_x_monotone_subcurve_2(
     compare_x_2(this->traits->compare_x_2_object()),
     compute_y_at_x(this->traits),
     construct_min_vertex_2(this->traits->construct_min_vertex_2_object()),
-    construct_max_vertex_2(this->traits->construct_max_vertex_2_object())
+    construct_max_vertex_2(this->traits->construct_max_vertex_2_object()),
+    parameter_space_in_x_2(this->traits)
 {
 }
 
@@ -396,10 +397,16 @@ auto Construct_x_monotone_subcurve_2<ArrTraits>::operator()(
   Point_2 pMin, pMax;
   bool unbounded_min = false;
   bool unbounded_max = false;
-  try { pMin = this->construct_min_vertex_2(curve); }
-  catch (...) { unbounded_min = true; }
-  try { pMax = this->construct_max_vertex_2(curve); }
-  catch (...) { unbounded_max = true; }
+
+  if (this->parameter_space_in_x_2(curve, CGAL::ARR_MIN_END) != CGAL::INTERIOR)
+    unbounded_min = true;
+  else
+    pMin = this->construct_min_vertex_2(curve);
+
+  if (this->parameter_space_in_x_2(curve, CGAL::ARR_MAX_END) != CGAL::INTERIOR)
+    unbounded_max = true;
+  else
+    pMax = this->construct_max_vertex_2(curve);
 
   X_monotone_curve_2 subcurve;
   X_monotone_curve_2 unusedTrimmings;
diff --git a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.h b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.h
index c09df74100b..a2f31717e28 100644
--- a/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.h
+++ b/Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils.h
@@ -14,6 +14,10 @@
 #include "GraphicsSceneMixin.h"
 #include "ArrTraitsAdaptor.h"
 
+#include <CGAL/tags.h>
+#include <CGAL/Arr_enums.h>
+#include <type_traits>
+
 class QGraphicsScene;
 
 template <typename ArrTraits >
@@ -276,23 +280,73 @@ public:
   double operator()(const Point_2& p, const X_monotone_curve_2& c) const;
 };
 
+// chcek if arrangement is a model of the concept ArrangementOpenBoundaryTraits_2
+template <typename ArrTraits>
+struct IsOpenBoundaryArrangement :
+    public CGAL::Boolean_tag<
+      std::is_convertible<
+        typename ArrTraits::Left_side_category,
+        CGAL::Arr_open_side_tag>::value &&
+      std::is_convertible<
+        typename ArrTraits::Bottom_side_category,
+        CGAL::Arr_open_side_tag>::value &&
+      std::is_convertible<
+        typename ArrTraits::Top_side_category,
+        CGAL::Arr_open_side_tag>::value &&
+      std::is_convertible<
+        typename ArrTraits::Right_side_category,
+        CGAL::Arr_open_side_tag>::value>
+{
+};
+
+template <typename ArrTraits, typename=void>
+class Param_space_in_x_2
+{
+public:
+  typedef typename ArrTraits::X_monotone_curve_2        X_monotone_curve_2;
+
+  Param_space_in_x_2(const ArrTraits*) {}
+  CGAL::Arr_parameter_space
+  operator()(const X_monotone_curve_2&, CGAL::Arr_curve_end)
+  {
+    return CGAL::INTERIOR;
+  }
+};
+
+template <typename ArrTraits>
+class Param_space_in_x_2<
+  ArrTraits, std::enable_if_t<IsOpenBoundaryArrangement<ArrTraits>::value>>
+{
+public:
+  typedef typename ArrTraits::X_monotone_curve_2        X_monotone_curve_2;
+  typedef typename ArrTraits::Parameter_space_in_x_2    Parameter_space_in_x_2;
+
+  Param_space_in_x_2(const ArrTraits* traits) :
+      parameter_space_in_x_2(traits->parameter_space_in_x_2_object())
+  {
+  }
+
+  CGAL::Arr_parameter_space
+  operator()(const X_monotone_curve_2& curve, CGAL::Arr_curve_end curve_end)
+  {
+    return this->parameter_space_in_x_2(curve, curve_end);
+  }
+
+private:
+  Parameter_space_in_x_2 parameter_space_in_x_2;
+};
+
 template <typename ArrTraits>
 class Construct_x_monotone_subcurve_2
 {
 public:
-  typedef typename ArrTraitsAdaptor<ArrTraits>::Kernel  Kernel;
   typedef typename ArrTraits::X_monotone_curve_2        X_monotone_curve_2;
   typedef typename ArrTraits::Split_2                   Split_2;
-  typedef typename ArrTraits::Intersect_2               Intersect_2;
-  typedef typename ArrTraits::Multiplicity              Multiplicity;
   typedef typename ArrTraits::Construct_min_vertex_2    Construct_min_vertex_2;
   typedef typename ArrTraits::Construct_max_vertex_2    Construct_max_vertex_2;
   typedef typename ArrTraits::Compare_x_2               Compare_x_2;
-  typedef typename Kernel::FT                           FT;
-  typedef typename ArrTraitsAdaptor< ArrTraits >::CoordinateType
-                                                        CoordinateType;
+  typedef Param_space_in_x_2<ArrTraits>                 Parameter_space_in_x_2;
   typedef typename ArrTraits::Point_2                   Point_2;
-  typedef typename Kernel::Point_2                      Kernel_point_2;
 
   Construct_x_monotone_subcurve_2( const ArrTraits* traits_ );
 
@@ -313,6 +367,7 @@ protected:
   Arr_compute_y_at_x_2< ArrTraits > compute_y_at_x;
   Construct_min_vertex_2 construct_min_vertex_2;
   Construct_max_vertex_2 construct_max_vertex_2;
+  Parameter_space_in_x_2 parameter_space_in_x_2;
 }; // class Construct_x_monotone_subcurve_2