diff --git a/Partition_2/doc/Partition_2/CGAL/partition_is_valid_2.h b/Partition_2/doc/Partition_2/CGAL/partition_is_valid_2.h
index 22419d85ae5..bac23840b1c 100644
--- a/Partition_2/doc/Partition_2/CGAL/partition_is_valid_2.h
+++ b/Partition_2/doc/Partition_2/CGAL/partition_is_valid_2.h
@@ -35,7 +35,7 @@ with the representation type determined by `std::iterator_traits<InputIterator>:
 \sa `CGAL::greene_approx_convex_partition_2()` 
 \sa `CGAL::optimal_convex_partition_2()` 
 \sa `CGAL::partition_is_valid_2()` 
-\sa `CGAL::Is_convex_2()` 
+\sa `CGAL::Is_convex_2` 
 
 \cgalHeading{Implementation}
 
@@ -99,7 +99,7 @@ with the representation type determined by `std::iterator_traits<InputIterator>:
 \sa `CGAL::optimal_convex_partition_2()` 
 \sa `CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>` 
 \sa `CGAL::y_monotone_partition_2()` 
-\sa `CGAL::Is_convex_2()` 
+\sa `CGAL::Is_convex_2` 
 
 \cgalHeading{Implementation}
 
diff --git a/Partition_2/examples/Partition_2/approx_convex_partition_2.cpp b/Partition_2/examples/Partition_2/approx_convex_partition_2.cpp
index c5b0401c22a..e1148e59037 100644
--- a/Partition_2/examples/Partition_2/approx_convex_partition_2.cpp
+++ b/Partition_2/examples/Partition_2/approx_convex_partition_2.cpp
@@ -1,8 +1,6 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Partition_traits_2.h>
 #include <CGAL/partition_2.h>
-#include <CGAL/point_generators_2.h>
-#include <CGAL/random_polygon_2.h>
 #include <cassert>
 #include <list>
 
@@ -11,10 +9,7 @@ typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 typedef CGAL::Partition_traits_2<K>                         Traits;
 typedef Traits::Point_2                                     Point_2;
 typedef Traits::Polygon_2                                   Polygon_2;
-typedef Polygon_2::Vertex_iterator                          Vertex_iterator;
 typedef std::list<Polygon_2>                                Polygon_list;
-typedef CGAL::Creator_uniform_2<int, Point_2>               Creator;
-typedef CGAL::Random_points_in_square_2<Point_2, Creator>   Point_generator;
 
 void make_polygon(Polygon_2& polygon)
 {
@@ -40,19 +35,14 @@ int main()
    Polygon_2    polygon;
    Polygon_list partition_polys;
 
-/*
-   CGAL::random_polygon_2(50, std::back_inserter(polygon),
-                          Point_generator(100));
-*/
    make_polygon(polygon);
-   Traits traits;
+
    CGAL::approx_convex_partition_2(polygon.vertices_begin(),
                                    polygon.vertices_end(),
-                                   std::back_inserter(partition_polys), traits);
+                                   std::back_inserter(partition_polys));
    assert(CGAL::convex_partition_is_valid_2(polygon.vertices_begin(),
                                             polygon.vertices_end(),
                                             partition_polys.begin(),
-                                            partition_polys.end(),
-                                            traits));
+                                            partition_polys.end()));
    return 0;
 }
diff --git a/Partition_2/examples/Partition_2/greene_approx_convex_partition_2.cpp b/Partition_2/examples/Partition_2/greene_approx_convex_partition_2.cpp
index 4b58cfb3fd3..1a07512462b 100644
--- a/Partition_2/examples/Partition_2/greene_approx_convex_partition_2.cpp
+++ b/Partition_2/examples/Partition_2/greene_approx_convex_partition_2.cpp
@@ -1,8 +1,6 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Partition_traits_2.h>
 #include <CGAL/partition_2.h>
-#include <CGAL/point_generators_2.h>
-#include <CGAL/random_polygon_2.h>
 #include <cassert>
 #include <list>
 
@@ -10,10 +8,7 @@ typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 typedef CGAL::Partition_traits_2<K>                         Traits;
 typedef Traits::Point_2                                     Point_2;
 typedef Traits::Polygon_2                                   Polygon_2;
-typedef Polygon_2::Vertex_iterator                          Vertex_iterator;
 typedef std::list<Polygon_2>                                Polygon_list;
-typedef CGAL::Creator_uniform_2<int, Point_2>               Creator;
-typedef CGAL::Random_points_in_square_2< Point_2, Creator > Point_generator;
 
 void make_polygon(Polygon_2& polygon)
 {
@@ -38,21 +33,14 @@ int main()
 {
    Polygon_2    polygon;
    Polygon_list partition_polys;
-   Traits       partition_traits;
 
-/*
-   CGAL::random_polygon_2(50, std::back_inserter(polygon),
-                          Point_generator(100));
-*/
    make_polygon(polygon);
    CGAL::greene_approx_convex_partition_2(polygon.vertices_begin(),
                                           polygon.vertices_end(),
-                                          std::back_inserter(partition_polys),
-                                          partition_traits);
+                                          std::back_inserter(partition_polys));
    assert(CGAL::convex_partition_is_valid_2(polygon.vertices_begin(),
                                             polygon.vertices_end(),
                                             partition_polys.begin(),
-                                            partition_polys.end(),
-                                            partition_traits));
+                                            partition_polys.end()));
    return 0;
 }
diff --git a/Partition_2/examples/Partition_2/optimal_convex_partition_2.cpp b/Partition_2/examples/Partition_2/optimal_convex_partition_2.cpp
index 2877e64e05c..1a4d63c68bd 100644
--- a/Partition_2/examples/Partition_2/optimal_convex_partition_2.cpp
+++ b/Partition_2/examples/Partition_2/optimal_convex_partition_2.cpp
@@ -1,25 +1,15 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Partition_traits_2.h>
-#include <CGAL/Partition_is_valid_traits_2.h>
-#include <CGAL/polygon_function_objects.h>
 #include <CGAL/partition_2.h>
-#include <CGAL/point_generators_2.h>
-#include <CGAL/random_polygon_2.h>
 #include <cassert>
 #include <list>
 
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 typedef CGAL::Partition_traits_2<K>                         Traits;
-typedef CGAL::Is_convex_2<Traits>                           Is_convex_2;
 typedef Traits::Polygon_2                                   Polygon_2;
 typedef Traits::Point_2                                     Point_2;
-typedef Polygon_2::Vertex_const_iterator                    Vertex_iterator;
 typedef std::list<Polygon_2>                                Polygon_list;
-typedef CGAL::Partition_is_valid_traits_2<Traits, Is_convex_2>
-                                                            Validity_traits;
-typedef CGAL::Creator_uniform_2<int, Point_2>               Creator;
-typedef CGAL::Random_points_in_square_2<Point_2, Creator>   Point_generator;
 
 void make_polygon(Polygon_2& polygon)
 {
@@ -43,22 +33,16 @@ int main()
 {
    Polygon_2             polygon;
    Polygon_list          partition_polys;
-   Traits                partition_traits;
-   Validity_traits       validity_traits(partition_traits);
-
-/*
-   CGAL::random_polygon_2(50, std::back_inserter(polygon),
-                          Point_generator(100));
-*/
+  
    make_polygon(polygon);
    CGAL::optimal_convex_partition_2(polygon.vertices_begin(),
                                     polygon.vertices_end(),
-                                    std::back_inserter(partition_polys),
-                                    partition_traits);
+                                    std::back_inserter(partition_polys));
+
    assert(CGAL::partition_is_valid_2(polygon.vertices_begin(),
                                      polygon.vertices_end(),
                                      partition_polys.begin(),
-                                     partition_polys.end(),
-                                     validity_traits));
+                                     partition_polys.end()));
+
    return 0;
 }
diff --git a/Partition_2/examples/Partition_2/y_monotone_partition_2.cpp b/Partition_2/examples/Partition_2/y_monotone_partition_2.cpp
index c6fcd97a472..5384989c2fd 100644
--- a/Partition_2/examples/Partition_2/y_monotone_partition_2.cpp
+++ b/Partition_2/examples/Partition_2/y_monotone_partition_2.cpp
@@ -1,8 +1,6 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Partition_traits_2.h>
 #include <CGAL/partition_2.h>
-#include <CGAL/point_generators_2.h>
-#include <CGAL/random_polygon_2.h>
 #include <cassert>
 #include <list>
 
@@ -12,8 +10,6 @@ typedef CGAL::Partition_traits_2<K>                         Traits;
 typedef Traits::Point_2                                     Point_2;
 typedef Traits::Polygon_2                                   Polygon_2;
 typedef std::list<Polygon_2>                                Polygon_list;
-typedef CGAL::Creator_uniform_2<int, Point_2>               Creator;
-typedef CGAL::Random_points_in_square_2<Point_2, Creator>   Point_generator;
 
 void make_polygon(Polygon_2& polygon)
 {
@@ -39,10 +35,6 @@ int main( )
    Polygon_2    polygon;
    Polygon_list partition_polys;
 
-/*
-   CGAL::random_polygon_2(50, std::back_inserter(polygon),
-                          Point_generator(100));
-*/
    make_polygon(polygon);
    CGAL::y_monotone_partition_2(polygon.vertices_begin(),
                                 polygon.vertices_end(),
diff --git a/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp b/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
index 19000dc7221..a4cbdf580a1 100644
--- a/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
+++ b/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
@@ -42,8 +42,8 @@ int main( )
 
   Polygon_list partition_polys;
 
-  CGAL::y_monotone_partition_2(polygon.begin(),
-                               polygon.end(),
+  CGAL::y_monotone_partition_2(polygon.vertices_begin(),
+                               polygon.vertices_end(),
                                std::back_inserter(partition_polys),
                                traits);
 
diff --git a/Partition_2/test/Partition_2/approx_convex_partition_2_test_C.cpp b/Partition_2/test/Partition_2/approx_convex_partition_2_test_C.cpp
index 08c57d67600..60d005777e9 100644
--- a/Partition_2/test/Partition_2/approx_convex_partition_2_test_C.cpp
+++ b/Partition_2/test/Partition_2/approx_convex_partition_2_test_C.cpp
@@ -28,14 +28,14 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
 typedef double                        NT;
-typedef CGAL::Cartesian<NT>           K;
+typedef CGAL::Simple_cartesian<NT>           K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/approx_convex_partition_2_test_H.cpp b/Partition_2/test/Partition_2/approx_convex_partition_2_test_H.cpp
index 1d74394f71e..a99c0778f86 100644
--- a/Partition_2/test/Partition_2/approx_convex_partition_2_test_H.cpp
+++ b/Partition_2/test/Partition_2/approx_convex_partition_2_test_H.cpp
@@ -26,14 +26,14 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
+#include <CGAL/Simple_homogeneous.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
 typedef double                        NT;
-typedef CGAL::Homogeneous<NT>         K;
+typedef CGAL::Simple_homogeneous<NT>         K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_C.cpp b/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_C.cpp
index 60a36c7c172..e022424c4b9 100644
--- a/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_C.cpp
+++ b/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_C.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>       K;
+typedef CGAL::Simple_cartesian<double>       K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_H.cpp b/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_H.cpp
index a4c2ede5901..d354b997a82 100644
--- a/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_H.cpp
+++ b/Partition_2/test/Partition_2/greene_approx_convex_partition_2_test_H.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
+#include <CGAL/Simple_homogeneous.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Homogeneous<double>     K;
+typedef CGAL::Simple_homogeneous<double>     K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/is_y_monotone_2_test.cpp b/Partition_2/test/Partition_2/is_y_monotone_2_test.cpp
index ca31d871099..f745c961b18 100644
--- a/Partition_2/test/Partition_2/is_y_monotone_2_test.cpp
+++ b/Partition_2/test/Partition_2/is_y_monotone_2_test.cpp
@@ -26,20 +26,20 @@
 // implementation: testing of is_y_monotone_2 function
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_homogeneous.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/is_y_monotone_2.h>
 #include <list>
 #include <vector>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>          CR;
+typedef CGAL::Simple_cartesian<double>   CR;
 typedef CR::Point_2                      CPoint_2;
 typedef std::list<CPoint_2>              CContainer;
 typedef CGAL::Polygon_2<CR, CContainer>  CPolygon_2;
 
-typedef CGAL::Homogeneous<double>        HR;
+typedef CGAL::Simple_homogeneous<double> HR;
 typedef HR::Point_2                      HPoint_2;
 typedef std::vector<HPoint_2>            HContainer;
 typedef CGAL::Polygon_2<HR, HContainer>  HPolygon_2;
diff --git a/Partition_2/test/Partition_2/kernel_def.h b/Partition_2/test/Partition_2/kernel_def.h
index e06415631cd..be07d4b18de 100644
--- a/Partition_2/test/Partition_2/kernel_def.h
+++ b/Partition_2/test/Partition_2/kernel_def.h
@@ -3,12 +3,12 @@
 
 #if TESTR==1
    typedef double               NT;
-   typedef CGAL::Cartesian<NT>  K;
+   typedef CGAL::Simple_cartesian<NT>  K;
 #endif 
 
 #if TESTR==2
    typedef double                NT;
-   typedef CGAL::Homogeneous<NT> K;
+   typedef CGAL::Simple_homogeneous<NT> K;
 #endif
 
 
diff --git a/Partition_2/test/Partition_2/kernel_include.h b/Partition_2/test/Partition_2/kernel_include.h
index 743250cda21..72f2e998f5f 100644
--- a/Partition_2/test/Partition_2/kernel_include.h
+++ b/Partition_2/test/Partition_2/kernel_include.h
@@ -1,7 +1,7 @@
 #if TESTR == 1
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #endif
 #if TESTR == 2
-#include <CGAL/Homogeneous.h>
+#include <CGAL/simple_homogeneous.h>
 #endif
 
diff --git a/Partition_2/test/Partition_2/optimal_convex_partition_2_test_C.cpp b/Partition_2/test/Partition_2/optimal_convex_partition_2_test_C.cpp
index 70aa4923fec..ef1c6769ce8 100644
--- a/Partition_2/test/Partition_2/optimal_convex_partition_2_test_C.cpp
+++ b/Partition_2/test/Partition_2/optimal_convex_partition_2_test_C.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>       K;
+typedef CGAL::Simple_cartesian<double>       K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/optimal_convex_partition_2_test_H.cpp b/Partition_2/test/Partition_2/optimal_convex_partition_2_test_H.cpp
index 88c44a3220f..cde71db7a20 100644
--- a/Partition_2/test/Partition_2/optimal_convex_partition_2_test_H.cpp
+++ b/Partition_2/test/Partition_2/optimal_convex_partition_2_test_H.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of convex partitioning functions
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
+#include <CGAL/Simple_homogeneous.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Homogeneous<double>     K;
+typedef CGAL::Simple_homogeneous<double>     K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/partition_2_defaults_test_C.cpp b/Partition_2/test/Partition_2/partition_2_defaults_test_C.cpp
index a686229697f..f8cc41a9471 100644
--- a/Partition_2/test/Partition_2/partition_2_defaults_test_C.cpp
+++ b/Partition_2/test/Partition_2/partition_2_defaults_test_C.cpp
@@ -26,13 +26,13 @@
 // implementation: testing of use of default traits classes for partitioning
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Partition_traits_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>       K;
+typedef CGAL::Simple_cartesian<double>       K;
 typedef CGAL::Partition_traits_2<K>   Traits;
 typedef Traits::Point_2               Point_2;
 typedef Traits::Polygon_2             Polygon_2;
diff --git a/Partition_2/test/Partition_2/partition_2_defaults_test_H.cpp b/Partition_2/test/Partition_2/partition_2_defaults_test_H.cpp
index c4e43ab982e..72213391e1d 100644
--- a/Partition_2/test/Partition_2/partition_2_defaults_test_H.cpp
+++ b/Partition_2/test/Partition_2/partition_2_defaults_test_H.cpp
@@ -26,13 +26,13 @@
 // implementation: testing of use of default traits classes for partitioning
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
+#include <CGAL/Simple_homogeneous.h>
 #include <CGAL/Partition_traits_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Homogeneous<double>                  K;
+typedef CGAL::Simple_homogeneous<double>           K;
 typedef CGAL::Partition_traits_2<K>                Traits;
 typedef Traits::Point_2                            Point_2;
 typedef Traits::Polygon_2                          Polygon_2;
diff --git a/Partition_2/test/Partition_2/y_monotone_partition_2_test_C.cpp b/Partition_2/test/Partition_2/y_monotone_partition_2_test_C.cpp
index f23090de67a..306bde31052 100644
--- a/Partition_2/test/Partition_2/y_monotone_partition_2_test_C.cpp
+++ b/Partition_2/test/Partition_2/y_monotone_partition_2_test_C.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of y-monotone partitioning function
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>       K;
+typedef CGAL::Simple_cartesian<double>       K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;
diff --git a/Partition_2/test/Partition_2/y_monotone_partition_2_test_H.cpp b/Partition_2/test/Partition_2/y_monotone_partition_2_test_H.cpp
index 835c3a9fa1f..42da2db7451 100644
--- a/Partition_2/test/Partition_2/y_monotone_partition_2_test_H.cpp
+++ b/Partition_2/test/Partition_2/y_monotone_partition_2_test_H.cpp
@@ -26,13 +26,13 @@
 // implementation: Testing of y-monotone partitioning function
 // ============================================================================
 
-#include <CGAL/Homogeneous.h>
+#include <CGAL/Simple_homogeneous.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/partition_2.h>
 #include <list>
 #include <cassert>
 
-typedef CGAL::Homogeneous<double>     K;
+typedef CGAL::Simple_homogeneous<double>     K;
 typedef K::Point_2                    Point_2;
 typedef std::list<Point_2>            Container;
 typedef CGAL::Polygon_2<K, Container> Polygon_2;