diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circles.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circles.cpp
index f12cfb5af63..11472775d8b 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circles.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circles.cpp
@@ -21,14 +21,16 @@ int main() {
   // Locate the vertex with maximal degree.
   auto vit = arr.vertices_begin();
   Arrangement::Vertex_const_handle v_max = vit;
-  for (++vit; vit != arr.vertices_end(); ++vit)
-    if (vit->degree() > v_max->degree()) v_max = vit;
+  for(++vit; vit != arr.vertices_end(); ++vit)
+    if(vit->degree() > v_max->degree())
+      v_max = vit;
 
   // Locate the vertex with maximum degree.
 
   std::cout << "The vertex with maximal degree in the arrangement is: "
             << "v_max = (" << v_max->point() << ") "
             << "with degree " << v_max->degree() << "." << std::endl;
-  CGAL::draw(arr);
+
+  CGAL::draw(arr, "circles");
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_arcs.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_arcs.cpp
index 11043fb5555..252983822b0 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_arcs.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_arcs.cpp
@@ -24,8 +24,7 @@ int main() {
   // Create a line segment (C4) with the same supporting line (y = x), but
   // having one endpoint with irrational coordinates.
   CoordNT sqrt_15 = CoordNT(0, 1, 15); // = sqrt(15)
-  curves.push_back(Curve(s3.supporting_line(),
-                         Point(3, 3), Point(sqrt_15, sqrt_15)));
+  curves.push_back(Curve(s3.supporting_line(), Point(3, 3), Point(sqrt_15, sqrt_15)));
 
   // Create a circular arc (C5) that is the upper half of the circle centered at
   // (1, 1) with squared radius 3. Create the circle with clockwise orientation,
@@ -51,13 +50,12 @@ int main() {
   // Create a circular arc (C7) defined by two endpoints and a midpoint,
   // all having rational coordinates. This arc is the upper right
   // quarter of a circle centered at the origin with radius 5.
-  curves.push_back(Curve(Rational_point(0, 5), Rational_point(3, 4),
-                         Rational_point(5, 0)));
+  curves.push_back(Curve(Rational_point(0, 5), Rational_point(3, 4), Rational_point(5, 0)));
 
   // Construct the arrangement of the curves and print its size.
-  Arrangement  arr;
+  Arrangement arr;
   insert(arr, curves.begin(), curves.end());
   print_arrangement_size(arr);
-  CGAL::draw(arr);
+  CGAL::draw(arr, "circular_arcs");
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/draw_arr.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/draw_arr.cpp
index 4a94d8b849b..0476648efa9 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/draw_arr.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/draw_arr.cpp
@@ -2,11 +2,11 @@
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Arrangement_2.h>
 #include <CGAL/Arr_segment_traits_2.h>
+#include <CGAL/Arr_non_caching_segment_traits_2.h>
 #include <CGAL/draw_arrangement_2.h>
-#include <iterator>
 
 using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
-using Traits = CGAL::Arr_segment_traits_2<Kernel>;
+using Traits = CGAL::Arr_non_caching_segment_traits_2<Kernel>;
 using Point = Traits::Point_2;
 using Arrangement_2 = CGAL::Arrangement_2<Traits>;
 
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/ellipses.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/ellipses.cpp
index 480b0eefe31..a83c3a69efc 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/ellipses.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/ellipses.cpp
@@ -17,14 +17,10 @@ int main() {
   auto ctr_cv = traits.construct_curve_2_object();
 
   // Insert a full x-major ellipse
-  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE,
-                           Point(4,0), Point(0,2)));
-  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE,
-                           Point(0,2), Point(-4,0)));
-  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE,
-                           Point(-4,0), Point(0,-2)));
-  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE,
-                           Point(0,-2), Point(4,0)));
+  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE, Point(4, 0), Point(0, 2)));
+  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE, Point(0, 2), Point(-4, 0)));
+  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE, Point(-4, 0), Point(0, -2)));
+  CGAL::insert(arr, ctr_cv(1, 4, 0, 0, 0, -16, CGAL::COUNTERCLOCKWISE, Point(0, -2), Point(4, 0)));
 
   // Insert a full y-major ellipse
   CGAL::insert(arr, ctr_cv(4, 1, 0, 0, 0, -16));
@@ -39,7 +35,7 @@ int main() {
 
   print_arrangement_size(arr);
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "ellipses");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/hyperbolas.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/hyperbolas.cpp
index 8c165cac9f6..ecc9961adf2 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/hyperbolas.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/hyperbolas.cpp
@@ -19,63 +19,46 @@ int main() {
   // Insert a hyperbolic arc (C1), supported by the hyperbola y = 1/x
   // (or: xy - 1 = 0) with the endpoints (1/4, 4) and (2, 1/2).
   // The arc is counterclockwise oriented.
-  CGAL::insert(arr, ctr_cv(0, 0, 1, 0, 0, -1, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(1,4), 4), Point(2, Rational(1,2))));
-  CGAL::insert(arr, ctr_cv(0, 0, -1, 0, 0, -1, CGAL::CLOCKWISE,
-                           Point(Rational(-1,4), 4), Point(-2, Rational(1,2))));
+  CGAL::insert(arr,
+               ctr_cv(0, 0, 1, 0, 0, -1, CGAL::COUNTERCLOCKWISE, Point(Rational(1, 4), 4), Point(2, Rational(1, 2))));
+  CGAL::insert(arr, ctr_cv(0, 0, -1, 0, 0, -1, CGAL::CLOCKWISE, Point(Rational(-1, 4), 4), Point(-2, Rational(1, 2))));
 
-  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE,
-                           Point(3, 4), Point(1, 0)));
-  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE,
-                           Point(1, 0), Point(3, -4)));
-  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::CLOCKWISE,
-                           Point(-3, 4), Point(-1, 0)));
-  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::CLOCKWISE,
-                           Point(-1, 0), Point(-3, -4)));
+  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE, Point(3, 4), Point(1, 0)));
+  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE, Point(1, 0), Point(3, -4)));
+  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::CLOCKWISE, Point(-3, 4), Point(-1, 0)));
+  CGAL::insert(arr, ctr_cv(2, -1, 0, 0, 0, -2, CGAL::CLOCKWISE, Point(-1, 0), Point(-3, -4)));
 
-  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::CLOCKWISE,
-                           Point(4, 3), Point(0, 1)));
-  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::CLOCKWISE,
-                           Point(0, 1), Point(-4, 3)));
-  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE,
-                           Point(4, -3), Point(0, -1)));
-  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE,
-                           Point(0, -1), Point(-4, -3)));
+  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::CLOCKWISE, Point(4, 3), Point(0, 1)));
+  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::CLOCKWISE, Point(0, 1), Point(-4, 3)));
+  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE, Point(4, -3), Point(0, -1)));
+  CGAL::insert(arr, ctr_cv(-1, 2, 0, 0, 0, -2, CGAL::COUNTERCLOCKWISE, Point(0, -1), Point(-4, -3)));
 
-  CGAL::insert(arr, ctr_cv(4, 46, -144, 0, 0, -100, CGAL::COUNTERCLOCKWISE,
-                           Point(-5, 0),
+  CGAL::insert(arr, ctr_cv(4, 46, -144, 0, 0, -100, CGAL::COUNTERCLOCKWISE, Point(-5, 0),
                            Point(Rational(14, 10), Rational(48, 10))));
-  CGAL::insert(arr, ctr_cv(4, 46, -144, 0, 0, -100, CGAL::COUNTERCLOCKWISE,
-                           Point(5, 0),
+  CGAL::insert(arr, ctr_cv(4, 46, -144, 0, 0, -100, CGAL::COUNTERCLOCKWISE, Point(5, 0),
                            Point(Rational(-14, 10), Rational(-48, 10))));
   // 4*x*x + 46*y*y - 144*x*y - 100
 
-  CGAL::insert(arr, ctr_cv(46, 4,  -144, 0, 0, -100, CGAL::CLOCKWISE,
-                           Point(0, -5),
-                           Point(Rational(48, 10), Rational(14, 10))));
-  CGAL::insert(arr, ctr_cv(46, 4,  -144, 0, 0, -100, CGAL::CLOCKWISE,
-                           Point(0, 5),
-                           Point(Rational(-48, 10), Rational(-14, 10))));
+  CGAL::insert(
+      arr, ctr_cv(46, 4, -144, 0, 0, -100, CGAL::CLOCKWISE, Point(0, -5), Point(Rational(48, 10), Rational(14, 10))));
+  CGAL::insert(
+      arr, ctr_cv(46, 4, -144, 0, 0, -100, CGAL::CLOCKWISE, Point(0, 5), Point(Rational(-48, 10), Rational(-14, 10))));
   // 46*x*x + 4*y*y - 144*x*y - 100
 
-  CGAL::insert(arr, ctr_cv(4, 46, 144, 0, 0, -100, CGAL::CLOCKWISE,
-                           Point(-5, 0),
-                           Point(Rational(14,10), Rational(-48,10))));
-  CGAL::insert(arr, ctr_cv(4, 46, 144, 0, 0, -100, CGAL::CLOCKWISE,
-                           Point(5, 0),
-                           Point(Rational(-14,10), Rational(48,10))));
+  CGAL::insert(
+      arr, ctr_cv(4, 46, 144, 0, 0, -100, CGAL::CLOCKWISE, Point(-5, 0), Point(Rational(14, 10), Rational(-48, 10))));
+  CGAL::insert(
+      arr, ctr_cv(4, 46, 144, 0, 0, -100, CGAL::CLOCKWISE, Point(5, 0), Point(Rational(-14, 10), Rational(48, 10))));
   // 4*x*x + 46*y*y + 144*x*y - 100
 
-  CGAL::insert(arr, ctr_cv(46, 4, 144, 0, 0, -100, CGAL::COUNTERCLOCKWISE,
-                           Point(0, -5),
-                           Point(Rational(-48,10), Rational(14,10))));
-  CGAL::insert(arr, ctr_cv(46, 4, 144, 0, 0, -100, CGAL::COUNTERCLOCKWISE,
-                           Point(0, 5),
-                           Point(Rational(48,10), Rational(-14,10))));
+  CGAL::insert(arr, ctr_cv(46, 4, 144, 0, 0, -100, CGAL::COUNTERCLOCKWISE, Point(0, -5),
+                           Point(Rational(-48, 10), Rational(14, 10))));
+  CGAL::insert(arr, ctr_cv(46, 4, 144, 0, 0, -100, CGAL::COUNTERCLOCKWISE, Point(0, 5),
+                           Point(Rational(48, 10), Rational(-14, 10))));
 
   print_arrangement_size(arr);
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "hyperbolas");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/linear_conics.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/linear_conics.cpp
index 071c118052e..abec7c1dc8b 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/linear_conics.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/linear_conics.cpp
@@ -20,8 +20,8 @@ int main() {
   Point p2(0, -1);
   Point p3(0, 1);
   Point p4(1, 0);
-  Point p5(Rational(1,2),Rational(1,2));
-  Point p6(Rational(-1,2),Rational(1,2));
+  Point p5(Rational(1, 2), Rational(1, 2));
+  Point p6(Rational(-1, 2), Rational(1, 2));
   Rat_point rp0(0, 0);
   Rat_point rp1(1, 0);
   Rat_point rp2(0, 1);
@@ -56,7 +56,7 @@ int main() {
 
   print_arrangement_size(arr);
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "linear_conics");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/parabolas.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/parabolas.cpp
index 7213b06f095..8b1faa498a7 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/parabolas.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/parabolas.cpp
@@ -18,62 +18,49 @@ int main() {
 
   // x-major
   // insert the parabola y = x^2; (-1,1)--(1,1)
-  CGAL::insert(arr, ctr_cv(1, 0, 0, 0, -1, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(-1, 1), Point(1, 1)));
+  CGAL::insert(arr, ctr_cv(1, 0, 0, 0, -1, 0, CGAL::COUNTERCLOCKWISE, Point(-1, 1), Point(1, 1)));
 
   // translated
   // Insert the parabola y = x^2 - 2x + 2; (1,1)--(2,2)
-  CGAL::insert(arr, ctr_cv(1, 0, 0, -2, -1, 2, CGAL::COUNTERCLOCKWISE,
-                           Point(1, 1), Point(2, 2)));
-  CGAL::insert(arr, ctr_cv(1, 0, 0, 2, -1, 2, CGAL::COUNTERCLOCKWISE,
-                           Point(-2, 2), Point(-1, 1)));
+  CGAL::insert(arr, ctr_cv(1, 0, 0, -2, -1, 2, CGAL::COUNTERCLOCKWISE, Point(1, 1), Point(2, 2)));
+  CGAL::insert(arr, ctr_cv(1, 0, 0, 2, -1, 2, CGAL::COUNTERCLOCKWISE, Point(-2, 2), Point(-1, 1)));
 
   // rotated
   // Insert the parabola y = x^2 rotated clockwise about theta, such that
   // sin(theta) = 0.6, cos(theta) = 0.8
-  CGAL::insert(arr, ctr_cv(16, 9, -24, -15, -20, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(-2,10), Rational(14,10)),
-                           Point(Rational(14,10), Rational(2,10))));
-  CGAL::insert(arr, ctr_cv(16, 9, 24, 15, -20, 0, CGAL::CLOCKWISE,
-                           Point(Rational(2,10), Rational(14,10)),
-                           Point(Rational(-14,10), Rational(2,10))));
-  CGAL::insert(arr, ctr_cv(16, 9, 24, -15, 20, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(14,10), Rational(-2,10)),
-                           Point(Rational(-2,10), Rational(-14,10))));
-  CGAL::insert(arr, ctr_cv(16, 9, -24, 15, 20, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(2,10), Rational(-14,10)),
-                           Point(Rational(-14,10), Rational(-2,10))));
+  CGAL::insert(arr, ctr_cv(16, 9, -24, -15, -20, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(-2, 10), Rational(14, 10)),
+                           Point(Rational(14, 10), Rational(2, 10))));
+  CGAL::insert(arr, ctr_cv(16, 9, 24, 15, -20, 0, CGAL::CLOCKWISE, Point(Rational(2, 10), Rational(14, 10)),
+                           Point(Rational(-14, 10), Rational(2, 10))));
+  CGAL::insert(arr, ctr_cv(16, 9, 24, -15, 20, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(14, 10), Rational(-2, 10)),
+                           Point(Rational(-2, 10), Rational(-14, 10))));
+  CGAL::insert(arr, ctr_cv(16, 9, -24, 15, 20, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(2, 10), Rational(-14, 10)),
+                           Point(Rational(-14, 10), Rational(-2, 10))));
 
   // 16*x*x+9*y*y-24*x*y-15*x-20*y
 
-  CGAL::insert(arr, ctr_cv(9, 16, -24, -20, -15, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(2,10), Rational(14,10)),
-                           Point(Rational(14,10), Rational(-2,10))));
-  CGAL::insert(arr, ctr_cv(9, 16, 24, -20, 15, 0, CGAL::CLOCKWISE,
-                           Point(Rational(2,10), Rational(-14,10)),
-                           Point(Rational(14,10), Rational(2,10))));
-  CGAL::insert(arr, ctr_cv(9, 16, 24, 20, -15, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(-14,10), Rational(-2,10)),
-                           Point(Rational(-2,10), Rational(14,10))));
-  CGAL::insert(arr, ctr_cv(9, 16, -24, 20, 15, 0, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(-2,10), Rational(-14,10)),
-                           Point(Rational(-14,10), Rational(2,10))));
+  CGAL::insert(arr, ctr_cv(9, 16, -24, -20, -15, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(2, 10), Rational(14, 10)),
+                           Point(Rational(14, 10), Rational(-2, 10))));
+  CGAL::insert(arr, ctr_cv(9, 16, 24, -20, 15, 0, CGAL::CLOCKWISE, Point(Rational(2, 10), Rational(-14, 10)),
+                           Point(Rational(14, 10), Rational(2, 10))));
+  CGAL::insert(arr, ctr_cv(9, 16, 24, 20, -15, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(-14, 10), Rational(-2, 10)),
+                           Point(Rational(-2, 10), Rational(14, 10))));
+  CGAL::insert(arr, ctr_cv(9, 16, -24, 20, 15, 0, CGAL::COUNTERCLOCKWISE, Point(Rational(-2, 10), Rational(-14, 10)),
+                           Point(Rational(-14, 10), Rational(2, 10))));
 
   // 9*x*x+16*y*y-24*x*y+20*x+15*y
 
   // rotated & translated
-  CGAL::insert(arr, ctr_cv(16, 9, -24, -23, -14, 36, CGAL::COUNTERCLOCKWISE,
-                           Point(Rational(8,10), Rational(24,10)),
-                           Point(Rational(24,10), Rational(12,10))));
-  CGAL::insert(arr, ctr_cv(16, 9, 24, 23, -14, 36, CGAL::CLOCKWISE,
-                           Point(Rational(-8,10), Rational(24,10)),
-                           Point(Rational(-24,10), Rational(12,10))));
+  CGAL::insert(arr, ctr_cv(16, 9, -24, -23, -14, 36, CGAL::COUNTERCLOCKWISE, Point(Rational(8, 10), Rational(24, 10)),
+                           Point(Rational(24, 10), Rational(12, 10))));
+  CGAL::insert(arr, ctr_cv(16, 9, 24, 23, -14, 36, CGAL::CLOCKWISE, Point(Rational(-8, 10), Rational(24, 10)),
+                           Point(Rational(-24, 10), Rational(12, 10))));
 
   // 16*x*x+9*y*y-24*x*y-23*x-14*y+36
 
   print_arrangement_size(arr);
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "parabolas");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polylines.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polylines.cpp
index 51fa18d82c8..1320b164323 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polylines.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polylines.cpp
@@ -45,7 +45,7 @@ int main() {
   insert(arr, pi1);
   insert(arr, pi2);
   insert(arr, pi3);
-  print_arrangement_size(arr);          // print the arrangement size
-  CGAL::draw(arr);
+  print_arrangement_size(arr); // print the arrangement size
+  CGAL::draw(arr, "polylines");
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/rational_functions.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/rational_functions.cpp
index df0c5f19bab..37f6d094eba 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/rational_functions.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/rational_functions.cpp
@@ -57,7 +57,7 @@ int main() {
   insert(arr, arcs.begin(), arcs.end());
   print_arrangement(arr);
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "rational_functions");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
index 2246f44bb96..132c4948bd3 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
@@ -51,7 +51,7 @@ int main() {
     std::cout << std::endl;
   }
 
-  CGAL::draw(arr);
+  CGAL::draw(arr, "unbounded_non_intersecting");
 
   return 0;
 }
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_approximate_point_2_at_x.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_approximate_point_2_at_x.h
index 71fe4de2d56..2141826219e 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_approximate_point_2_at_x.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_approximate_point_2_at_x.h
@@ -2,12 +2,12 @@
 #define CGAL_DRAW_AOS_ARR_APPROXIMATE_POINT_2_AT_X_H
 #include <boost/iterator/function_output_iterator.hpp>
 
-#include "CGAL/number_utils.h"
-#include "CGAL/Arr_rational_function_traits_2.h"
-#include "CGAL/Draw_aos/Arr_construct_curve_end.h"
-#include "CGAL/Draw_aos/Arr_construct_segments.h"
-#include "CGAL/Draw_aos/Arr_approximate_point_2.h"
-#include "CGAL/Draw_aos/type_utils.h"
+#include <CGAL/Arr_enums.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/Arr_rational_function_traits_2.h>
+#include <CGAL/Draw_aos/Arr_construct_segments.h>
+#include <CGAL/Draw_aos/Arr_approximate_point_2.h>
+#include <CGAL/Draw_aos/type_utils.h>
 
 namespace CGAL {
 namespace draw_aos {
@@ -89,20 +89,19 @@ class Arr_approximate_point_2_at_x<Arr_rational_function_traits_2<Kernel>>
   using X_monotone_curve_2 = typename Traits_adaptor<Geom_traits>::X_monotone_curve_2;
   using FT = typename Traits_adaptor<Geom_traits>::FT;
   using Approx_point = typename Arr_approximation_geometry_traits<Geom_traits>::Approx_point;
-  using Construct_curve_end = Arr_construct_curve_end<Geom_traits>;
 
 public:
-  Arr_approximate_point_2_at_x(const Geom_traits& traits)
-      : m_cst_curve_end(traits) {}
+  Arr_approximate_point_2_at_x(const Geom_traits&)
+      : to_ft() {}
 
   std::optional<Approx_point> operator()(const X_monotone_curve_2& curve, FT x) const {
-    std::optional<Point_2> min_end = m_cst_curve_end(curve, ARR_MIN_END);
-    if(min_end.has_value() && x < min_end->x()) {
-      return std::nullopt;
-    }
-    std::optional<Point_2> max_end = m_cst_curve_end(curve, ARR_MAX_END);
-    if(max_end.has_value() && x > max_end->x()) {
-      return std::nullopt;
+    FT xmin = curve.left_parameter_space_in_x() == ARR_INTERIOR ? curve.left_x()
+                                                                : to_ft(std::numeric_limits<double>::lowest());
+    FT xmax = curve.right_parameter_space_in_x() == ARR_INTERIOR ? curve.right_x()
+                                                                 : to_ft(std::numeric_limits<double>::max());
+
+    if(x < xmin || x > xmax) {
+      return std::nullopt; // x is out of bounds
     }
 
     using Bound = typename Geom_traits::Bound;
@@ -115,7 +114,7 @@ public:
   }
 
 private:
-  const Construct_curve_end m_cst_curve_end;
+  const Construct_coordinate<Geom_traits> to_ft;
 };
 
 } // namespace draw_aos
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h
index d6a780ef8be..fbc839a9d3e 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h
@@ -8,11 +8,10 @@
 #include <optional>
 #include <vector>
 
-#include "CGAL/Arr_enums.h"
-#include "CGAL/Draw_aos/Arr_approximate_point_2_at_x.h"
-#include "CGAL/Draw_aos/Arr_render_context.h"
-#include "CGAL/Draw_aos/type_utils.h"
-#include "CGAL/basic.h"
+#include <CGAL/Arr_enums.h>
+#include <CGAL/Draw_aos/Arr_approximate_point_2_at_x.h>
+#include <CGAL/Draw_aos/Arr_render_context.h>
+#include <CGAL/Draw_aos/type_utils.h>
 
 namespace CGAL {
 namespace draw_aos {
@@ -50,6 +49,7 @@ class Arr_bounded_approximate_curve_2_impl<Arrangement, false>
                       const Intersections_vector& bottom_inters,
                       Polyline_geom& polyline)
         : Arr_context_delegator<Bounded_render_context>(ctx)
+        , to_ft()
         , curve(curve)
         , m_approx_pt_at_x(approx_pt_at_x)
         , top_inters(top_inters)
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_face_2.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_face_2.h
index 9f2d6190b30..9bb295ffeb3 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_face_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_approximate_face_2.h
@@ -10,13 +10,13 @@
 
 #include <boost/iterator/function_output_iterator.hpp>
 
-#include "CGAL/Arr_enums.h"
-#include "CGAL/Bbox_2.h"
-#include "CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h"
-#include "CGAL/Draw_aos/Arr_bounded_approximate_point_2.h"
-#include "CGAL/Draw_aos/Arr_bounded_face_triangulator.h"
-#include "CGAL/Draw_aos/Arr_render_context.h"
-#include "CGAL/Draw_aos/type_utils.h"
+#include <CGAL/Arr_enums.h>
+#include <CGAL/Bbox_2.h>
+#include <CGAL/Draw_aos/Arr_bounded_approximate_curve_2.h>
+#include <CGAL/Draw_aos/Arr_bounded_approximate_point_2.h>
+#include <CGAL/Draw_aos/Arr_bounded_face_triangulator.h>
+#include <CGAL/Draw_aos/Arr_render_context.h>
+#include <CGAL/Draw_aos/type_utils.h>
 
 namespace CGAL {
 
@@ -212,7 +212,7 @@ class Arr_bounded_approximate_face_2
   using Bounded_render_context = Arr_bounded_render_context<Arrangement>;
 
   using Triangulator = Arr_bounded_face_triangulator<Arrangement>;
-  using Patch_boundary = Patch_boundary<Geom_traits>;
+  using Patch = Patch_boundary<Geom_traits>;
   using Simplifier = Colinear_simplifier<Geom_traits, typename Triangulator::Insert_iterator>;
 
   struct Left_to_right_tag
@@ -236,13 +236,13 @@ private:
     using Insert_iterator = boost::function_output_iterator<std::function<void(Approx_point pt)>>;
 
     Execution_context(const Bounded_render_context& ctx,
-                      const Patch_boundary& patch_boundary,
+                      const Patch& patch,
                       Output_iterator out_it,
                       const Bounded_approximate_point_2& bounded_approx_pt,
                       const Bounded_approximate_curve_2& bounded_approx_curve)
         : Arr_context_delegator<Bounded_render_context>(ctx)
         , base_out_it(out_it)
-        , patch_boundary(patch_boundary)
+        , patch(patch)
         , bounded_approx_pt(bounded_approx_pt)
         , bounded_approx_curve(bounded_approx_curve) {
       this->out_it = boost::make_function_output_iterator(std::function([this](Approx_point pt) {
@@ -257,7 +257,7 @@ private:
         }
 
         if(passed_fictitious_edge && last_pt.has_value()) {
-          this->patch_boundary(last_pt.value(), pt, base_out_it);
+          this->patch(last_pt.value(), pt, base_out_it);
         }
         passed_fictitious_edge = false;
 
@@ -280,7 +280,7 @@ private:
     std::optional<Approx_point> last_pt, first_pt;
     bool passed_fictitious_edge{false};
     Output_iterator base_out_it;
-    const Patch_boundary& patch_boundary;
+    const Patch& patch;
   };
 
 private:
@@ -419,9 +419,9 @@ private:
 
     if constexpr(Unbounded) {
       if(ctx.first_pt.has_value()) {
-        ctx.patch_boundary(ctx.last_pt.value(), ctx.first_pt.value(), ctx.base_out_it);
+        ctx.patch(ctx.last_pt.value(), ctx.first_pt.value(), ctx.base_out_it);
       } else {
-        ctx.patch_boundary(ctx.base_out_it);
+        ctx.patch(ctx.base_out_it);
       }
     }
   }
@@ -431,7 +431,7 @@ public:
                                  const Bounded_approximate_point_2& bounded_approx_pt,
                                  const Bounded_approximate_curve_2& bounded_approx_curve)
       : m_ctx(ctx)
-      , m_patch_boundary(ctx.bbox())
+      , m_patch(ctx.bbox())
       , m_bounded_approx_pt(bounded_approx_pt)
       , m_bounded_approx_curve(bounded_approx_curve) {}
 
@@ -468,8 +468,8 @@ public:
 
     auto triangulator = Triangulator(m_ctx);
     auto simplifier = Simplifier(triangulator.insert_iterator(), m_ctx.bbox());
-    auto ctx = Execution_context(m_ctx, m_patch_boundary, simplifier.insert_iterator(), m_bounded_approx_pt,
-                                 m_bounded_approx_curve);
+    auto ctx =
+        Execution_context(m_ctx, m_patch, simplifier.insert_iterator(), m_bounded_approx_pt, m_bounded_approx_curve);
 
     if(fh->is_unbounded()) {
       approximate_ccb<Outer_ccb_tag, true>(ctx, fh->outer_ccb());
@@ -486,7 +486,7 @@ private:
   const Bounded_render_context& m_ctx;
   const Bounded_approximate_point_2& m_bounded_approx_pt;
   const Bounded_approximate_curve_2& m_bounded_approx_curve;
-  const Patch_boundary m_patch_boundary;
+  const Patch m_patch;
 };
 
 } // namespace draw_aos
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_renderer.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_renderer.h
index 8ee79ebd442..98030b55f5c 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_renderer.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_bounded_renderer.h
@@ -209,7 +209,8 @@ public:
       return cache;
     }
 
-    Execution_context ctx(Arr_bounded_render_context(m_ctx, m_bbox, cache));
+    Bounded_render_context bounded_ctx(m_ctx, m_bbox, cache);
+    Execution_context ctx(bounded_ctx);
 
     auto top = ctx->cst_horizontal_segment(to_ft(ctx->ymax()), to_ft(ctx->xmin()), to_ft(ctx->xmax()));
     auto bottom = ctx->cst_horizontal_segment(to_ft(ctx->ymin()), to_ft(ctx->xmin()), to_ft(ctx->xmax()));
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_construct_segments.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_construct_segments.h
index 80195c95f2d..d3d179bb9b3 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_construct_segments.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_construct_segments.h
@@ -59,7 +59,14 @@ public:
 template <typename GeomTraits>
 class Arr_construct_segment_impl<GeomTraits, false>
 {
-  static_assert(false, "Not implemented yet!");
+  using Geom_traits = GeomTraits;
+  using X_monotone_curve_2 = typename Traits_adaptor<Geom_traits>::X_monotone_curve_2;
+  using FT = typename Traits_adaptor<Geom_traits>::FT;
+
+public:
+  Arr_construct_segment_impl(const GeomTraits&) { CGAL_assertion_msg(false, "Not implemented yet"); }
+
+  X_monotone_curve_2 operator()(FT, FT, FT, FT) const {}
 };
 
 template <typename GeomTraits>
@@ -109,6 +116,7 @@ class Arr_construct_vertical_segment<Arr_rational_function_traits_2<Kernel>>
   using X_monotone_curve_2 = typename Traits_adaptor<Geom_traits>::X_monotone_curve_2;
   using Construct_x_monotone_curve_2 = typename Geom_traits::Construct_x_monotone_curve_2;
   using FT = typename Traits_adaptor<Geom_traits>::FT;
+  using Bound = typename Geom_traits::Bound;
   using Polynomial_1 = typename Geom_traits::Polynomial_1;
 
 public:
@@ -123,11 +131,12 @@ public:
     Polynomial_1 x0_num(CORE::numerator(x0.lower()));
     Polynomial_1 x0_denum(CORE::denominator(x0.lower()));
     double k = 100;
-    double xmin = ymin.to_double() / k + x0.to_double();
-    double xmax = ymax.to_double() / k + x0.to_double();
+    Bound xmin = ymin.lower() / k + x0.lower();
+    Bound xmax = ymax.lower() / k + x0.lower();
     Polynomial_1 p_num = x0_num * k * x - k * x0_denum;
     Polynomial_1 p_denum = x0_denum;
-    return cst_x_curve(p_num, p_denum, xmin, xmax);
+    auto cv = cst_x_curve(p_num, p_denum, FT(xmin), FT(xmax));
+    return cv;
   }
 };
 
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_render_context.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_render_context.h
index 54ac11a3054..79ff791f464 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_render_context.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/Arr_render_context.h
@@ -64,7 +64,8 @@ class Arr_bounds_context_mixin
 
 protected:
   Arr_bounds_context_mixin(const Bbox_2& bbox)
-      : m_bbox(bbox) {}
+      : m_bbox(bbox)
+      , to_ft() {}
 
 public:
   double xmin() const { return m_bbox.xmin(); }
diff --git a/Arrangement_on_surface_2/include/CGAL/Draw_aos/type_utils.h b/Arrangement_on_surface_2/include/CGAL/Draw_aos/type_utils.h
index 0dd41e29f00..778bdb8676e 100644
--- a/Arrangement_on_surface_2/include/CGAL/Draw_aos/type_utils.h
+++ b/Arrangement_on_surface_2/include/CGAL/Draw_aos/type_utils.h
@@ -1,16 +1,14 @@
 #ifndef CGAL_DRAW_AOS_TYPE_UTILS_H
 #define CGAL_DRAW_AOS_TYPE_UTILS_H
-#include "CGAL/Arr_polycurve_traits_2.h"
-#include "CGAL/Arr_polyline_traits_2.h"
-#include "CGAL/Cartesian.h"
 #include <type_traits>
 
+#include <CGAL/Arr_non_caching_segment_traits_2.h>
+#include <CGAL/Arr_polycurve_traits_2.h>
+#include <CGAL/Arr_polyline_traits_2.h>
 #include <CGAL/Arr_segment_traits_2.h>
 #include <CGAL/Arr_linear_traits_2.h>
 #include <CGAL/Arr_circle_segment_traits_2.h>
 #include <CGAL/Arr_conic_traits_2.h>
-#include <CGAL/Arr_circular_arc_traits_2.h>
-#include <CGAL/Arr_Bezier_curve_traits_2.h>
 #include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>
 #include <CGAL/Arr_rational_function_traits_2.h>
 #include <CGAL/Arr_algebraic_segment_traits_2.h>
@@ -115,6 +113,23 @@ public:
   using Approximate_point_2 = typename Geom_traits::Approximate_point_2;
 };
 
+template <typename Kernel>
+struct Traits_adaptor<Arr_non_caching_segment_traits_2<Kernel>>
+    : public Traits_adaptor_base<Arr_non_caching_segment_traits_2<Kernel>>
+{
+private:
+  using Geom_traits = Arr_non_caching_segment_traits_2<Kernel>;
+
+public:
+  constexpr static bool Has_unbounded_curves = false;
+  constexpr static double Approximation_sizing_factor = 1.0;
+  using FT = typename Kernel::FT;
+  using Approximate_2 = typename Geom_traits::Approximate_2;
+  using Approximate_number_type = typename Geom_traits::Approximate_number_type;
+  using Approximate_kernel = typename Geom_traits::Approximate_kernel;
+  using Approximate_point_2 = typename Geom_traits::Approximate_point_2;
+};
+
 template <typename SegmentTraits>
 struct Traits_adaptor<Arr_polyline_traits_2<SegmentTraits>>
     : public Traits_adaptor_base<Arr_polyline_traits_2<SegmentTraits>>
@@ -204,20 +219,6 @@ public:
   using Approximate_point_2 = typename Geom_traits::Approximate_point_2;
 };
 
-template <typename RatKernel, typename AlgKernel, typename NtTraits>
-struct Traits_adaptor<Arr_Bezier_curve_traits_2<RatKernel, AlgKernel, NtTraits>>
-    : public Traits_adaptor_base<Arr_Bezier_curve_traits_2<RatKernel, AlgKernel, NtTraits>>
-{
-  static_assert(false, "Approximate_2 not yet modeled by this geometry traits class.");
-};
-
-template <typename Kernel>
-struct Traits_adaptor<Arr_circular_line_arc_traits_2<Kernel>>
-    : public Traits_adaptor_base<Arr_circular_line_arc_traits_2<Kernel>>
-{
-  static_assert(false, "Approximate_2 not yet modeled by this geometry traits class.");
-};
-
 template <typename Kernel>
 struct Traits_adaptor<Arr_rational_function_traits_2<Kernel>>
     : public Traits_adaptor_base<Arr_rational_function_traits_2<Kernel>>
diff --git a/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h b/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
index c87cf6805ed..7812116c3e4 100644
--- a/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
@@ -630,7 +630,7 @@ void draw(const CGAL_ARR_TYPE& aos, const char* title = "2D Arrangement on Surfa
     CGAL::Random random((size_t(vh.ptr())));
     return get_random_color(random);
   };
-  auto viewer = draw_aos::Arr_viewer(app.activeWindow(), aos, gso, "Arrangement Viewer");
+  auto viewer = draw_aos::Arr_viewer(app.activeWindow(), aos, gso, title);
   viewer.show();
   app.exec();
 }