diff --git a/.gitattributes b/.gitattributes
index edbc8d1a5f8..097cb4a8d21 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -1283,6 +1283,7 @@ Circular_kernel_2/demo/Circular_kernel_2/help/sweeper.jpeg -text svneol=unset#im
 Circular_kernel_2/demo/Circular_kernel_2/help/trash.jpeg -text svneol=unset#image/jpeg
 Circular_kernel_2/doc_tex/Circular_kernel_2/fig/Boolean_operation.png -text
 Circular_kernel_2/doc_tex/Circular_kernel_2/fig/Boolean_operation_detail.png -text
+Circular_kernel_2/doc_tex/Circular_kernel_2_ref/global_functions.tex -text
 Circular_kernel_2/examples/Circular_kernel_2/functor_has_on_2.cpp -text
 Circular_kernel_2/include/CGAL/Circular_kernel_intersections.h -text
 Circular_kernel_2/include/CGAL/Filtered_bbox_circular_kernel_2/interface_macros.h -text
diff --git a/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/global_functions.tex b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/global_functions.tex
new file mode 100644
index 00000000000..5d262eb1256
--- /dev/null
+++ b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/global_functions.tex
@@ -0,0 +1,104 @@
+\begin{ccRefFunction}{x_extremal_point}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{Circular_arc_point_2<CircularKernel>
+  x_extremal_point(const Circle_2<CircularKernel> & c, bool i);}
+{Returns the $i^{th}$ $x$-extremal point of the circle.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{y_extremal_point}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{Circular_arc_point_2<CircularKernel>
+  y_extremal_point(const Circle_2<CircularKernel> & c, bool i);}
+{Returns the $i^{th}$ $y$-extremal point of the circle.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{x_extremal_points}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{template < class OutputIterator >
+  OutputIterator
+  x_extremal_points(const Circle_2<CircularKernel> & c,
+  OutputIterator res);}
+{Copies in the output iterator the $x$-extremal points of the
+  circle. \ccc{res} iterates on elements of type
+  \ccc{Circular_arc_point_2<CircularKernel>}, sorted in $x$.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{y_extremal_points}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{template < class OutputIterator >
+  OutputIterator
+  y_extremal_points(const Circle_2<CircularKernel> & c,
+                    OutputIterator res);}
+{Copies in the output iterator the $y$-extremal points of the
+  circle. \ccc{res} iterates on elements of type
+  \ccc{Circular_arc_point_2<CircularKernel>}, sorted in $y$.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{has_on}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{bool
+  has_on(const Circle_2<CircularKernel> &c, 
+         const Circular_arc_point_2<CircularKernel> &p);}
+{Checks whether the point lies on the circle.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{compare_y_to_right}
+
+\ccFunction{CGAL::Comparison_result 
+  compare_y_to_right(const Circular_arc_2<CircularKernel> &ca1,
+                     const Circular_arc_2<CircularKernel> &ca2,
+                     Circular_arc_point_2<CircularKernel> &p);}
+{Compares vertically the two arcs, to the right of the point $p$,
+\ccPrecond{$p$ is an intersection point of the arcs, and the arcs are
+  defined to the right of $p$.}}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{point_in_x_range}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{bool 
+  point_in_x_range(const Circular_arc_2<CircularKernel> &ca, 
+                   const Circular_arc_point_2<CircularKernel> &p);}
+{Checks whether the point lies in the vertical range defined by the
+  arc.}
+
+\ccFunction{bool 
+  point_in_x_range(const Line_arc_2<CircularKernel> &ca, 
+                   const Circular_arc_point_2<CircularKernel> &p);}
+{Checks whether the point lies in the vertical range defined by the
+  line segment.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{make_x_monotone}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{template < class OutputIterator >
+  OutputIterator
+  make_x_monotone(const Circular_arc_2<CircularKernel> &ca, 
+                  OutputIterator res);}
+{Copies in the output iterator the $x$-monotone sub-arcs of $ca$.}
+
+\end{ccRefFunction}
+\begin{ccRefFunction}{make_xy_monotone}
+
+\ccInclude{CGAL/global_functions_circular_kernel_2.h}
+
+\ccFunction{template < class OutputIterator >
+  OutputIterator
+  make_xy_monotone(const Circular_arc_2<CircularKernel> &ca, 
+                  OutputIterator res);}
+{Copies in the output iterator the $xy$-monotone sub-arcs of $ca$.}
+
+\end{ccRefFunction}
\ No newline at end of file
diff --git a/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/intro.tex b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/intro.tex
index 2c9c5f7fcee..6950f3af411 100644
--- a/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/intro.tex
+++ b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/intro.tex
@@ -54,7 +54,8 @@
 \ccRefConceptPage{CircularKernel::IsXMonotone_2}\\
 \ccRefConceptPage{CircularKernel::IsYMonotone_2}
 
-\ccRefConceptPage{CircularKernel::MakeXMonotone_2}
+\ccRefConceptPage{CircularKernel::MakeXMonotone_2}\\
+\ccRefConceptPage{CircularKernel::MakeXYMonotone_2}
 
 \ccRefConceptPage{CircularKernel::Intersect_2}
 
@@ -84,9 +85,28 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Geometric Global Functions}	
 
+\ccRefIdfierPage{CGAL::compare_x}\\
+\ccRefIdfierPage{CGAL::compare_y}\\
+\ccRefIdfierPage{CGAL::compare_xy}
+
+\ccRefIdfierPage{CGAL::compare_y_at_x}\\
+\ccRefIdfierPage{CGAL::compare_y_to_right}\\
+\ccRefIdfierPage{CGAL::point_in_x_range}
+
+\ccRefIdfierPage{CGAL::has_on}
+
 \ccRefIdfierPage{CGAL::do_intersect}\\
 \ccRefIdfierPage{CGAL::intersection}
 
+\ccRefIdfierPage{CGAL::x_extremal_point}\\
+\ccRefIdfierPage{CGAL::y_extremal_point}\\
+\ccRefIdfierPage{CGAL::x_extremal_points}\\
+\ccRefIdfierPage{CGAL::y_extremal_points}
+
+\ccRefIdfierPage{CGAL::make_x_monotone}\\
+\ccRefIdfierPage{CGAL::make_xy_monotone}
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Algebraic Concepts}
 
diff --git a/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/main.tex b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/main.tex
index f7202f5fc5b..709d16f0403 100644
--- a/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/main.tex
+++ b/Circular_kernel_2/doc_tex/Circular_kernel_2_ref/main.tex
@@ -30,6 +30,10 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
+\input{Circular_kernel_2_ref/global_functions}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 \input{Circular_kernel_2_ref/AlgebraicKernelForCircles} %concept
 \input{Circular_kernel_2_ref/Algebraic_kernel_for_circles_2_2}