diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_euclidean_vs_hyperbolic.txt b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_euclidean_vs_hyperbolic.txt
new file mode 100644
index 00000000000..e185befc423
--- /dev/null
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_euclidean_vs_hyperbolic.txt
@@ -0,0 +1,23 @@
+---- for best results, make sure that you have compiled me in Release mode ----
+iteration 1: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 50.3773 secs)
+iteration 1: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 20.7566 secs)
+iteration 2: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 58.7336 secs)
+iteration 2: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 24.6808 secs)
+iteration 3: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 57.6734 secs)
+iteration 3: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 23.9461 secs)
+iteration 4: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 54.9728 secs)
+iteration 4: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 21.1166 secs)
+iteration 5: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 51.4028 secs)
+iteration 5: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 21.3222 secs)
+iteration 6: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 50.6842 secs)
+iteration 6: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 21.144 secs)
+iteration 7: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 52.2119 secs)
+iteration 7: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 21.848 secs)
+iteration 8: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 52.7987 secs)
+iteration 8: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 23.4349 secs)
+iteration 9: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 56.7236 secs)
+iteration 9: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 22.5812 secs)
+iteration 10: inserting into hyperbolic periodic triangulation...    DONE! (# of vertices = 1000000, time = 56.6275 secs)
+iteration 10: inserting into Euclidean non-periodic triangulation... DONE! (# of vertices = 1000000, time = 22.441 secs)
+Hyperbolic periodic     triangulation: average time = 54.2206
+Euclidean  non-periodic triangulation: average time = 22.3271
\ No newline at end of file
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_complex.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_complex.cpp
index e210d06236c..3f8c01197ee 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_complex.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_complex.cpp
@@ -1,6 +1,6 @@
 #include <iostream>
 #include <CGAL/CORE_Expr.h>
-#include <CGAL/Exact_complex.h>
+#include <CGAL/internal/Exact_complex.h>
 #include <CGAL/Point_2.h>
 #include <CGAL/Circle_2.h>
 #include <CGAL/Cartesian.h>
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_dummy_points.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_dummy_points.cpp
index 4610cd02e18..b6b7b33d319 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_dummy_points.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_dummy_points.cpp
@@ -7,7 +7,7 @@
 
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_2.h>
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
-#include <CGAL/Periodic_4_hyperbolic_triangulation_dummy_14.h>
+#include <CGAL/internal/Periodic_4_hyperbolic_triangulation_dummy_14.h>
 #include <CGAL/Hyperbolic_octagon_translation.h>
 #include <CGAL/Algebraic_kernel_for_circles_2_2.h>
 #include <CGAL/Circular_kernel_2.h>
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_hyperbolic_vs_euclidean.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_hyperbolic_vs_euclidean.cpp
index f826bb6a1f7..45d89c25e29 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_hyperbolic_vs_euclidean.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_hyperbolic_vs_euclidean.cpp
@@ -4,7 +4,7 @@
 #include <boost/random/uniform_smallint.hpp>
 #include <boost/random/variate_generator.hpp>
 #include <CGAL/point_generators_2.h>
-#include <CGAL/Hyperbolic_random_points_in_disc_2.h>
+//#include <CGAL/Hyperbolic_random_points_in_disc_2.h>
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_2.h>
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
 #include <CGAL/Hyperbolic_octagon_translation.h>
@@ -61,21 +61,18 @@ int main(int argc, char** argv) {
 
     for (int exec = 1; exec <= iters; exec++) {
 
-        std::vector<Point_double> v;
         std::vector<Point> pts;
-
-        Hyperbolic_random_points_in_disc_2_double(v, 5*N, -1, 0.159);
+        CGAL::Random_points_in_disc_2<Point_double, Creator> g(0.85);
 
         int cnt = 0;
-        int idx = 0;
         do {    
-            Point pt = Point(v[idx].x(), v[idx].y());
+            Point_double pd = *(++g);
+            Point pt = Point(pd.x(), pd.y());
             if (pred(pt) != CGAL::ON_UNBOUNDED_SIDE) {
                 pts.push_back(pt);
                 cnt++;
             } 
-            idx++;
-        } while (cnt < N && idx < v.size());
+        } while (cnt < N);
 
         if (cnt < N) {
             cout << "I failed to generate all the random points! Exiting..." << endl;
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion.cpp
index 72fdf5313eb..bc1e5f2adbe 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion.cpp
@@ -100,7 +100,7 @@ int main(int argc, char** argv) {
 
         CGAL::Timer tt;
         tt.start();
-        tr.insert(pts.begin(), pts.end(), true);
+        tr.insert(pts.begin(), pts.end());
         tt.stop();
         cout << "DONE! (# of vertices = " << tr.number_of_vertices() << ", time = " << tt.time() << " secs)" << endl;
         extime += tt.time();
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion_euclidean.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion_euclidean.cpp
index 9c2dd139b7c..b2a7baa6f11 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion_euclidean.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_insertion_euclidean.cpp
@@ -8,7 +8,8 @@
 #include <CGAL/Delaunay_triangulation_2.h>
 #include <CGAL/Cartesian.h>
 #include <CGAL/determinant.h>
-
+#include <CGAL/CORE_Expr.h>
+#include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
 #include <CGAL/Timer.h>
 
 typedef double                                                                  NT;
@@ -18,6 +19,13 @@ typedef Kernel::Point_2
 typedef Triangulation::Vertex_handle                                            Vertex_handle;
 typedef CGAL::Creator_uniform_2<double, Point>                                  Creator;
 
+
+typedef CORE::Expr                                                              NT2;
+typedef CGAL::Cartesian<NT2>                                                    Kernel2;
+typedef CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_traits_2<Kernel2,
+                                      CGAL::Hyperbolic_octagon_translation>     Traits2;
+typedef Traits2::Side_of_original_octagon                                       Side_of_original_octagon;
+
 using std::cout;
 using std::endl;
 
@@ -37,23 +45,27 @@ int main(int argc, char** argv) {
     cout << "---- for best results, make sure that you have compiled me in Release mode ----" << endl;
     
     double extime = 0.0;
+    Side_of_original_octagon pred;
 
     for (int exec = 1; exec <= iters; exec++) {
         std::vector<Point> pts;
-        pts.reserve(N);
-        CGAL::Random_points_in_disc_2<Point, Creator> g(1.0);
-        CGAL::cpp11::copy_n( g, N, std::back_inserter(pts));
+        CGAL::Random_points_in_disc_2<Point, Creator> g(0.85);
+
+        int cnt = 0;
+        do {    
+            Point pt = *(++g);
+            if (pred(pt) != CGAL::ON_UNBOUNDED_SIDE) {
+                pts.push_back(pt);
+                cnt++;
+            } 
+        } while (cnt < N);
 
         cout << "iteration " << exec << ": inserting into triangulation (rational dummy points)... "; cout.flush();
         Triangulation tr;
-        //tr.insert_dummy_points(true);  
 
         CGAL::Timer tt;
         tt.start();
         tr.insert(pts.begin(), pts.end());
-        //for (int j = 0; j < pts.size(); j++) {
-        //    tr.insert(pts[j]);
-        //}
         tt.stop();
         cout << "DONE! (# of vertices = " << tr.number_of_vertices() << ", time = " << tt.time() << " secs)" << endl;
         extime += tt.time();
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_locate.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_locate.cpp
index cdd662ba722..d45a9ad24db 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_locate.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_locate.cpp
@@ -7,7 +7,7 @@
 
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_2.h>
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
-#include <CGAL/Periodic_4_hyperbolic_triangulation_dummy_14.h>
+#include <CGAL/internal/Periodic_4_hyperbolic_triangulation_dummy_14.h>
 #include <CGAL/Hyperbolic_octagon_translation.h>
 #include <CGAL/Algebraic_kernel_for_circles_2_2.h>
 #include <CGAL/Circular_kernel_2.h>
@@ -55,7 +55,7 @@ int main(void) {
     cout << "---- locating dummy points (all should be vertices) ----" << endl;
     for (int j = 0; j < 14; j++) {
         Point query = tr.get_dummy_point(j); 
-        fh = tr.locate(query, lt, li);
+        fh = tr.hyperbolic_locate(query, lt, li);
         assert(lt == Triangulation::VERTEX);
         cout << "   dummy point " << j << ": OK " << endl;
     }
@@ -63,13 +63,13 @@ int main(void) {
     cout << "---- locating the midpoint of a Euclidean segment ----" << endl;
     Point p1 = tr.get_dummy_point(0), p2 = tr.get_dummy_point(1);
     Point query = midpoint(p1, p2);
-    fh = tr.locate(query, lt, li);
+    fh = tr.hyperbolic_locate(query, lt, li);
     assert(lt == Triangulation::EDGE);
     cout << "   located as edge OK" << endl;
 
     cout << "---- inserting a single point and locating it ----" << endl;
     Vertex_handle v = tr.insert(Point(-0.4, -0.1));
-    fh = tr.locate(v->point(), lt, li);
+    fh = tr.hyperbolic_locate(v->point(), lt, li);
     assert(lt == Triangulation::VERTEX);
     cout << "   located as vertex OK" << endl;
 
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_matrix.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_matrix.cpp
index 8c12b65c1a7..f3fbc8f62e5 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_matrix.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_matrix.cpp
@@ -3,8 +3,8 @@
 #include <CGAL/Point_2.h>
 #include <CGAL/Circle_2.h>
 #include <CGAL/Cartesian.h>
-#include <CGAL/Exact_complex.h>
-#include <CGAL/Hyperbolic_octagon_translation_matrix.h>
+#include <CGAL/internal/Exact_complex.h>
+#include <CGAL/internal/Hyperbolic_octagon_translation_matrix.h>
 #include <vector>
 
 using namespace CGAL;
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_remove_dummy_points.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_remove_dummy_points.cpp
index 896c91fbb10..9d87667396c 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_remove_dummy_points.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_remove_dummy_points.cpp
@@ -5,7 +5,7 @@
 #include <boost/random/uniform_smallint.hpp>
 #include <boost/random/variate_generator.hpp>
 #include <CGAL/point_generators_2.h>
-#include <CGAL/Hyperbolic_random_points_in_disc_2.h>
+//#include <CGAL/Random_points_in_disc_2.h>
 
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_2.h>
 #include <CGAL/Periodic_4_hyperbolic_Delaunay_triangulation_traits_2.h>
@@ -44,10 +44,10 @@ int main(int argc, char** argv) {
     int max = -1;
     double mean = 0.0;
     for (int j = 0; j < iter; j++) {
-        cout << "Iteration " << (j+1) << "/" << iter << "..." << endl;
+        //cout << "Iteration " << (j+1) << "/" << iter << "..." << endl;
         
         std::vector<Point_double> v;
-        Hyperbolic_random_points_in_disc_2_double(v, N, -1, 0.159);
+        CGAL::Random_points_in_disc_2<Point_double, Creator> g(0.85);
 
         Triangulation tr;  
         assert(tr.is_valid(true));
@@ -55,7 +55,7 @@ int main(int argc, char** argv) {
         int cnt = 0;
         int idx = 0;
         do {
-            Point_double pt = v[idx++];
+            Point_double pt = *(++g);
             if (pred(pt) != CGAL::ON_UNBOUNDED_SIDE) {
                 tr.insert(Point(pt.x(), pt.y()));
                 cnt++;
@@ -66,7 +66,7 @@ int main(int argc, char** argv) {
             continue;
         }
         assert(tr.is_valid());
-
+        std::cout << cnt << std::endl;
         if (cnt > max)
             max = cnt;
         if (cnt < min)
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_triangulation.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_triangulation.cpp
index 7f3087b3d07..466c72d098c 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_triangulation.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_triangulation.cpp
@@ -23,7 +23,7 @@ int main(void) {
     Triangulation tr;
     CGAL_assertion(tr.is_valid());
 
-    cout << "triangulation works!" << 
+    cout << "triangulation works!" << std::endl;
     cout << "nb of vertices: " << tr.number_of_vertices() << endl;
     cout << "nb of faces: " << tr.number_of_faces() << endl;
 
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_words.cpp b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_words.cpp
index 770bb7d0200..cc8e623c90c 100644
--- a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_words.cpp
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_p4ht2_words.cpp
@@ -4,7 +4,7 @@
 #include <CGAL/Circle_2.h>
 #include <CGAL/Cartesian.h>
 // #include <CGAL/Hyperbolic_octagon_translation_matrix.h>
-#include <CGAL/Exact_complex.h>
+#include <CGAL/internal/Exact_complex.h>
 #include <CGAL/Hyperbolic_octagon_translation.h>
 #include <vector>
 
diff --git a/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_remove_dummy_points_euclidean.txt b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_remove_dummy_points_euclidean.txt
new file mode 100644
index 00000000000..8fab40bb961
--- /dev/null
+++ b/Periodic_4_hyperbolic_triangulation_2/test/Periodic_4_hyperbolic_triangulation_2/test_remove_dummy_points_euclidean.txt
@@ -0,0 +1,13 @@
+Test ran on 04/06/2018, 11:18am
+=================================================
+Finished 100 iterations!
+Minimum number of points inserted: 30
+Maximum number of points inserted: 147
+Average number of points inserted: 61.66
+
+
+Context
+=================================================
+There were some doubts about how correct it is to say that we used random points 
+uniformly distributed in the hyperbolic metric. I ran the test with points 
+distributed uniformly in the Euclidean metric, and these are the results.
\ No newline at end of file