diff --git a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
index dad73e6596e..8fd9d3dea39 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
index 1e60dfb961f..3ebb14854f4 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
index cc24b22f2e2..b7629d63077 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/spec_oops.tex b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/spec_oops.tex
index a744e9e47a9..f3e82c7772f 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/spec_oops.tex
+++ b/Packages/Min_quadrilateral_2/doc_tex/Optimisation_ref/spec_oops.tex
@@ -42,22 +42,21 @@
   exactly this point is written to \ccc{o}.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
   
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}. Otherwise \ccc{VT}
+    is \ccc{CGAL::Point_2<Kernel>} for some kernel \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -65,7 +64,7 @@
   \ccRefIdfierPage{CGAL::min_parallelogram_2}\\
   \ccRefIdfierPage{CGAL::min_strip_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm \cite{t-sgprc-83}
@@ -111,22 +110,22 @@
   exactly this point is written to \ccc{o}.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
 
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}. Otherwise
+    \ccc{VT} is \ccc{CGAL::Point_2<Kernel>} for some Kernel
+    \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -134,7 +133,7 @@
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
   \ccRefIdfierPage{CGAL::min_strip_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm
@@ -180,22 +179,21 @@
   remains unchanged.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
 
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise \ccc{VT}
+    is \ccc{CGAL::Point_2<Kernel>} for some kernel \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -203,7 +201,7 @@
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
   \ccRefIdfierPage{CGAL::min_parallelogram_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm \cite{t-sgprc-83}
@@ -217,14 +215,14 @@
 
 \end{ccRefFunction}
     
-\begin{ccRefClass}{Min_quadrilateral_default_traits_2<R>}
+\begin{ccRefClass}{Min_quadrilateral_default_traits_2<Kernel>}
   \ccCreationVariable{t}\ccTagFullDeclarations
   
   \ccDefinition The class \ccRefName\ is a traits class for the
   functions \ccc{min_rectangle_2}, \ccc{min_parallelogram_2} and
-  \ccc{min_strip_2} using the two-dimensional \cgal\ kernel.
+  \ccc{min_strip_2} using a two-dimensional \cgal\ kernel.
   
-  \ccRequirements The template parameter \ccc{R} is a model for
+  \ccRequirements The template parameter \ccc{Kernel} is a model for
   \ccc{Kernel}.
   
   \ccInclude{CGAL/Min_quadrilateral_traits_2.h}
@@ -236,11 +234,13 @@
   
   \ccTwo{Minq_traits::Rotate_direction_by_multiple_of_pi_22}{}
   
-  \ccNestedType{Point_2}{typedef to \ccc{R::Point_2}}
+  \ccNestedType{Point_2}{\ccRefConceptPage{Kernel::Point_2}.}
   
-  \ccNestedType{Direction_2}{typedef to \ccc{R::Direction_2}}
+  \ccNestedType{Vector_2}{\ccRefConceptPage{Kernel::Vector_2}.}
   
-  \ccNestedType{Line_2}{typedef to \ccc{R::Line_2}}
+  \ccNestedType{Direction_2}{\ccRefConceptPage{Kernel::Direction_2}.}
+  
+  \ccNestedType{Line_2}{\ccRefConceptPage{Kernel::Line_2}.}
   
   \ccNestedType{Rectangle_2}{internal type.}
   
@@ -248,42 +248,19 @@
   
   \ccNestedType{Strip_2}{internal type.}
   
-  \ccNestedType{Equal_2}{AdaptableBinaryFunction class\\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    Returns true, iff the two points are equal.}
+  \ccHeading{Predicates}
+
+  \ccNestedType{Equal_2}{\ccRefConceptPage{Kernel::Equal_2}.}
   
-  \ccNestedType{Less_x_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    smaller than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_xy_2}{\ccRefConceptPage{Kernel::Less_xy_2}.}
   
-  \ccNestedType{Less_y_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    smaller than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_yx_2}{\ccRefConceptPage{Kernel::Less_yx_2}.}
   
-  \ccNestedType{Greater_x_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    greater than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Has_on_negative_side_2}
+  {\ccRefConceptPage{Kernel::Has_on_negative_side_2}.}
   
-  \ccNestedType{Greater_y_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    greater than the $y$-coordinate of \ccc{q}.}
-  
-  \ccNestedType{Right_of_implicit_line_2}{Function class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(p1,p2,d)} returns true, iff
-    the \ccc{p1} is strictly to the right of the oriented line
-    through \ccc{p2} with direction \ccc{d}.}
-  
-  \ccNestedType{Less_rotate_ccw_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Direction_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(d1,d2)} returns true, iff
-    the slope of \ccc{d1} is less than the slope of \ccc{d2}.}
+  \ccNestedType{Compare_angle_with_x_axis_2}
+  {\ccRefConceptPage{Kernel::Compare_angle_with_x_axis_2}.}
   
   \ccNestedType{Area_less_rectangle_2}{AdaptableBinaryFunction class
     \\\ccc{op}: \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2}
@@ -301,18 +278,25 @@
     \ccc{bool}.\\ \ccc{op(s1,s2)} returns true, iff the width of
     $s1$ is strictly less than the width of $s2$.}
   
-  \ccNestedType{Rotate_direction_by_multiple_of_pi_2}{
-    AdaptableBinaryFunction class \\\ccc{op}: \ccc{Direction_2}
-    $\times$ \ccc{int} $\rightarrow$ \ccc{Direction_2}.\\ For a
-    direction $d$ and $i,\, 0 \le i < 4$ \ccc{op(d,i)} returns the
-    direction that results from clockwise rotating $d$ by $i \cdot
-    \pi$.}
+  \ccHeading{Constructions}
+
+  \ccNestedType{Construct_vector_2}{\ccRefConceptPage{Kernel::Construct_vector_2}.}
+
+  \ccNestedType{Construct_vector_from_direction_2}{AdaptableFunctor
+  \\\ccc{op}: \ccc{Direction_2} $\rightarrow$ \ccc{Vector_2}.\\
+  \ccc{op(d)} returns a vector in direction \ccc{d}.}
+
+  \ccNestedType{Construct_perpendicular_vector_2}
+  {\ccRefConceptPage{Kernel::Construct_perpendicular_vector_2}.}
   
-  \ccNestedType{Construct_direction_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
-    \ccc{Direction_2}.\\ \ccc{op(p,q)} returns the direction of the
-    vector from $p$ to $q$.}
+  \ccNestedType{Construct_direction_2}
+  {\ccRefConceptPage{Kernel::Construct_direction_2}.}
   
+  \ccNestedType{Construct_opposite_direction_2}
+  {\ccRefConceptPage{Kernel::Construct_opposite_direction_2}.}
+
+  \ccNestedType{Construct_line_2}{\ccRefConceptPage{Kernel::Construct_line_2}.}
+
   \ccNestedType{Construct_rectangle_2}{Function class \\\ccc{op}:
     \ccc{Point_2} $\times$ \ccc{Direction_2} $\times$ \ccc{Point_2}
     $\times$ \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
@@ -356,38 +340,15 @@
     copy_strip_lines_2(const Strip_2& s, OutputIterator o)
     const;}{copies the two lines bounding \ccc{s} to \ccc{o}.}
 
-  The following functions just return the corresponding function
-  object.
-  
-  \ccThree{Rotate_direction_by_multiple_of_pi_2}{
-    rotate_direction_by_multiple_of_pi_2_object();}{}
-  
-  \ccMemberFunction{Equal_2 equal_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_x_2 less_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_y_2 less_y_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_x_2 greater_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_y_2 greater_y_2_object() const;}{}
-  
-  \ccGlue\ccMemberFunction{Right_of_implicit_line_2
-    right_of_implicit_line_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_rotate_ccw_2
-    less_rotate_ccw_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_rectangle_2
-    area_less_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_parallelogram_2
-    area_less_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Width_less_strip_2
-    width_less_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_direction_2
-    construct_direction_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_rectangle_2
-    construct_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_parallelogram_2
-    construct_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_strip_2
-    construct_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Rotate_direction_by_multiple_of_pi_2
-    rotate_direction_by_multiple_of_pi_2_object() const;}{}
+  Additionally, for each of the predicate and construction functor
+  types listed above, there is a member function that requires no
+  arguments and returns an instance of that functor type. The name of
+  the member function is the uncapitalized name of the type returned
+  with the suffix \ccc{_object} appended. For example, for the functor
+  type \ccc{Construct_vector_2} the following member function exists:
+
+  \ccMemberFunction{Construct_vector_2 construct_vector_2_object()
+    const ;}{}
   
   \ccSeeAlso
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
@@ -406,10 +367,12 @@
   
   \ccTypes 
   
-  \ccTwo{Minq_traits::Rotate_direction_by_multiple_of_pi_22}{}
+  \ccTwo{Minq_traits::Construct_perpendicular_vector_2}{}
 
   \ccNestedType{Point_2}{type for representing points.}
   
+  \ccNestedType{Vector_2}{type for representing vectors.}
+  
   \ccNestedType{Direction_2}{type for representing directions.}
   
   \ccNestedType{Line_2}{type for representing lines.}
@@ -423,70 +386,58 @@
   \ccNestedType{Strip_2}{type for representing strips, that is the
     closed region bounded by two parallel lines.}
   
-  \ccNestedType{Equal_2}{AdaptableBinaryFunction class\\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    Returns true, iff the two points are equal.}
+  \ccHeading{Predicates}
+
+  \ccNestedType{Equal_2}{a model for \ccRefConceptPage{Kernel::Equal_2}.}
   
-  \ccNestedType{Less_x_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    smaller than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_xy_2}{a model for
+    \ccRefConceptPage{Kernel::Less_xy_2}.}
+
+  \ccNestedType{Less_yx_2}{a model for
+    \ccRefConceptPage{Kernel::Less_yx_2}.}
   
-  \ccNestedType{Less_y_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    smaller than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Has_on_negative_side_2}{a model for
+    \ccRefConceptPage{Kernel::Has_on_negative_side_2}.}
   
-  \ccNestedType{Greater_x_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    greater than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Compare_angle_with_x_axis_2}{a model for
+    \ccRefConceptPage{Kernel::Compare_angle_with_x_axis_2}.}
   
-  \ccNestedType{Greater_y_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    greater than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Area_less_rectangle_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2} $\rightarrow$
+    \ccc{bool}.\\ \ccc{op(r1,r2)} returns true, iff the area of $r1$ is
+    strictly less than the area of $r2$.}
   
-  \ccNestedType{Right_of_implicit_line_2}{Function class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(p1,p2,d)} returns true, iff
-    the \ccc{p1} is strictly to the right of the oriented line
-    through \ccc{p2} with direction \ccc{d}.}
+  \ccNestedType{Area_less_parallelogram_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Parallelogram_2} $\times$
+    \ccc{Parallelogram_2} $\rightarrow$ \ccc{bool}.\\
+    \ccc{op(p1,p2)} returns true, iff the area of $p1$ is strictly less
+    than the area of $p2$.}
   
-  \ccNestedType{Less_rotate_ccw_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Direction_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(d1,d2)} returns true, iff
-    the slope of \ccc{d1} is less than the slope of \ccc{d2}.}
+  \ccNestedType{Width_less_strip_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Strip_2} $\times$ \ccc{Strip_2} $\rightarrow$ \ccc{bool}.\\ 
+    \ccc{op(s1,s2)} returns true, iff the width of $s1$ is strictly less
+    than the width of $s2$.}
   
-  \ccNestedType{Area_less_rectangle_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(r1,r2)} returns true, iff
-    the area of $r1$ is strictly less than the area of $r2$.}
+  \ccHeading{Constructions}
+
+  \ccNestedType{Construct_vector_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_vector_2}.}
   
-  \ccNestedType{Area_less_parallelogram_2}{AdaptableBinaryFunction
-    class \\\ccc{op}: \ccc{Parallelogram_2} $\times$
-    \ccc{Parallelogram_2} $\rightarrow$ \ccc{bool}.\\ 
-    \ccc{op(p1,p2)} returns true, iff the area of $p1$ is strictly
-    less than the area of $p2$.}
+  \ccNestedType{Construct_vector_from_direction_2}{AdaptableFunctor
+  \\\ccc{op}: \ccc{Direction_2} $\rightarrow$ \ccc{Vector_2}.\\
+  \ccc{op(d)} returns a vector in direction \ccc{d}.}
+
+  \ccNestedType{Construct_perpendicular_vector_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_perpendicular_vector_2}.}
   
-  \ccNestedType{Width_less_strip_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Strip_2} $\times$ \ccc{Strip_2} $\rightarrow$
-    \ccc{bool}.\\ \ccc{op(s1,s2)} returns true, iff the width of
-    $s1$ is strictly less than the width of $s2$.}
+  \ccNestedType{Construct_direction_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_direction_2}.}
   
-  \ccNestedType{Rotate_direction_by_multiple_of_pi_2}{
-    AdaptableBinaryFunction class \\\ccc{op}: \ccc{Direction_2}
-    $\times$ \ccc{int} $\rightarrow$ \ccc{Direction_2}.\\ For a
-    direction $d$ and $i,\, 0 \le i < 4$ \ccc{op(d,i)} returns the
-    direction that results from clockwise rotating $d$ by $i \cdot
-    \pi$.}
+  \ccNestedType{Construct_opposite_direction_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_opposite_direction_2}.}
   
-  \ccNestedType{Construct_direction_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
-    \ccc{Direction_2}.\\ \ccc{op(p,q)} returns the direction of the
-    vector from $p$ to $q$.}
+  \ccNestedType{Construct_line_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_line_2}.}
   
   \ccNestedType{Construct_rectangle_2}{Function class \\\ccc{op}:
     \ccc{Point_2} $\times$ \ccc{Direction_2} $\times$ \ccc{Point_2}
@@ -531,41 +482,19 @@
     copy_strip_lines_2(const Strip_2& s, OutputIterator o)
     const;}{copies the two lines bounding \ccc{s} to \ccc{o}.}
 
-  The following functions just return the corresponding function
-  object.
-  
-  \ccThree{Rotate_direction_by_multiple_of_pi_2}{
-    rotate_direction_by_multiple_of_pi_2_object();}{}
-  
-  \ccMemberFunction{Equal_2 equal_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_x_2 less_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_y_2 less_y_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_x_2 greater_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_y_2 greater_y_2_object() const;}{}
-  
-  \ccGlue\ccMemberFunction{Right_of_implicit_line_2
-    right_of_implicit_line_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_rotate_ccw_2
-    less_rotate_ccw_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_rectangle_2
-    area_less_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_parallelogram_2
-    area_less_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Width_less_strip_2
-    width_less_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_direction_2
-    construct_direction_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_rectangle_2
-    construct_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_parallelogram_2
-    construct_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_strip_2
-    construct_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Rotate_direction_by_multiple_of_pi_2
-    rotate_direction_by_multiple_of_pi_2_object() const;}{}
-  
+  Additionally, for each of the predicate and construction functor
+  types listed above, there must exist a member function that requires
+  no arguments and returns an instance of that functor type. The name
+  of the member function is the uncapitalized name of the type
+  returned with the suffix \ccc{_object} appended. For example, for
+  the functor type \ccc{Construct_vector_2} the following member
+  function must exist:
+
+  \ccMemberFunction{Construct_vector_2 construct_vector_2_object()
+    const ;}{}
+
   \ccHasModels
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
 
   \ccSeeAlso
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
diff --git a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
index dad73e6596e..8fd9d3dea39 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_parallelogram_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
index 1e60dfb961f..3ebb14854f4 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_rectangle_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
index cc24b22f2e2..b7629d63077 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
+++ b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/minimum_enclosing_strip_2_example_noheader.C
@@ -14,14 +14,14 @@ using std::back_inserter;
 using std::cout;
 using std::endl;
 
-typedef CGAL::Cartesian< double >                      R;
-typedef R::Point_2                                     Point_2;
-typedef R::Line_2                                      Line_2;
-typedef CGAL::Polygon_traits_2< R >                    P_traits;
-typedef std::vector< Point_2 >                         Cont;
-typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
-typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
-typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;
+typedef CGAL::Cartesian<double>                     Kernel;
+typedef Kernel::Point_2                             Point_2;
+typedef Kernel::Line_2                              Line_2;
+typedef CGAL::Polygon_traits_2<Kernel>              P_traits;
+typedef std::vector<Point_2>                        Cont;
+typedef CGAL::Polygon_2<P_traits,Cont>              Polygon_2;
+typedef CGAL::Creator_uniform_2<double,Point_2>     Creator;
+typedef Random_points_in_square_2<Point_2,Creator>  Point_generator;
 
 int main()
 {
diff --git a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/spec_oops.tex b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/spec_oops.tex
index a744e9e47a9..f3e82c7772f 100644
--- a/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/spec_oops.tex
+++ b/Packages/Min_quadrilateral_2/doc_tex/basic/Optimisation_ref/spec_oops.tex
@@ -42,22 +42,21 @@
   exactly this point is written to \ccc{o}.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
   
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}. Otherwise \ccc{VT}
+    is \ccc{CGAL::Point_2<Kernel>} for some kernel \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -65,7 +64,7 @@
   \ccRefIdfierPage{CGAL::min_parallelogram_2}\\
   \ccRefIdfierPage{CGAL::min_strip_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm \cite{t-sgprc-83}
@@ -111,22 +110,22 @@
   exactly this point is written to \ccc{o}.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
 
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}. Otherwise
+    \ccc{VT} is \ccc{CGAL::Point_2<Kernel>} for some Kernel
+    \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -134,7 +133,7 @@
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
   \ccRefIdfierPage{CGAL::min_strip_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm
@@ -180,22 +179,21 @@
   remains unchanged.
   
   \ccPrecond The points denoted by the range [\ccc{points_begin},
-  \ccc{points_end}) form the boundary of a convex polygon $P$ in
-  counterclockwise orientation.
+  \ccc{points_end}) form the boundary of a simple convex polygon $P$
+  in counterclockwise orientation.
 
   The geometric types and operations to be used for the computation
   are specified by the traits class parameter \ccc{t}. The parameter
   can be omitted if \ccc{ForwardIterator} refers to a point type from
   the 2D-Kernel. In this case, a default traits class
-  (\ccc{Min_quadrilateral_default_traits_2<R>}) is used.
+  (\ccc{Min_quadrilateral_default_traits_2<Kernel>}) is used.
   
   \ccRequire
   \begin{enumerate}
   \item If \ccc{Traits} is specified, it is a model for
     \ccc{MinQuadrilateralTraits_2} and the value type \ccc{VT} of
-    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise
-    \ccc{VT} is \ccc{CGAL::Point_2<R>} for some representation class
-    \ccc{R}.
+    \ccc{ForwardIterator} is \ccc{Traits::Point_2}.  Otherwise \ccc{VT}
+    is \ccc{CGAL::Point_2<Kernel>} for some kernel \ccc{Kernel}.
   \item \ccc{OutputIterator} accepts \ccc{VT} as value type.
   \end{enumerate}
   
@@ -203,7 +201,7 @@
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
   \ccRefIdfierPage{CGAL::min_parallelogram_2}\\
   \ccRefConceptPage{MinQuadrilateralTraits_2}\\
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
   
   \ccImplementation We use a rotating caliper
   \ccIndexMainItem[t]{rotating caliper} algorithm \cite{t-sgprc-83}
@@ -217,14 +215,14 @@
 
 \end{ccRefFunction}
     
-\begin{ccRefClass}{Min_quadrilateral_default_traits_2<R>}
+\begin{ccRefClass}{Min_quadrilateral_default_traits_2<Kernel>}
   \ccCreationVariable{t}\ccTagFullDeclarations
   
   \ccDefinition The class \ccRefName\ is a traits class for the
   functions \ccc{min_rectangle_2}, \ccc{min_parallelogram_2} and
-  \ccc{min_strip_2} using the two-dimensional \cgal\ kernel.
+  \ccc{min_strip_2} using a two-dimensional \cgal\ kernel.
   
-  \ccRequirements The template parameter \ccc{R} is a model for
+  \ccRequirements The template parameter \ccc{Kernel} is a model for
   \ccc{Kernel}.
   
   \ccInclude{CGAL/Min_quadrilateral_traits_2.h}
@@ -236,11 +234,13 @@
   
   \ccTwo{Minq_traits::Rotate_direction_by_multiple_of_pi_22}{}
   
-  \ccNestedType{Point_2}{typedef to \ccc{R::Point_2}}
+  \ccNestedType{Point_2}{\ccRefConceptPage{Kernel::Point_2}.}
   
-  \ccNestedType{Direction_2}{typedef to \ccc{R::Direction_2}}
+  \ccNestedType{Vector_2}{\ccRefConceptPage{Kernel::Vector_2}.}
   
-  \ccNestedType{Line_2}{typedef to \ccc{R::Line_2}}
+  \ccNestedType{Direction_2}{\ccRefConceptPage{Kernel::Direction_2}.}
+  
+  \ccNestedType{Line_2}{\ccRefConceptPage{Kernel::Line_2}.}
   
   \ccNestedType{Rectangle_2}{internal type.}
   
@@ -248,42 +248,19 @@
   
   \ccNestedType{Strip_2}{internal type.}
   
-  \ccNestedType{Equal_2}{AdaptableBinaryFunction class\\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    Returns true, iff the two points are equal.}
+  \ccHeading{Predicates}
+
+  \ccNestedType{Equal_2}{\ccRefConceptPage{Kernel::Equal_2}.}
   
-  \ccNestedType{Less_x_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    smaller than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_xy_2}{\ccRefConceptPage{Kernel::Less_xy_2}.}
   
-  \ccNestedType{Less_y_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    smaller than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_yx_2}{\ccRefConceptPage{Kernel::Less_yx_2}.}
   
-  \ccNestedType{Greater_x_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    greater than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Has_on_negative_side_2}
+  {\ccRefConceptPage{Kernel::Has_on_negative_side_2}.}
   
-  \ccNestedType{Greater_y_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    greater than the $y$-coordinate of \ccc{q}.}
-  
-  \ccNestedType{Right_of_implicit_line_2}{Function class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(p1,p2,d)} returns true, iff
-    the \ccc{p1} is strictly to the right of the oriented line
-    through \ccc{p2} with direction \ccc{d}.}
-  
-  \ccNestedType{Less_rotate_ccw_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Direction_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(d1,d2)} returns true, iff
-    the slope of \ccc{d1} is less than the slope of \ccc{d2}.}
+  \ccNestedType{Compare_angle_with_x_axis_2}
+  {\ccRefConceptPage{Kernel::Compare_angle_with_x_axis_2}.}
   
   \ccNestedType{Area_less_rectangle_2}{AdaptableBinaryFunction class
     \\\ccc{op}: \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2}
@@ -301,18 +278,25 @@
     \ccc{bool}.\\ \ccc{op(s1,s2)} returns true, iff the width of
     $s1$ is strictly less than the width of $s2$.}
   
-  \ccNestedType{Rotate_direction_by_multiple_of_pi_2}{
-    AdaptableBinaryFunction class \\\ccc{op}: \ccc{Direction_2}
-    $\times$ \ccc{int} $\rightarrow$ \ccc{Direction_2}.\\ For a
-    direction $d$ and $i,\, 0 \le i < 4$ \ccc{op(d,i)} returns the
-    direction that results from clockwise rotating $d$ by $i \cdot
-    \pi$.}
+  \ccHeading{Constructions}
+
+  \ccNestedType{Construct_vector_2}{\ccRefConceptPage{Kernel::Construct_vector_2}.}
+
+  \ccNestedType{Construct_vector_from_direction_2}{AdaptableFunctor
+  \\\ccc{op}: \ccc{Direction_2} $\rightarrow$ \ccc{Vector_2}.\\
+  \ccc{op(d)} returns a vector in direction \ccc{d}.}
+
+  \ccNestedType{Construct_perpendicular_vector_2}
+  {\ccRefConceptPage{Kernel::Construct_perpendicular_vector_2}.}
   
-  \ccNestedType{Construct_direction_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
-    \ccc{Direction_2}.\\ \ccc{op(p,q)} returns the direction of the
-    vector from $p$ to $q$.}
+  \ccNestedType{Construct_direction_2}
+  {\ccRefConceptPage{Kernel::Construct_direction_2}.}
   
+  \ccNestedType{Construct_opposite_direction_2}
+  {\ccRefConceptPage{Kernel::Construct_opposite_direction_2}.}
+
+  \ccNestedType{Construct_line_2}{\ccRefConceptPage{Kernel::Construct_line_2}.}
+
   \ccNestedType{Construct_rectangle_2}{Function class \\\ccc{op}:
     \ccc{Point_2} $\times$ \ccc{Direction_2} $\times$ \ccc{Point_2}
     $\times$ \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
@@ -356,38 +340,15 @@
     copy_strip_lines_2(const Strip_2& s, OutputIterator o)
     const;}{copies the two lines bounding \ccc{s} to \ccc{o}.}
 
-  The following functions just return the corresponding function
-  object.
-  
-  \ccThree{Rotate_direction_by_multiple_of_pi_2}{
-    rotate_direction_by_multiple_of_pi_2_object();}{}
-  
-  \ccMemberFunction{Equal_2 equal_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_x_2 less_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_y_2 less_y_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_x_2 greater_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_y_2 greater_y_2_object() const;}{}
-  
-  \ccGlue\ccMemberFunction{Right_of_implicit_line_2
-    right_of_implicit_line_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_rotate_ccw_2
-    less_rotate_ccw_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_rectangle_2
-    area_less_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_parallelogram_2
-    area_less_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Width_less_strip_2
-    width_less_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_direction_2
-    construct_direction_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_rectangle_2
-    construct_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_parallelogram_2
-    construct_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_strip_2
-    construct_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Rotate_direction_by_multiple_of_pi_2
-    rotate_direction_by_multiple_of_pi_2_object() const;}{}
+  Additionally, for each of the predicate and construction functor
+  types listed above, there is a member function that requires no
+  arguments and returns an instance of that functor type. The name of
+  the member function is the uncapitalized name of the type returned
+  with the suffix \ccc{_object} appended. For example, for the functor
+  type \ccc{Construct_vector_2} the following member function exists:
+
+  \ccMemberFunction{Construct_vector_2 construct_vector_2_object()
+    const ;}{}
   
   \ccSeeAlso
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
@@ -406,10 +367,12 @@
   
   \ccTypes 
   
-  \ccTwo{Minq_traits::Rotate_direction_by_multiple_of_pi_22}{}
+  \ccTwo{Minq_traits::Construct_perpendicular_vector_2}{}
 
   \ccNestedType{Point_2}{type for representing points.}
   
+  \ccNestedType{Vector_2}{type for representing vectors.}
+  
   \ccNestedType{Direction_2}{type for representing directions.}
   
   \ccNestedType{Line_2}{type for representing lines.}
@@ -423,70 +386,58 @@
   \ccNestedType{Strip_2}{type for representing strips, that is the
     closed region bounded by two parallel lines.}
   
-  \ccNestedType{Equal_2}{AdaptableBinaryFunction class\\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    Returns true, iff the two points are equal.}
+  \ccHeading{Predicates}
+
+  \ccNestedType{Equal_2}{a model for \ccRefConceptPage{Kernel::Equal_2}.}
   
-  \ccNestedType{Less_x_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    smaller than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Less_xy_2}{a model for
+    \ccRefConceptPage{Kernel::Less_xy_2}.}
+
+  \ccNestedType{Less_yx_2}{a model for
+    \ccRefConceptPage{Kernel::Less_yx_2}.}
   
-  \ccNestedType{Less_y_2}{AdaptableBinaryFunction class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    smaller than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Has_on_negative_side_2}{a model for
+    \ccRefConceptPage{Kernel::Has_on_negative_side_2}.}
   
-  \ccNestedType{Greater_x_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $x$-coordinate of \ccc{p} is
-    greater than the $x$-coordinate of \ccc{q}.}
+  \ccNestedType{Compare_angle_with_x_axis_2}{a model for
+    \ccRefConceptPage{Kernel::Compare_angle_with_x_axis_2}.}
   
-  \ccNestedType{Greater_y_2}{AdaptableBinaryFunction class
-    \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$ \ccc{bool}.\\
-    \ccc{op(p,q)} returns true, iff the $y$-coordinate of \ccc{p} is
-    greater than the $y$-coordinate of \ccc{q}.}
+  \ccNestedType{Area_less_rectangle_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2} $\rightarrow$
+    \ccc{bool}.\\ \ccc{op(r1,r2)} returns true, iff the area of $r1$ is
+    strictly less than the area of $r2$.}
   
-  \ccNestedType{Right_of_implicit_line_2}{Function class \\\ccc{op}:
-    \ccc{Point_2} $\times$ \ccc{Point_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(p1,p2,d)} returns true, iff
-    the \ccc{p1} is strictly to the right of the oriented line
-    through \ccc{p2} with direction \ccc{d}.}
+  \ccNestedType{Area_less_parallelogram_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Parallelogram_2} $\times$
+    \ccc{Parallelogram_2} $\rightarrow$ \ccc{bool}.\\
+    \ccc{op(p1,p2)} returns true, iff the area of $p1$ is strictly less
+    than the area of $p2$.}
   
-  \ccNestedType{Less_rotate_ccw_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Direction_2} $\times$ \ccc{Direction_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(d1,d2)} returns true, iff
-    the slope of \ccc{d1} is less than the slope of \ccc{d2}.}
+  \ccNestedType{Width_less_strip_2}{AdaptableFunctor \\\ccc{op}:
+    \ccc{Strip_2} $\times$ \ccc{Strip_2} $\rightarrow$ \ccc{bool}.\\ 
+    \ccc{op(s1,s2)} returns true, iff the width of $s1$ is strictly less
+    than the width of $s2$.}
   
-  \ccNestedType{Area_less_rectangle_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Rectangle_2} $\times$ \ccc{Rectangle_2}
-    $\rightarrow$ \ccc{bool}.\\ \ccc{op(r1,r2)} returns true, iff
-    the area of $r1$ is strictly less than the area of $r2$.}
+  \ccHeading{Constructions}
+
+  \ccNestedType{Construct_vector_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_vector_2}.}
   
-  \ccNestedType{Area_less_parallelogram_2}{AdaptableBinaryFunction
-    class \\\ccc{op}: \ccc{Parallelogram_2} $\times$
-    \ccc{Parallelogram_2} $\rightarrow$ \ccc{bool}.\\ 
-    \ccc{op(p1,p2)} returns true, iff the area of $p1$ is strictly
-    less than the area of $p2$.}
+  \ccNestedType{Construct_vector_from_direction_2}{AdaptableFunctor
+  \\\ccc{op}: \ccc{Direction_2} $\rightarrow$ \ccc{Vector_2}.\\
+  \ccc{op(d)} returns a vector in direction \ccc{d}.}
+
+  \ccNestedType{Construct_perpendicular_vector_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_perpendicular_vector_2}.}
   
-  \ccNestedType{Width_less_strip_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Strip_2} $\times$ \ccc{Strip_2} $\rightarrow$
-    \ccc{bool}.\\ \ccc{op(s1,s2)} returns true, iff the width of
-    $s1$ is strictly less than the width of $s2$.}
+  \ccNestedType{Construct_direction_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_direction_2}.}
   
-  \ccNestedType{Rotate_direction_by_multiple_of_pi_2}{
-    AdaptableBinaryFunction class \\\ccc{op}: \ccc{Direction_2}
-    $\times$ \ccc{int} $\rightarrow$ \ccc{Direction_2}.\\ For a
-    direction $d$ and $i,\, 0 \le i < 4$ \ccc{op(d,i)} returns the
-    direction that results from clockwise rotating $d$ by $i \cdot
-    \pi$.}
+  \ccNestedType{Construct_opposite_direction_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_opposite_direction_2}.}
   
-  \ccNestedType{Construct_direction_2}{AdaptableBinaryFunction class
-    \\\ccc{op}: \ccc{Point_2} $\times$ \ccc{Point_2} $\rightarrow$
-    \ccc{Direction_2}.\\ \ccc{op(p,q)} returns the direction of the
-    vector from $p$ to $q$.}
+  \ccNestedType{Construct_line_2}{a model for
+    \ccRefConceptPage{Kernel::Construct_line_2}.}
   
   \ccNestedType{Construct_rectangle_2}{Function class \\\ccc{op}:
     \ccc{Point_2} $\times$ \ccc{Direction_2} $\times$ \ccc{Point_2}
@@ -531,41 +482,19 @@
     copy_strip_lines_2(const Strip_2& s, OutputIterator o)
     const;}{copies the two lines bounding \ccc{s} to \ccc{o}.}
 
-  The following functions just return the corresponding function
-  object.
-  
-  \ccThree{Rotate_direction_by_multiple_of_pi_2}{
-    rotate_direction_by_multiple_of_pi_2_object();}{}
-  
-  \ccMemberFunction{Equal_2 equal_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_x_2 less_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_y_2 less_y_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_x_2 greater_x_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Greater_y_2 greater_y_2_object() const;}{}
-  
-  \ccGlue\ccMemberFunction{Right_of_implicit_line_2
-    right_of_implicit_line_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Less_rotate_ccw_2
-    less_rotate_ccw_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_rectangle_2
-    area_less_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Area_less_parallelogram_2
-    area_less_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Width_less_strip_2
-    width_less_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_direction_2
-    construct_direction_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_rectangle_2
-    construct_rectangle_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_parallelogram_2
-    construct_parallelogram_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Construct_strip_2
-    construct_strip_2_object() const;}{}
-  \ccGlue\ccMemberFunction{Rotate_direction_by_multiple_of_pi_2
-    rotate_direction_by_multiple_of_pi_2_object() const;}{}
-  
+  Additionally, for each of the predicate and construction functor
+  types listed above, there must exist a member function that requires
+  no arguments and returns an instance of that functor type. The name
+  of the member function is the uncapitalized name of the type
+  returned with the suffix \ccc{_object} appended. For example, for
+  the functor type \ccc{Construct_vector_2} the following member
+  function must exist:
+
+  \ccMemberFunction{Construct_vector_2 construct_vector_2_object()
+    const ;}{}
+
   \ccHasModels
-  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}
+  \ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<Kernel>}
 
   \ccSeeAlso
   \ccRefIdfierPage{CGAL::min_rectangle_2}\\
diff --git a/Packages/Min_quadrilateral_2/include/CGAL/Min_quadrilateral_traits_2.h b/Packages/Min_quadrilateral_2/include/CGAL/Min_quadrilateral_traits_2.h
index 46ceb8f70d6..d8bf56ff9dd 100644
--- a/Packages/Min_quadrilateral_2/include/CGAL/Min_quadrilateral_traits_2.h
+++ b/Packages/Min_quadrilateral_2/include/CGAL/Min_quadrilateral_traits_2.h
@@ -322,12 +322,6 @@ public:
   
     tmpo = isec(line(r.p1, r.d1), line(r.p2, r.d2));
     if (assign(tmp, tmpo)) {
-  #ifdef CGAL_TRACE
-      if (!line(r.p1, r.d1).has_on(tmp) ||
-          !line(r.p2, r.d2).has_on(tmp))
-        std::cerr << "ERROR!" << std::endl;
-      else std::cerr << "---   OK1" << std::endl;
-  #endif // CGAL_TRACE
       *o++ = tmp;
     } else {
       CGAL_optimisation_assertion_code(bool test1 =)
@@ -337,12 +331,6 @@ public:
     }
     tmpo = isec(line(r.p3, r.d1), line(r.p2, r.d2));
     if (assign(tmp, tmpo)) {
-  #ifdef CGAL_TRACE
-      if (!line(r.p3, r.d1).has_on(tmp) ||
-          !line(r.p2, r.d2).has_on(tmp))
-        std::cerr << "ERROR!" << std::endl;
-      else std::cerr << "---   OK2" << std::endl;
-  #endif // CGAL_TRACE
       *o++ = tmp;
     } else {
       CGAL_optimisation_assertion_code(bool test1 =)
@@ -352,12 +340,6 @@ public:
     }
     tmpo = isec(line(r.p3, r.d1), line(r.p4, r.d2));
     if (assign(tmp, tmpo)) {
-  #ifdef CGAL_TRACE
-      if (!line(r.p3, r.d1).has_on(tmp) ||
-          !line(r.p4, r.d2).has_on(tmp))
-        std::cerr << "ERROR!" << std::endl;
-      else std::cerr << "---   OK3" << std::endl;
-  #endif // CGAL_TRACE
       *o++ = tmp;
     } else {
       CGAL_optimisation_assertion_code(bool test1 =)
@@ -367,12 +349,6 @@ public:
     }
     tmpo = isec(line(r.p1, r.d1), line(r.p4, r.d2));
     if (assign(tmp, tmpo)) {
-  #ifdef CGAL_TRACE
-      if (!line(r.p1, r.d1).has_on(tmp) ||
-          !line(r.p4, r.d2).has_on(tmp))
-        std::cerr << "ERROR!" << std::endl;
-      else std::cerr << "---   OK4" << std::endl;
-  #endif // CGAL_TRACE
       *o++ = tmp;
     } else {
       CGAL_optimisation_assertion_code(bool test1 =)
diff --git a/Packages/Min_quadrilateral_2/include/CGAL/min_quadrilateral_2.h b/Packages/Min_quadrilateral_2/include/CGAL/min_quadrilateral_2.h
index 62771b042da..048cfbc03f7 100644
--- a/Packages/Min_quadrilateral_2/include/CGAL/min_quadrilateral_2.h
+++ b/Packages/Min_quadrilateral_2/include/CGAL/min_quadrilateral_2.h
@@ -447,13 +447,6 @@ min_rectangle_2(
   return t.copy_rectangle_vertices_2(rect_so_far, o);
 
 } // min_rectangle_2( f, l, o , t)
-#ifdef CGAL_TRACE
-CGAL_END_NAMESPACE
-#include <CGAL/IO/Ostream_iterator.h>
-#include <CGAL/IO/leda_window.h>
-#include <CGAL/leda_real.h>
-CGAL_BEGIN_NAMESPACE
-#endif // CGAL_TRACE
 
 template < class ForwardIterator, class OutputIterator, class BTraits >
 OutputIterator
@@ -501,22 +494,6 @@ min_parallelogram_2(ForwardIterator f,
   // initialised to the points defining the bounding box
   convex_bounding_box_2(first, l, curr, t);
 
-#ifdef CGAL_TRACE
-  /*
-  ForwardIterator mmix = std::min_element(first, l, t.less_xy_2_object());
-  ForwardIterator mmax = std::max_element(first, l, t.less_xy_2_object());
-  ForwardIterator mmiy = std::min_element(first, l, t.less_yx_2_object());
-  ForwardIterator mmay = std::max_element(first, l, t.less_yx_2_object());
-  CGAL_assertion(!t.less_xy_2_object()(*mmix, *(curr[3])));
-  CGAL_assertion(!t.less_xy_2_object()(*(curr[3]), *mmix));
-  CGAL_assertion(!t.less_xy_2_object()(*mmax, *(curr[1])));
-  CGAL_assertion(!t.less_xy_2_object()(*(curr[1]), *mmax));
-  CGAL_assertion(!t.less_yx_2_object()(*mmiy, *(curr[0])));
-  CGAL_assertion(!t.less_yx_2_object()(*(curr[0]), *mmiy));
-  CGAL_assertion(!t.less_yx_2_object()(*mmay, *(curr[2])));
-  CGAL_assertion(!t.less_yx_2_object()(*(curr[2]), *mmay));
-  */
-#endif
 
   ForwardIterator low   = curr[0];
   ForwardIterator upp   = curr[2];
@@ -644,73 +621,12 @@ min_parallelogram_2(ForwardIterator f,
     Parallelogram_2 test_para =
       parallelogram(*low, next_dir, *right, d_leftright, *upp, *left);
 
-#ifdef CGAL_TRACE
-    {
-      typedef typename
-        std::iterator_traits< ForwardIterator >::value_type Point;
-      typedef Polygon_traits_2< typename Traits::Kernel > P_traits;
-      typedef std::vector< Point >                   Cont;
-      typedef CGAL::Polygon_2< P_traits, Cont >      Polygon_2;
-      Polygon_2 p;
-      t.copy_parallelogram_vertices_2(test_para, std::back_inserter(p));
-      CGAL_assertion(p.is_simple());
-      CGAL_assertion(p.is_convex());
-      cout << "p_area = " << p.area() << endl;
-      for (ForwardIterator ii = first; ii != l; ++ii)
-        CGAL_assertion(!p.has_on_unbounded_side(*ii));
-    }
-#endif // CGAL_TRACE
 
     if (area_less(test_para, para_so_far))
       para_so_far = test_para;
 
   } // for (;;)
 
-#ifdef CGAL_TRACE
-   typedef typename
-     std::iterator_traits< ForwardIterator >::value_type Point;
-   Point p[4];
-   t.copy_parallelogram_vertices_2(para_so_far, p);
-   leda_window w;
-   w.init(-50, 450, -35);
-   w.display();
-   Ostream_iterator< Point, leda_window > oip(w);
-   //std::ostream_iterator< Point > oipc(std::cerr, "\n");
-   std::copy(first, l, oip);
-   w << YELLOW;
-   w.set_node_width(7);
-   {
-     ForwardIterator ii = curr[3];
-     while (ii != curr[1]) {
-       *oip++ = *ii;
-       if (++ii == l) ii = first;
-     }
-     *oip++ = *ii;
-   }
-   w.set_node_width(5);
-   w << GREEN << para_so_far.p1 << para_so_far.p2
-     << para_so_far.p3 << para_so_far.p4;
-   {
-     typedef typename Traits::Line_2 Line_2;
-     Line_2 l1(para_so_far.p1, para_so_far.d1);
-     Line_2 l2(para_so_far.p2, para_so_far.d2);
-     Line_2 l3(para_so_far.p3, para_so_far.d1);
-     Line_2 l4(para_so_far.p4, para_so_far.d2);
-     if (l1 == l2) cout << "l1 == l2" << endl;
-     if (l1 == l3) cout << "l1 == l3" << endl;
-     if (l1 == l4) cout << "l1 == l4" << endl;
-     w << BLUE << l1 << l2 << l3 << l4;
-   }
-   w.set_node_width(3);
-   w << RED << p[0] << p[1] << p[2] << p[3];
-   w.read_mouse();
-   std::cerr << "ZAP" << std::endl;
-   *o++ = p[0];
-   *o++ = p[1];
-   *o++ = p[2];
-   *o++ = p[3];
-   return o;
- #endif
 
    return t.copy_parallelogram_vertices_2(para_so_far, o);
  } // min_parallelogram_2(f, l, o , t)
diff --git a/Packages/Min_quadrilateral_2/test/Min_quadrilateral_2/cgal_test b/Packages/Min_quadrilateral_2/test/Min_quadrilateral_2/cgal_test
index c277ee189c4..d1a850ba096 100755
--- a/Packages/Min_quadrilateral_2/test/Min_quadrilateral_2/cgal_test
+++ b/Packages/Min_quadrilateral_2/test/Min_quadrilateral_2/cgal_test
@@ -42,7 +42,7 @@ compile_and_run()
     fi
     echo "Executing $1 ... "
     echo
-    if eval 2>&1 $COMMAND > $OUTPUTFILE ; then
+    if eval $COMMAND > $OUTPUTFILE 2>&1 ; then
       echo "   succesful execution   of $1" >> $ERRORFILE
     else
       echo "   ERROR:    execution   of $1" >> $ERRORFILE
@@ -51,7 +51,7 @@ compile_and_run()
     echo   "   ERROR:    not executed   $1" >> $ERRORFILE
   fi
 
-  eval "2>&1 make CGAL_MAKEFILE=$CGAL_MAKEFILE clean > /dev/null "
+  eval "make CGAL_MAKEFILE=$CGAL_MAKEFILE clean > /dev/null 2>&1 "
 }
 
 #---------------------------------------------------------------------#
diff --git a/Packages/Min_quadrilateral_2/version b/Packages/Min_quadrilateral_2/version
index 64106e3c9ca..2c5cdb25dd3 100644
--- a/Packages/Min_quadrilateral_2/version
+++ b/Packages/Min_quadrilateral_2/version
@@ -1 +1 @@
-1.24 (26 August 2003)
+1.25 (26 August 2003)