The free function must call the functor

Cartesian_kernel/include/CGAL/Cartesian/function_objects.h

@@ -2741,6 +2741,7 @@ namespace CartesianKernelFunctors {
   {
     typedef typename K::FT        FT;
     typedef typename K::Point_2   Point_2;
+    typedef typename K::Segment_2 Segment_2;
   public:
     typedef Point_2          result_type;
 
@@ -2752,6 +2753,17 @@ namespace CartesianKernelFunctors {
       midpointC2(p.x(), p.y(), q.x(), q.y(), x, y);
       return construct_point_2(x, y);
     }
+
+    Point_2
+    operator()(const Segment_2& s) const
+    {
+      typename K::Construct_point_2 construct_point_2;
+      FT x, y;
+      const Point_2& p = s.source();
+      const Point_2& q = s.target();
+      midpointC2(p.x(), p.y(), q.x(), q.y(), x, y);
+      return construct_point_2(x, y);
+    }
   };
 
   template <typename K>
@@ -2759,6 +2771,7 @@ namespace CartesianKernelFunctors {
   {
     typedef typename K::FT        FT;
     typedef typename K::Point_3   Point_3;
+    typedef typename K::Segment_3 Segment_3;
   public:
     typedef Point_3               result_type;
 
@@ -2770,6 +2783,17 @@ namespace CartesianKernelFunctors {
       midpointC3(p.x(), p.y(), p.z(), q.x(), q.y(), q.z(), x, y, z);
       return construct_point_3(x, y, z);
     }
+
+    Point_3
+    operator()(const Segment_3& s) const
+    {
+      const Point_3& p = s.source();
+      const Point_3& q = s.target();
+      typename K::Construct_point_3 construct_point_3;
+      FT x, y, z;
+      midpointC3(p.x(), p.y(), p.z(), q.x(), q.y(), q.z(), x, y, z);
+      return construct_point_3(x, y, z);
+    }
   };
 
   template <typename K>