From 8855eb54c305ffeaec32cb6bc49bfb0a2e465cc2 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Mon, 26 Aug 2013 14:36:09 +0200
Subject: [PATCH 01/15] Performance Improvements - changed Cartesian to
 Simple_cartesian in the examples - changed list to vector in the code -
 removed unnecessary includes - introduced multipass_distance

---
 .../barycenter.cpp                            | 16 ++++-----
 .../bounding_box.cpp                          | 16 ++++-----
 .../Principal_component_analysis/centroid.cpp | 18 +++++-----
 .../linear_least_squares_fitting_points_2.cpp | 14 ++++----
 ...near_least_squares_fitting_triangles_3.cpp | 18 +++++-----
 .../include/CGAL/centroid.h                   | 30 ++++++++++------
 .../CGAL/linear_least_squares_fitting_2.h     |  5 ++-
 .../CGAL/linear_least_squares_fitting_3.h     |  6 ++--
 .../linear_least_squares_fitting_circles_2.h  |  1 -
 .../linear_least_squares_fitting_cuboids_3.h  | 15 ++++----
 .../linear_least_squares_fitting_points_2.h   |  1 -
 .../linear_least_squares_fitting_points_3.h   |  1 -
 ...inear_least_squares_fitting_rectangles_2.h | 10 +++---
 .../linear_least_squares_fitting_segments_2.h |  5 +--
 .../linear_least_squares_fitting_segments_3.h |  8 +++--
 .../linear_least_squares_fitting_spheres_3.h  |  1 -
 ...inear_least_squares_fitting_tetrahedra_3.h | 21 +++++++----
 ...linear_least_squares_fitting_triangles_2.h |  6 ++--
 ...linear_least_squares_fitting_triangles_3.h | 19 +++++-----
 .../include/CGAL/multipass_distance.h         | 35 +++++++++++++++++++
 20 files changed, 150 insertions(+), 96 deletions(-)
 create mode 100755 STL_Extension/include/CGAL/multipass_distance.h

diff --git a/Principal_component_analysis/examples/Principal_component_analysis/barycenter.cpp b/Principal_component_analysis/examples/Principal_component_analysis/barycenter.cpp
index 66aba742b50..c9198c13230 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/barycenter.cpp
+++ b/Principal_component_analysis/examples/Principal_component_analysis/barycenter.cpp
@@ -1,21 +1,21 @@
 // Example program for the barycenter() function for 2D and 3D points.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/barycenter.h>
 
-#include <list>
+#include <vector>
 #include <iostream>
 #include <utility>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Point_2           Point_2;
-typedef K::Point_3           Point_3;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Point_2                  Point_2;
+typedef K::Point_3                  Point_3;
 
 int main()
 {
   // barycenter of 2D weighted points
-  std::list<std::pair<Point_2, FT> > points_2;
+  std::vector<std::pair<Point_2, FT> > points_2;
   points_2.push_back(std::make_pair(Point_2(1.0, 0.0),  1.0));
   points_2.push_back(std::make_pair(Point_2(2.0, 2.0),  2.0));
   points_2.push_back(std::make_pair(Point_2(3.0, 5.0), -2.0));
@@ -24,7 +24,7 @@ int main()
   std::cout << c2 << std::endl;
 
   // barycenter of 3D weighted points
-  std::list<std::pair<Point_3, FT> > points_3;
+  std::vector<std::pair<Point_3, FT> > points_3;
   points_3.push_back(std::make_pair(Point_3(1.0, 0.0, 0.5),  1.0));
   points_3.push_back(std::make_pair(Point_3(2.0, 2.0, 1.2),  2.0));
   points_3.push_back(std::make_pair(Point_3(3.0, 5.0, 4.5), -5.0));
diff --git a/Principal_component_analysis/examples/Principal_component_analysis/bounding_box.cpp b/Principal_component_analysis/examples/Principal_component_analysis/bounding_box.cpp
index b034f52e2cf..9d2d0b840ec 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/bounding_box.cpp
+++ b/Principal_component_analysis/examples/Principal_component_analysis/bounding_box.cpp
@@ -1,20 +1,20 @@
 // Example program for the bounding_box() function for 2D points and 3D points.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/bounding_box.h>
 
-#include <list>
+#include <vector>
 #include <iostream>
 
-typedef double              FT;
-typedef CGAL::Cartesian<FT> K;
-typedef K::Point_2          Point_2;
-typedef K::Point_3          Point_3;
+typedef double                     FT;
+typedef CGAL::Simple_cartesian<FT> K;
+typedef K::Point_2                 Point_2;
+typedef K::Point_3                 Point_3;
 
 int main()
 {
   // axis-aligned bounding box of 2D points
-  std::list<Point_2> points_2;
+  std::vector<Point_2> points_2;
   points_2.push_back(Point_2(1.0, 0.0));
   points_2.push_back(Point_2(2.0, 2.0));
   points_2.push_back(Point_2(3.0, 5.0));
@@ -23,7 +23,7 @@ int main()
   std::cout << c2 << std::endl;
 
   // axis-aligned bounding box of 3D points
-  std::list<Point_3> points_3;
+  std::vector<Point_3> points_3;
   points_3.push_back(Point_3(1.0, 0.0, 0.5));
   points_3.push_back(Point_3(2.0, 2.0, 1.2));
   points_3.push_back(Point_3(3.0, 5.0, 4.5));
diff --git a/Principal_component_analysis/examples/Principal_component_analysis/centroid.cpp b/Principal_component_analysis/examples/Principal_component_analysis/centroid.cpp
index d39594f47ed..eeba74e6a50 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/centroid.cpp
+++ b/Principal_component_analysis/examples/Principal_component_analysis/centroid.cpp
@@ -1,21 +1,21 @@
 // Example program for the centroid() function for 2D points, 3D points and 3D triangles.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/centroid.h>
 
-#include <list>
+#include <vector>
 #include <iostream>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Point_2           Point_2;
-typedef K::Point_3           Point_3;
-typedef K::Triangle_3        Triangle_3;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Point_2                  Point_2;
+typedef K::Point_3                  Point_3;
+typedef K::Triangle_3               Triangle_3;
 
 int main()
 {
   // centroid of 2D points
-  std::list<Point_2> points_2;
+  std::vector<Point_2> points_2;
   points_2.push_back(Point_2(1.0, 0.0));
   points_2.push_back(Point_2(2.0, 2.0));
   points_2.push_back(Point_2(3.0, 5.0));
@@ -23,7 +23,7 @@ int main()
   std::cout << c2 << std::endl;
 
   // centroid of 3D points
-  std::list<Point_3> points_3;
+  std::vector<Point_3> points_3;
   points_3.push_back(Point_3(1.0, 0.0, 0.5));
   points_3.push_back(Point_3(2.0, 2.0, 1.2));
   points_3.push_back(Point_3(3.0, 5.0, 4.5));
diff --git a/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_points_2.cpp b/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_points_2.cpp
index 01bee4976c3..c16a580b450 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_points_2.cpp
+++ b/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_points_2.cpp
@@ -1,16 +1,16 @@
 // Example program for linear least squares fitting of a 2D point set
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
-#include <list>
+#include <vector>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Line_2            Line;
-typedef K::Point_2           Point;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Line_2                   Line;
+typedef K::Point_2                  Point;
 
 int main()
 {
-  std::list<Point> points;
+  std::vector<Point> points;
   points.push_back(Point(1.0,2.0));
   points.push_back(Point(3.0,4.0));
   points.push_back(Point(5.0,6.0));
diff --git a/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp b/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp
index 6641b423b05..f8d03464deb 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp
+++ b/Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp
@@ -1,19 +1,19 @@
 // Example program for the linear_least_square_fitting function
 // on a set of 3D triangles
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
-#include <list>
+#include <vector>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Line_3            Line;
-typedef K::Plane_3           Plane;
-typedef K::Point_3           Point;
-typedef K::Triangle_3        Triangle;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Line_3                   Line;
+typedef K::Plane_3                  Plane;
+typedef K::Point_3                  Point;
+typedef K::Triangle_3               Triangle;
 
 int main(void)
 {
-  std::list<Triangle> triangles;
+  std::vector<Triangle> triangles;
   Point a(1.0,2.0,3.0);
   Point b(4.0,0.0,6.0);
   Point c(7.0,8.0,9.0);
diff --git a/Principal_component_analysis/include/CGAL/centroid.h b/Principal_component_analysis/include/CGAL/centroid.h
index f23ad7b3046..c23f2c4dc75 100644
--- a/Principal_component_analysis/include/CGAL/centroid.h
+++ b/Principal_component_analysis/include/CGAL/centroid.h
@@ -27,12 +27,13 @@
 #include <CGAL/Dimension.h>
 #include <CGAL/Origin.h>
 #include <CGAL/Kernel/global_functions.h>
+#include <CGAL/multipass_distance.h>
 
 #include <CGAL/is_iterator.h>
 #include <boost/utility.hpp>
 
 #include <iterator>
-#include <list>
+#include <vector>
 
 // Functions to compute the centroid of N points.
 // Works in 2D and 3D.
@@ -92,7 +93,8 @@ centroid(InputIterator begin,
   
   CGAL_precondition(begin != end);
   
-  std::list<Point> points;  
+  std::vector<Point> points;  
+  points.reserve(2 * multipass_distance(begin, end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -155,7 +157,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(3* multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -184,7 +187,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(3 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -318,7 +322,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(4 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -348,7 +353,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(4 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -477,7 +483,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(3 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -506,7 +513,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(3 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -640,7 +648,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(8 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -674,7 +683,8 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(12 * multipass_distance(begin,end));
   for(InputIterator it = begin;
       it != end;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
index e1cd4102de9..3ef8b8ca794 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
@@ -21,9 +21,8 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
-#include <CGAL/Algebraic_structure_traits.h>
-#include <CGAL/IO/io.h>
+//#include <CGAL/Algebraic_structure_traits.h>
+//#include <CGAL/IO/io.h>
 #include <CGAL/linear_least_squares_fitting_points_2.h>
 #include <CGAL/linear_least_squares_fitting_segments_2.h>
 #include <CGAL/linear_least_squares_fitting_triangles_2.h>
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
index d4173110b63..553fb285900 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
@@ -21,9 +21,8 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
-#include <CGAL/Algebraic_structure_traits.h>
-#include <CGAL/IO/io.h>
+//#include <CGAL/Algebraic_structure_traits.h>
+//#include <CGAL/IO/io.h>
 
 #include <CGAL/linear_least_squares_fitting_points_3.h>
 #include <CGAL/linear_least_squares_fitting_segments_3.h>
@@ -35,7 +34,6 @@
 #include <CGAL/Dimension.h>
 
 #include <iterator>
-#include <list>
 #include <string>
 
 namespace CGAL {
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_circles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_circles_2.h
index aa57977d187..dd9bc675e70 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_circles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_circles_2.h
@@ -21,7 +21,6 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_CIRCLES_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
 #include <CGAL/eigen.h>
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
index d122173a020..2b39fb0a12e 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
@@ -21,11 +21,10 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_CUBOIDS_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
-
+#include <CGAL/multipass_distance.h>
 #include <CGAL/linear_least_squares_fitting_points_3.h>
 #include <CGAL/linear_least_squares_fitting_segments_3.h>
 
@@ -115,7 +114,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(12 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -158,7 +158,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(8 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -258,7 +259,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(12 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -301,7 +303,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(8 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
index 96e1b81e7ef..7d1d6a9036e 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
@@ -21,7 +21,6 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_POINTS_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
index b4459bad20d..15355929e91 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
@@ -21,7 +21,6 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_POINTS_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
index 7086dcc0fd2..e999032cce5 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
@@ -21,12 +21,12 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_RECTANGLES_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
+#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 #include <vector>
@@ -168,8 +168,8 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Segment_2> segments;
-  
+  std::vector<Segment_2> segments;
+  segments.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -204,8 +204,8 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Point_2> points;
-  
+  std::vector<Point_2> points;
+  points..reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
index e076e8b166b..5b2552410fb 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
@@ -21,12 +21,12 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
+#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 #include <vector>
@@ -156,7 +156,8 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Point> points;  
+  std::vector<Point> points;  
+  points.reserve(2 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
index b444339b3f5..2245e76fff6 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
@@ -21,11 +21,11 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
 #include <CGAL/linear_least_squares_fitting_points_3.h>
+#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 
@@ -81,7 +81,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(2 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -144,7 +145,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(2 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
index 5de7d04a91c..1ae42e2957e 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
@@ -21,7 +21,6 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_SPHERES_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
index 2dded736a77..787cded68eb 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
@@ -21,7 +21,6 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_TETRAHEDRA_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 
@@ -29,6 +28,7 @@
 #include <CGAL/linear_least_squares_fitting_points_3.h>
 #include <CGAL/linear_least_squares_fitting_segments_3.h>
 #include <CGAL/linear_least_squares_fitting_triangles_3.h>
+#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 
@@ -83,7 +83,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Triangle> triangles;
+  std::vector<Triangle> triangles;
+  triangles.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -118,7 +119,9 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(6 * multipass_distance(first,beyond));
+
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -155,7 +158,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -220,7 +224,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Triangle> triangles;
+  std::vector<Triangle> triangles;
+  triangles.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -255,7 +260,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(6 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -292,7 +298,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
index 509a9d20136..9e6ba28b5f7 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
@@ -21,17 +21,16 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_2_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
+#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 #include <vector>
 #include <cmath>
-#include <list>
 
 namespace CGAL {
 
@@ -203,7 +202,8 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Point> points;  
+  std::vector<Point> points;  
+  points.reserve(3 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
index 835756c6f49..c40d2891a8c 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
@@ -21,11 +21,12 @@
 #define CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_3_H
 
 #include <CGAL/basic.h>
-#include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
+#include <CGAL/multipass_distance.h>
 
+#include <vector>
 #include <iterator>
 
 namespace CGAL {
@@ -80,7 +81,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(3* multipass_distance(first, beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -113,8 +115,8 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
-  
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(3* multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -178,7 +180,8 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::list<Segment> segments;
+  std::vector<Segment> segments;
+  segments.reserve(3* multipass_distance(first, beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -204,15 +207,15 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
-			                         const CGAL::Dimension_tag<0>& tag)
+                               const CGAL::Dimension_tag<0>& tag)
 {
   typedef typename K::Triangle_3  Triangle;
   typedef typename K::Point_3  Point;
 
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
-  
-  std::list<Point> points;
+  std::vector<Point> points;
+  points.reserve(3* multipass_distance(first, beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/STL_Extension/include/CGAL/multipass_distance.h b/STL_Extension/include/CGAL/multipass_distance.h
new file mode 100755
index 00000000000..e3ef04ba847
--- /dev/null
+++ b/STL_Extension/include/CGAL/multipass_distance.h
@@ -0,0 +1,35 @@
+#ifndef CGAL_MULTIPASS_DISTANCE_H
+#define CGAL_MULTIPASS_DISTANCE_H
+
+#include <iterator>
+
+namespace CGAL {
+
+
+  template <typename I, typename Cat>
+  typename std::iterator_traits<I>::difference_type
+  multipass_distance(const I& begin, const I& beyond, const Cat&)
+  {
+    return std::distance(begin, beyond);
+  }
+
+  template <typename I>
+  typename std::iterator_traits<I>::difference_type
+  multipass_distance(const I& begin, const I& beyond, const std::input_iterator_tag&)
+  {
+    return 0;
+  }
+
+
+  template <typename I>
+  typename std::iterator_traits<I>::difference_type
+  multipass_distance(const I& begin, const I& beyond)
+  {
+    return multipass_distance(begin, beyond, typename std::iterator_traits<I>::iterator_category());
+  }
+
+
+}
+
+
+#endif // CGAL_MULTIPASS_DISTANCE_H

From ca18c33778c6ded3d72c1902ef20802a428d0bf9 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Mon, 26 Aug 2013 15:52:09 +0200
Subject: [PATCH 02/15] Switching to Simple_cartesian gives better performance"

---
 Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp    | 4 ++--
 .../Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp      | 5 +++--
 Polyhedron/examples/Polyhedron/polyhedron_prog_traits.cpp    | 4 ++--
 Polyhedron/examples/Polyhedron/polyhedron_prog_vector.cpp    | 4 ++--
 4 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
index 7fb57529184..009841ff69a 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <iostream>
@@ -6,7 +6,7 @@
 #include <vector>
 #include <cmath>
 
-typedef CGAL::Cartesian<double>                              Kernel;
+typedef CGAL::Simple_cartesian<double>                       Kernel;
 typedef Kernel::Vector_3                                     Vector;
 typedef Kernel::Point_3                                      Point;
 typedef CGAL::Polyhedron_3<Kernel>                           Polyhedron;
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
index 96eb892efaa..90ead40b2ff 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <iostream>
@@ -8,7 +8,7 @@
 #include <cctype>
 #include <cmath>
 
-typedef CGAL::Cartesian<double>                              Kernel;
+typedef CGAL::Simple_cartesian<double>                              Kernel;
 typedef Kernel::Vector_3                                     Vector;
 typedef Kernel::Point_3                                      Point;
 typedef CGAL::Polyhedron_3<Kernel>                           Polyhedron;
@@ -188,6 +188,7 @@ int main( int argc, char* argv[]) {
     }
     Polyhedron P;
     cin >> P;
+
     for ( int i = 0; i != n; ++i) {
         cerr << "Subdivision " << i+1 << " ..." << endl;
         subdiv( P);
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_traits.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_traits.cpp
index c77d71484de..5fd41789fe7 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_traits.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_traits.cpp
@@ -1,8 +1,8 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_traits_3.h>
 #include <CGAL/Polyhedron_3.h>
 
-typedef CGAL::Cartesian<double>            Kernel;
+typedef CGAL::Simple_cartesian<double>     Kernel;
 typedef CGAL::Polyhedron_traits_3<Kernel>  Traits;
 typedef CGAL::Polyhedron_3<Traits>         Polyhedron;
 typedef Polyhedron::Halfedge_handle        Halfedge_handle;
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_vector.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_vector.cpp
index b90e7456373..d9f2894b0d2 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_vector.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_vector.cpp
@@ -1,9 +1,9 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/HalfedgeDS_vector.h>
 #include <CGAL/Polyhedron_3.h>
 #include <iostream>
 
-typedef CGAL::Cartesian<double>                        Kernel;
+typedef CGAL::Simple_cartesian<double>                 Kernel;
 typedef Kernel::Point_3                                Point_3;
 typedef CGAL::Polyhedron_3< Kernel,
                             CGAL::Polyhedron_items_3,

From 46ee658eb7963f21820585dc613def3126dd27ff Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Mon, 26 Aug 2013 16:36:02 +0200
Subject: [PATCH 03/15] Cartesian -> Simple_cartesian

---
 BGL/examples/BGL_polyhedron_3/distance.cpp               | 4 ++--
 BGL/examples/BGL_polyhedron_3/kruskal.cpp                | 4 ++--
 BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/BGL/examples/BGL_polyhedron_3/distance.cpp b/BGL/examples/BGL_polyhedron_3/distance.cpp
index 6c38bfacf70..1885bde3c84 100644
--- a/BGL/examples/BGL_polyhedron_3/distance.cpp
+++ b/BGL/examples/BGL_polyhedron_3/distance.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Polyhedron_items_with_id_3.h>
@@ -9,7 +9,7 @@
 
 #include <fstream>
 
-typedef CGAL::Cartesian<double>                                      Kernel;
+typedef CGAL::Simple_cartesian<double>                               Kernel;
 typedef Kernel::Point_3                                              Point;
 typedef CGAL::Polyhedron_3<Kernel,CGAL::Polyhedron_items_with_id_3>  Polyhedron;
 
diff --git a/BGL/examples/BGL_polyhedron_3/kruskal.cpp b/BGL/examples/BGL_polyhedron_3/kruskal.cpp
index 4dbc8d5f5c8..c8df3ab4ca8 100644
--- a/BGL/examples/BGL_polyhedron_3/kruskal.cpp
+++ b/BGL/examples/BGL_polyhedron_3/kruskal.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
@@ -10,7 +10,7 @@
 #include <boost/graph/kruskal_min_spanning_tree.hpp>
 
 
-typedef CGAL::Cartesian<double>                              Kernel;
+typedef CGAL::Simple_cartesian<double>                       Kernel;
 typedef Kernel::Vector_3                                     Vector;
 typedef Kernel::Point_3                                      Point;
 typedef CGAL::Polyhedron_3<Kernel>                           Polyhedron;
diff --git a/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp b/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
index 00b82a409e9..c25f10af425 100644
--- a/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
+++ b/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/Polyhedron_items_with_id_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
@@ -10,7 +10,7 @@
 
 #include <boost/graph/kruskal_min_spanning_tree.hpp>
 
-typedef CGAL::Cartesian<double>                                      Kernel;
+typedef CGAL::Simple_cartesian<double>                               Kernel;
 typedef Kernel::Point_3                                              Point;
 typedef CGAL::Polyhedron_3<Kernel,CGAL::Polyhedron_items_with_id_3>  Polyhedron;
 

From 4250b800b95a1a695b16001d85e993f3071c1b29 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Mon, 26 Aug 2013 17:06:42 +0200
Subject: [PATCH 04/15] Cartesian -> Simple_cartesian

---
 .../Authalic_parameterization.cpp                         | 4 ++--
 .../Complete_parameterization_example.cpp                 | 6 ++----
 .../Eigen_parameterization.cpp                            | 8 ++++----
 .../Mesh_cutting_parameterization.cpp                     | 4 ++--
 .../Simple_parameterization.cpp                           | 4 ++--
 .../Square_border_parameterization.cpp                    | 4 ++--
 .../Taucs_parameterization.cpp                            | 6 ++----
 .../Surface_mesh_parameterization/include/Mesh_cutter.h   | 2 --
 .../Surface_mesh_parameterization/include/Polyhedron_ex.h | 4 ++--
 .../polyhedron_ex_parameterization.cpp                    | 1 -
 10 files changed, 18 insertions(+), 25 deletions(-)

diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Authalic_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Authalic_parameterization.cpp
index e3caf0baf95..6665e621f15 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Authalic_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Authalic_parameterization.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -14,7 +14,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Complete_parameterization_example.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Complete_parameterization_example.cpp
index 7f6f126014c..e0d23c9b9aa 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Complete_parameterization_example.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Complete_parameterization_example.cpp
@@ -1,6 +1,4 @@
-#include <CGAL/basic.h> // include basic.h before testing #defines
-
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -20,7 +18,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 // Polyhedron adaptor
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Eigen_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Eigen_parameterization.cpp
index 4116388e924..7c97b3f8823 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Eigen_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Eigen_parameterization.cpp
@@ -1,6 +1,4 @@
-#include <CGAL/basic.h> // include basic.h before testing #defines
-
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -17,7 +15,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>             Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 
@@ -67,6 +65,7 @@ int main(int argc, char * argv[])
 
     typedef CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron>
                                             Parameterization_polyhedron_adaptor;
+
     Parameterization_polyhedron_adaptor mesh_adaptor(mesh);
 
     //***************************************
@@ -88,6 +87,7 @@ int main(int argc, char * argv[])
                                                         Parameterizer;
 
     Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer());
+
     switch(err) {
     case Parameterizer::OK: // Success
         break;
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp
index 5985dbea6c8..413ecb4eaf0 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -13,7 +13,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 // Polyhedron adaptor
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Simple_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Simple_parameterization.cpp
index d241d807bff..490a3761e26 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Simple_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Simple_parameterization.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -12,7 +12,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Square_border_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Square_border_parameterization.cpp
index 751a5c68784..e6c5335d124 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Square_border_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Square_border_parameterization.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -13,7 +13,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Taucs_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Taucs_parameterization.cpp
index c583d59c55a..670c7e92d03 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Taucs_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/Taucs_parameterization.cpp
@@ -1,6 +1,4 @@
-#include <CGAL/basic.h> // include basic.h before testing #defines
-
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Parameterization_polyhedron_adaptor_3.h>
@@ -17,7 +15,7 @@
 // Private types
 // ----------------------------------------------------------------------------
 
-typedef CGAL::Cartesian<double>             Kernel;
+typedef CGAL::Simple_cartesian<double>      Kernel;
 typedef CGAL::Polyhedron_3<Kernel>          Polyhedron;
 
 
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Mesh_cutter.h b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Mesh_cutter.h
index 0158ee33cba..5d96126157d 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Mesh_cutter.h
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Mesh_cutter.h
@@ -16,8 +16,6 @@
 #ifndef MESH_CUTTER_H
 #define MESH_CUTTER_H
 
-#include <CGAL/Cartesian.h>
-
 #include "Polyhedron_ex.h"
 
 #include <list>
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Polyhedron_ex.h b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Polyhedron_ex.h
index c2f8213c96b..402db914954 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Polyhedron_ex.h
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/include/Polyhedron_ex.h
@@ -1,7 +1,7 @@
 #ifndef POLYHEDRON_EX_H_INCLUDED
 #define POLYHEDRON_EX_H_INCLUDED
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 
@@ -13,7 +13,7 @@
 
 
 // CGAL kernel
-typedef CGAL::Cartesian<double> My_kernel;
+typedef CGAL::Simple_cartesian<double> My_kernel;
 
 
 // compute facet center
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
index cd601d226d9..254c8614169 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
@@ -30,7 +30,6 @@
 // polyhedron_ex_parameterization -t lscm -b 2pts mesh.off mesh.obj
 
 
-#include <CGAL/Cartesian.h>
 #include <CGAL/Timer.h>
 #include <CGAL/parameterize.h>
 #include <CGAL/Parameterization_mesh_patch_3.h>

From 60ebed5255bfb00ebf35ac9f117d244fc15f774d Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Tue, 27 Aug 2013 09:28:10 +0200
Subject: [PATCH 05/15] Passing to Simple_cartesian makes it 30% faster Seeding
 random makes it reproducible

---
 .../Spatial_searching/searching_with_circular_query.cpp  | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/Spatial_searching/examples/Spatial_searching/searching_with_circular_query.cpp b/Spatial_searching/examples/Spatial_searching/searching_with_circular_query.cpp
index abc2b5cc35a..221181cd185 100644
--- a/Spatial_searching/examples/Spatial_searching/searching_with_circular_query.cpp
+++ b/Spatial_searching/examples/Spatial_searching/searching_with_circular_query.cpp
@@ -1,24 +1,25 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Kd_tree.h>
 #include <CGAL/Search_traits_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/Fuzzy_sphere.h>
 
-typedef CGAL::Cartesian<double> K;
+typedef CGAL::Simple_cartesian<double> K;
 typedef K::Point_2 Point;
 typedef CGAL::Random_points_in_square_2<Point> Random_points_iterator;
 typedef CGAL::Counting_iterator<Random_points_iterator> N_Random_points_iterator;
 typedef CGAL::Search_traits_2<K> Traits;
 typedef CGAL::Fuzzy_sphere<Traits> Fuzzy_circle;
 typedef CGAL::Kd_tree<Traits> Tree;
-
+typedef CGAL::Random Random;
 int main() {
 
   const int N=1000;
 
   // generator for random data points in the square ( (-1,-1), (1,1) )
-  Random_points_iterator rpit( 1.0);
+  Random rnd(0);
+  Random_points_iterator rpit(1.0, rnd);
 
   // Insert also the N points in the tree
   Tree tree(N_Random_points_iterator(rpit,0),

From d2f0eff3cb08a99770f39eb6882a776fbbdfe328 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Tue, 27 Aug 2013 09:56:39 +0200
Subject: [PATCH 06/15] Switch to Simple_cartesian. Remove a superfluous .cpp
 Reorder #includes

---
 Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp | 9 +++++----
 Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.cpp  | 9 ---------
 Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.h    | 4 ++--
 .../examples/Jet_fitting_3/Single_estimation.cpp         | 7 +++----
 4 files changed, 10 insertions(+), 19 deletions(-)
 delete mode 100644 Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.cpp

diff --git a/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp b/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
index 27f3325a631..29f0db53dbd 100644
--- a/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
+++ b/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
@@ -1,11 +1,10 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Monge_via_jet_fitting.h>
+#include <CGAL/property_map.h>
 
 #include <fstream>
 #include <cassert>
 
-#include <CGAL/property_map.h>
-
 #ifdef CGAL_USE_BOOST_PROGRAM_OPTIONS
 #include <boost/program_options.hpp>
 namespace po = boost::program_options;
@@ -19,7 +18,7 @@ using namespace std;
 
 //Kernel of the PolyhedralSurf
 typedef double                DFT;
-typedef CGAL::Cartesian<DFT>  Data_Kernel;
+typedef CGAL::Simple_cartesian<DFT>  Data_Kernel;
 typedef Data_Kernel::Point_3  DPoint;
 typedef Data_Kernel::Vector_3 DVector;
 
@@ -305,5 +304,7 @@ int main()
     out_verbose->close();
     delete out_verbose;
   }  
+
+  std::cerr << "done" << std::endl;
   return 0;
 }
diff --git a/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.cpp b/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.cpp
deleted file mode 100644
index 23d08fa6a16..00000000000
--- a/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.cpp
+++ /dev/null
@@ -1,9 +0,0 @@
-#include "PolyhedralSurf.h"
-
-
-
-// Vector_3 PolyhedralSurf::getHalfedge_vector(Halfedge * h)
-// {
-//   Vector_3 v = h->opposite()->vertex()->point() - h->vertex()->point();
-//   return v;
-// }
diff --git a/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.h b/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.h
index 910cf7ec9dd..d3f3ffcb650 100644
--- a/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.h
+++ b/Jet_fitting_3/examples/Jet_fitting_3/PolyhedralSurf.h
@@ -1,7 +1,7 @@
 #ifndef CGAL_POLYHEDRALSURF_H_
 #define CGAL_POLYHEDRALSURF_H_
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 
@@ -180,7 +180,7 @@ struct Wrappers_VFH:public CGAL::Polyhedron_items_3 {
 
 
 typedef double                DFT;
-typedef CGAL::Cartesian<DFT>  Data_Kernel;
+typedef CGAL::Simple_cartesian<DFT>  Data_Kernel;
 typedef CGAL::Polyhedron_3 < Data_Kernel, Wrappers_VFH > Polyhedron;
 typedef Data_Kernel::Vector_3 Vector_3;
 
diff --git a/Jet_fitting_3/examples/Jet_fitting_3/Single_estimation.cpp b/Jet_fitting_3/examples/Jet_fitting_3/Single_estimation.cpp
index 7a435006f82..fd02d41dbb5 100644
--- a/Jet_fitting_3/examples/Jet_fitting_3/Single_estimation.cpp
+++ b/Jet_fitting_3/examples/Jet_fitting_3/Single_estimation.cpp
@@ -1,12 +1,11 @@
-#include <CGAL/Cartesian.h>
-
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Monge_via_jet_fitting.h>
 
 #include <fstream>
 #include <vector>
 
-#include <CGAL/Monge_via_jet_fitting.h>
 typedef double                   DFT;
-typedef CGAL::Cartesian<DFT>     Data_Kernel;
+typedef CGAL::Simple_cartesian<DFT>     Data_Kernel;
 typedef Data_Kernel::Point_3     DPoint;
 typedef CGAL::Monge_via_jet_fitting<Data_Kernel> My_Monge_via_jet_fitting;
 typedef My_Monge_via_jet_fitting::Monge_form     My_Monge_form;

From 8ad719e2698621f984b4b3404594c703bf6a5ea4 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Tue, 27 Aug 2013 10:20:13 +0200
Subject: [PATCH 07/15] Passed to Simple_cartesian Cleanup of inclusion order,
 and what files gets included

---
 Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics.cpp | 9 +++++----
 Ridges_3/examples/Ridges_3/PolyhedralSurf.h            | 4 ++--
 2 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics.cpp b/Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics.cpp
index d04367e216e..bc60a62b675 100644
--- a/Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics.cpp
+++ b/Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics.cpp
@@ -1,4 +1,8 @@
-#include <CGAL/Cartesian.h>
+
+//this is an enriched Polyhedron with facet normals
+#include "PolyhedralSurf.h"
+#include "PolyhedralSurf_rings.h"
+
 #include <CGAL/Ridges.h>
 #include <CGAL/Umbilics.h>
 #include <CGAL/Monge_via_jet_fitting.h>
@@ -12,9 +16,6 @@ namespace po = boost::program_options;
 
 using namespace std;
 
-//this is an enriched Polyhedron with facets' normal
-#include "PolyhedralSurf.h"
-#include "PolyhedralSurf_rings.h"
 
 typedef PolyhedralSurf::Traits          Kernel;
 typedef Kernel::FT                      FT;
diff --git a/Ridges_3/examples/Ridges_3/PolyhedralSurf.h b/Ridges_3/examples/Ridges_3/PolyhedralSurf.h
index 0bde81af0d8..9b2ecb03541 100644
--- a/Ridges_3/examples/Ridges_3/PolyhedralSurf.h
+++ b/Ridges_3/examples/Ridges_3/PolyhedralSurf.h
@@ -1,7 +1,7 @@
 #ifndef CGAL_POLYHEDRALSURF_H_
 #define CGAL_POLYHEDRALSURF_H_
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 
@@ -59,7 +59,7 @@ struct Wrappers_VFH:public CGAL::Polyhedron_items_3 {
 //PolyhedralSurf with facet normal operations
 //------------------------------------------------
 typedef double                FT;
-typedef CGAL::Cartesian<FT>  Kernel;
+typedef CGAL::Simple_cartesian<FT>  Kernel;
 typedef CGAL::Polyhedron_3 < Kernel, Wrappers_VFH > Polyhedron;
 typedef Kernel::Vector_3 Vector_3;
 

From b599bd387263077430f8e29b6b4c54b531207a9b Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Tue, 27 Aug 2013 10:52:05 +0200
Subject: [PATCH 08/15] Switching to Simple_cartesian leads to a performance
 gain of 50% for 100K points

---
 .../examples/Inscribed_areas/largest_empty_rectangle.cpp      | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp b/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
index 2a37da9c0e0..5128e958d84 100644
--- a/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
+++ b/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
@@ -1,11 +1,11 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Iso_rectangle_2.h>
 #include <CGAL/Largest_empty_iso_rectangle_2.h>
 
 #include <fstream>
 
 typedef double                                 Number_Type;
-typedef CGAL::Cartesian<Number_Type>           K;
+typedef CGAL::Simple_cartesian<Number_Type>    K;
 typedef CGAL::Largest_empty_iso_rectangle_2<K> Largest_empty_iso_rect_2;
 typedef K::Iso_rectangle_2                     Iso_rectangle_2;
 typedef K::Point_2                             Point_2;

From 0eeaccfb030dfdbe3c82732912bc3892b67822da Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Tue, 27 Aug 2013 11:00:08 +0200
Subject: [PATCH 09/15] Remove unused include

---
 .../examples/Straight_skeleton_2/Low_level_API.cpp               | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Straight_skeleton_2/examples/Straight_skeleton_2/Low_level_API.cpp b/Straight_skeleton_2/examples/Straight_skeleton_2/Low_level_API.cpp
index 36259c3e729..1cba9c43bd8 100644
--- a/Straight_skeleton_2/examples/Straight_skeleton_2/Low_level_API.cpp
+++ b/Straight_skeleton_2/examples/Straight_skeleton_2/Low_level_API.cpp
@@ -6,7 +6,6 @@
 
 #include<boost/shared_ptr.hpp>
 
-#include<CGAL/Cartesian.h>
 #include<CGAL/Polygon_2.h>
 #include<CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include<CGAL/Straight_skeleton_builder_2.h>

From a971b5e9baf44ae683c116e378c7be805f71d25e Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Wed, 28 Aug 2013 14:29:01 +0200
Subject: [PATCH 10/15] Switch to Simple_cartesian

---
 .../minimum_enclosing_parallelogram_2.cpp                   | 5 ++---
 .../Min_quadrilateral_2/minimum_enclosing_rectangle_2.cpp   | 4 ++--
 .../Min_quadrilateral_2/minimum_enclosing_strip_2.cpp       | 4 ++--
 .../Rectangular_p_center_2/rectangular_p_center_2.cpp       | 4 ++--
 .../examples/Inscribed_areas/extremal_polygon_2_area.cpp    | 4 ++--
 .../Inscribed_areas/extremal_polygon_2_perimeter.cpp        | 4 ++--
 .../examples/RangeSegmentTrees/range_tree_map_2.cpp         | 6 +++---
 .../examples/RangeSegmentTrees/range_tree_set_2.cpp         | 6 +++---
 .../examples/RangeSegmentTrees/segment_tree_map_2.cpp       | 6 +++---
 .../examples/RangeSegmentTrees/segment_tree_set_2.cpp       | 6 +++---
 .../examples/RangeSegmentTrees/segment_tree_set_3.cpp       | 6 +++---
 11 files changed, 27 insertions(+), 28 deletions(-)

diff --git a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_parallelogram_2.cpp b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_parallelogram_2.cpp
index e95b462b816..f4c6d3ef568 100644
--- a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_parallelogram_2.cpp
+++ b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_parallelogram_2.cpp
@@ -1,12 +1,11 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_convex_set_2.h>
 #include <CGAL/min_quadrilateral_2.h>
 #include <iostream>
 
-struct Kernel : public CGAL::Cartesian<double> {};
-
+typedef CGAL::Simple_cartesian<double>                   Kernel;
 typedef Kernel::Point_2                           Point_2;
 typedef Kernel::Line_2                            Line_2;
 typedef CGAL::Polygon_2<Kernel>                   Polygon_2;
diff --git a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_rectangle_2.cpp b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_rectangle_2.cpp
index 3127cbb47ad..66db5cef267 100644
--- a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_rectangle_2.cpp
+++ b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_rectangle_2.cpp
@@ -1,11 +1,11 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_convex_set_2.h>
 #include <CGAL/min_quadrilateral_2.h>
 #include <iostream>
 
-struct Kernel : public CGAL::Cartesian<double> {};
+typedef CGAL::Simple_cartesian<double>            Kernel;
 
 typedef Kernel::Point_2                           Point_2;
 typedef Kernel::Line_2                            Line_2;
diff --git a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_strip_2.cpp b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_strip_2.cpp
index bf87a3377a8..0bbfe6f8242 100644
--- a/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_strip_2.cpp
+++ b/Bounding_volumes/examples/Min_quadrilateral_2/minimum_enclosing_strip_2.cpp
@@ -1,11 +1,11 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_convex_set_2.h>
 #include <CGAL/min_quadrilateral_2.h>
 #include <iostream>
 
-struct Kernel : public CGAL::Cartesian<double> {};
+typedef CGAL::Simple_cartesian<double>            Kernel;
 
 typedef Kernel::Point_2                           Point_2;
 typedef Kernel::Line_2                            Line_2;
diff --git a/Bounding_volumes/examples/Rectangular_p_center_2/rectangular_p_center_2.cpp b/Bounding_volumes/examples/Rectangular_p_center_2/rectangular_p_center_2.cpp
index 7af6bb7b543..ed47f2667eb 100644
--- a/Bounding_volumes/examples/Rectangular_p_center_2/rectangular_p_center_2.cpp
+++ b/Bounding_volumes/examples/Rectangular_p_center_2/rectangular_p_center_2.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/rectangular_p_center_2.h>
 #include <CGAL/IO/Ostream_iterator.h>
@@ -9,7 +9,7 @@
 
 typedef double                                      FT;
 
-typedef CGAL::Cartesian<FT>                         Kernel;
+typedef CGAL::Simple_cartesian<FT>                  Kernel;
 
 typedef Kernel::Point_2                             Point;
 typedef std::vector<Point>                          Cont;
diff --git a/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_area.cpp b/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_area.cpp
index 0e75643eb9e..df77ff62998 100644
--- a/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_area.cpp
+++ b/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_area.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_convex_set_2.h>
@@ -8,7 +8,7 @@
 
 typedef double                                    FT;
 
-typedef CGAL::Cartesian<FT>                       Kernel;
+typedef CGAL::Simple_cartesian<FT>                Kernel;
 
 typedef Kernel::Point_2                           Point;
 typedef std::vector<int>                          Index_cont;
diff --git a/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_perimeter.cpp b/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_perimeter.cpp
index b22cbf5bb06..f4a6ffedccb 100644
--- a/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_perimeter.cpp
+++ b/Inscribed_areas/examples/Inscribed_areas/extremal_polygon_2_perimeter.cpp
@@ -1,4 +1,4 @@
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_convex_set_2.h>
@@ -8,7 +8,7 @@
 
 typedef double                                    FT;
 
-typedef CGAL::Cartesian<FT>                       Kernel;
+typedef CGAL::Simple_cartesian<FT>                Kernel;
 
 typedef Kernel::Point_2                           Point;
 typedef std::vector<int>                          Index_cont;
diff --git a/SearchStructures/examples/RangeSegmentTrees/range_tree_map_2.cpp b/SearchStructures/examples/RangeSegmentTrees/range_tree_map_2.cpp
index e57cc5b79ea..6924c9d7dbb 100644
--- a/SearchStructures/examples/RangeSegmentTrees/range_tree_map_2.cpp
+++ b/SearchStructures/examples/RangeSegmentTrees/range_tree_map_2.cpp
@@ -3,7 +3,7 @@
 // Ti is the type of each dimension of the tree.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Range_segment_tree_traits.h>
 #include <CGAL/Range_tree_k.h>
 #include <iostream>
@@ -12,8 +12,8 @@
 #include <iterator>
 
 
-typedef CGAL::Cartesian<double> Representation;
-typedef CGAL::Range_tree_map_traits_2<Representation, char> Traits;
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Range_tree_map_traits_2<K, char> Traits;
 typedef CGAL::Range_tree_2<Traits> Range_tree_2_type;
 
 int main()
diff --git a/SearchStructures/examples/RangeSegmentTrees/range_tree_set_2.cpp b/SearchStructures/examples/RangeSegmentTrees/range_tree_set_2.cpp
index 43f2017b711..46518a75283 100644
--- a/SearchStructures/examples/RangeSegmentTrees/range_tree_set_2.cpp
+++ b/SearchStructures/examples/RangeSegmentTrees/range_tree_set_2.cpp
@@ -3,7 +3,7 @@
 // Ti is the type of each dimension of the tree.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Range_segment_tree_traits.h>
 #include <CGAL/Range_tree_k.h>
 #include <iostream>
@@ -11,8 +11,8 @@
 #include <vector>
 #include <iterator>
 
-typedef CGAL::Cartesian<double> Representation;
-typedef CGAL::Range_segment_tree_set_traits_2<Representation> Traits;
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Range_segment_tree_set_traits_2<K> Traits;
 typedef CGAL::Range_tree_2<Traits> Range_tree_2_type;
 
 int main()
diff --git a/SearchStructures/examples/RangeSegmentTrees/segment_tree_map_2.cpp b/SearchStructures/examples/RangeSegmentTrees/segment_tree_map_2.cpp
index 9bb5bcde3cc..809960c5bf7 100644
--- a/SearchStructures/examples/RangeSegmentTrees/segment_tree_map_2.cpp
+++ b/SearchStructures/examples/RangeSegmentTrees/segment_tree_map_2.cpp
@@ -7,14 +7,14 @@
 #include <vector>
 #include <iterator>
 #include <list>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Segment_tree_k.h>
 #include <CGAL/Range_segment_tree_traits.h>
 
 
 
-typedef CGAL::Cartesian<double> Representation;
-typedef CGAL::Segment_tree_map_traits_2<Representation, char> Traits;
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Segment_tree_map_traits_2<K, char> Traits;
 typedef CGAL::Segment_tree_2<Traits > Segment_tree_2_type;
 
 int main()
diff --git a/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_2.cpp b/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_2.cpp
index 3d4ef8ccd48..bb49f6da73e 100644
--- a/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_2.cpp
+++ b/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_2.cpp
@@ -11,12 +11,12 @@
 #include <vector>
 #include <iterator>
 #include <list>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Segment_tree_k.h>
 #include <CGAL/Range_segment_tree_traits.h>
 
-typedef CGAL::Cartesian<double> Representation;
-typedef CGAL::Range_segment_tree_set_traits_2<Representation> Traits;
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Range_segment_tree_set_traits_2<K> Traits;
 typedef CGAL::Segment_tree_2<Traits > Segment_tree_2_type;
 
 int main()
diff --git a/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_3.cpp b/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_3.cpp
index 4e674b1dbb2..ae7ec3e8973 100644
--- a/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_3.cpp
+++ b/SearchStructures/examples/RangeSegmentTrees/segment_tree_set_3.cpp
@@ -6,12 +6,12 @@
 #include <utility>
 #include <iterator>
 #include <list>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Segment_tree_k.h>
 #include <CGAL/Range_segment_tree_traits.h>
 
-typedef CGAL::Cartesian<double> Representation;
-typedef CGAL::Range_segment_tree_set_traits_3<Representation> Traits;
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Range_segment_tree_set_traits_3<K> Traits;
 typedef CGAL::Segment_tree_3<Traits > Segment_tree_3_type;
 
 int main()

From a07b6620e402b7855772d7a209c188bab29ada15 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Thu, 29 Aug 2013 07:11:28 +0200
Subject: [PATCH 11/15] class..method() -> class.method()

---
 .../include/CGAL/linear_least_squares_fitting_rectangles_2.h    | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
index e999032cce5..5f95e12c240 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
@@ -205,7 +205,7 @@ linear_least_squares_fitting_2(InputIterator first,
   CGAL_precondition(first != beyond);
 
   std::vector<Point_2> points;
-  points..reserve(4 * multipass_distance(first,beyond));
+  points.reserve(4 * multipass_distance(first,beyond));
   for(InputIterator it = first;
       it != beyond;
       it++)

From a601b7bc06eee86f9c8a310ab188fab6280bb4c2 Mon Sep 17 00:00:00 2001
From: Laurent Rineau <laurent.rineau@cgal.org>
Date: Thu, 29 Aug 2013 11:16:54 +0200
Subject: [PATCH 12/15] Remove a superfluous .cpp (also from the documentation)

Follow-up to the following commit:
  | commit d2f0eff3cb08a99770f39eb6882a776fbbdfe328
  | Author: Andreas Fabri <andreas.fabri@geometryfactory.com>
  | Date:   Tue Aug 27 09:56:39 2013 +0200
  |
  |     Switch to Simple_cartesian.
  |     Remove a superfluous .cpp
  |     Reorder #includes
---
 Jet_fitting_3/doc/Jet_fitting_3/examples.txt | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Jet_fitting_3/doc/Jet_fitting_3/examples.txt b/Jet_fitting_3/doc/Jet_fitting_3/examples.txt
index a3a9ef2f0bb..86021482c02 100644
--- a/Jet_fitting_3/doc/Jet_fitting_3/examples.txt
+++ b/Jet_fitting_3/doc/Jet_fitting_3/examples.txt
@@ -1,5 +1,4 @@
 /*!
 \example Jet_fitting_3/Mesh_estimation.cpp
-\example Jet_fitting_3/PolyhedralSurf.cpp
 \example Jet_fitting_3/Single_estimation.cpp
 */

From 97d04b8f37897e5c4c18dbf7a35c2a884f78f4d2 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Thu, 5 Sep 2013 10:56:15 +0200
Subject: [PATCH 13/15] switch to Simple_cartesian

---
 Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp | 2 +-
 Jet_fitting_3/include/CGAL/Monge_via_jet_fitting.h       | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp b/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
index 29f0db53dbd..fa9c191941c 100644
--- a/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
+++ b/Jet_fitting_3/examples/Jet_fitting_3/Mesh_estimation.cpp
@@ -65,7 +65,7 @@ typedef boost::associative_property_map<Facet2normal_map_type> Facet_PM_type;
 typedef T_PolyhedralSurf_facet_ops<PolyhedralSurf, Facet_PM_type> Poly_facet_ops;
 
 typedef double                   LFT;
-typedef CGAL::Cartesian<LFT>     Local_Kernel;
+typedef CGAL::Simple_cartesian<LFT>     Local_Kernel;
 typedef CGAL::Monge_via_jet_fitting<Data_Kernel> My_Monge_via_jet_fitting;
 typedef My_Monge_via_jet_fitting::Monge_form My_Monge_form;
 
diff --git a/Jet_fitting_3/include/CGAL/Monge_via_jet_fitting.h b/Jet_fitting_3/include/CGAL/Monge_via_jet_fitting.h
index e60f694a191..a13aee6da7d 100644
--- a/Jet_fitting_3/include/CGAL/Monge_via_jet_fitting.h
+++ b/Jet_fitting_3/include/CGAL/Monge_via_jet_fitting.h
@@ -19,7 +19,7 @@
 #ifndef CGAL_MONGE_VIA_JET_FITTING_H_
 #define CGAL_MONGE_VIA_JET_FITTING_H_
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/circulator.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/eigen.h>
@@ -46,10 +46,10 @@ unsigned int fact(unsigned int n){
 
 ////////////////////// CLASS Monge_via_jet_fitting ////////////////////////
 #ifdef CGAL_EIGEN3_ENABLED
-template < class DataKernel, class LocalKernel = Cartesian<double>, class SvdTraits = Eigen_svd >
+template < class DataKernel, class LocalKernel = Simple_cartesian<double>, class SvdTraits = Eigen_svd >
 #else
 #ifdef CGAL_LAPACK_ENABLED
-template < class DataKernel, class LocalKernel = Cartesian<double>, class SvdTraits = Lapack_svd>  
+template < class DataKernel, class LocalKernel = Simple_cartesian<double>, class SvdTraits = Lapack_svd>  
 #else
 template < class DataKernel, class LocalKernel, class SvdTraits >  
 #endif

From 179ad6975bf0e038d06c4e7df6f4141be851b525 Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Wed, 11 Sep 2013 16:18:51 +0200
Subject: [PATCH 14/15] undo of switching to vector and multipass_distance

---
 .../include/CGAL/multipass_distance.h         | 35 -------------------
 1 file changed, 35 deletions(-)
 delete mode 100755 STL_Extension/include/CGAL/multipass_distance.h

diff --git a/STL_Extension/include/CGAL/multipass_distance.h b/STL_Extension/include/CGAL/multipass_distance.h
deleted file mode 100755
index e3ef04ba847..00000000000
--- a/STL_Extension/include/CGAL/multipass_distance.h
+++ /dev/null
@@ -1,35 +0,0 @@
-#ifndef CGAL_MULTIPASS_DISTANCE_H
-#define CGAL_MULTIPASS_DISTANCE_H
-
-#include <iterator>
-
-namespace CGAL {
-
-
-  template <typename I, typename Cat>
-  typename std::iterator_traits<I>::difference_type
-  multipass_distance(const I& begin, const I& beyond, const Cat&)
-  {
-    return std::distance(begin, beyond);
-  }
-
-  template <typename I>
-  typename std::iterator_traits<I>::difference_type
-  multipass_distance(const I& begin, const I& beyond, const std::input_iterator_tag&)
-  {
-    return 0;
-  }
-
-
-  template <typename I>
-  typename std::iterator_traits<I>::difference_type
-  multipass_distance(const I& begin, const I& beyond)
-  {
-    return multipass_distance(begin, beyond, typename std::iterator_traits<I>::iterator_category());
-  }
-
-
-}
-
-
-#endif // CGAL_MULTIPASS_DISTANCE_H

From 557c593afffcdbbb53293f770c054f3f3c43cdfd Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Wed, 11 Sep 2013 16:20:04 +0200
Subject: [PATCH 15/15] undo of switching to vector and multipass_distance

---
 .../include/CGAL/centroid.h                   | 30 +++++++------------
 .../linear_least_squares_fitting_cuboids_3.h  | 14 ++++-----
 ...inear_least_squares_fitting_rectangles_2.h |  9 ++----
 .../linear_least_squares_fitting_segments_2.h |  6 ++--
 .../linear_least_squares_fitting_segments_3.h |  8 ++---
 ...inear_least_squares_fitting_tetrahedra_3.h | 19 ++++--------
 ...linear_least_squares_fitting_triangles_2.h |  4 +--
 ...linear_least_squares_fitting_triangles_3.h | 15 ++++------
 8 files changed, 35 insertions(+), 70 deletions(-)

diff --git a/Principal_component_analysis/include/CGAL/centroid.h b/Principal_component_analysis/include/CGAL/centroid.h
index c23f2c4dc75..f23ad7b3046 100644
--- a/Principal_component_analysis/include/CGAL/centroid.h
+++ b/Principal_component_analysis/include/CGAL/centroid.h
@@ -27,13 +27,12 @@
 #include <CGAL/Dimension.h>
 #include <CGAL/Origin.h>
 #include <CGAL/Kernel/global_functions.h>
-#include <CGAL/multipass_distance.h>
 
 #include <CGAL/is_iterator.h>
 #include <boost/utility.hpp>
 
 #include <iterator>
-#include <vector>
+#include <list>
 
 // Functions to compute the centroid of N points.
 // Works in 2D and 3D.
@@ -93,8 +92,7 @@ centroid(InputIterator begin,
   
   CGAL_precondition(begin != end);
   
-  std::vector<Point> points;  
-  points.reserve(2 * multipass_distance(begin, end));
+  std::list<Point> points;  
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -157,8 +155,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Point> points;
-  points.reserve(3* multipass_distance(begin,end));
+  std::list<Point> points;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -187,8 +184,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Segment> segments;
-  segments.reserve(3 * multipass_distance(begin,end));
+  std::list<Segment> segments;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -322,8 +318,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Point> points;
-  points.reserve(4 * multipass_distance(begin,end));
+  std::list<Point> points;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -353,8 +348,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Segment> segments;
-  segments.reserve(4 * multipass_distance(begin,end));
+  std::list<Segment> segments;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -483,8 +477,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Point> points;
-  points.reserve(3 * multipass_distance(begin,end));
+  std::list<Point> points;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -513,8 +506,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Segment> segments;
-  segments.reserve(3 * multipass_distance(begin,end));
+  std::list<Segment> segments;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -648,8 +640,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Point> points;
-  points.reserve(8 * multipass_distance(begin,end));
+  std::list<Point> points;
   for(InputIterator it = begin;
       it != end;
       it++)
@@ -683,8 +674,7 @@ centroid(InputIterator begin,
 
   CGAL_precondition(begin != end);
   
-  std::vector<Segment> segments;
-  segments.reserve(12 * multipass_distance(begin,end));
+  std::list<Segment> segments;
   for(InputIterator it = begin;
       it != end;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
index 2b39fb0a12e..4bfcbdf601c 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
@@ -24,10 +24,10 @@
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
-#include <CGAL/multipass_distance.h>
 #include <CGAL/linear_least_squares_fitting_points_3.h>
 #include <CGAL/linear_least_squares_fitting_segments_3.h>
 
+#include <list>
 #include <iterator>
 
 namespace CGAL {
@@ -114,8 +114,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Segment> segments;
-  segments.reserve(12 * multipass_distance(first,beyond));
+  std::list<Segment> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -158,8 +157,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Point> points;
-  points.reserve(8 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -259,8 +257,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Segment> segments;
-  segments.reserve(12 * multipass_distance(first,beyond));
+  std::list<Segment> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -303,8 +300,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Point> points;
-  points.reserve(8 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
index 5f95e12c240..a1879152bf7 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
@@ -26,10 +26,9 @@
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
-#include <CGAL/multipass_distance.h>
 
 #include <iterator>
-#include <vector>
+#include <list>
 #include <cmath>
 
 namespace CGAL {
@@ -168,8 +167,7 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Segment_2> segments;
-  segments.reserve(4 * multipass_distance(first,beyond));
+  std::list<Segment_2> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -204,8 +202,7 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Point_2> points;
-  points.reserve(4 * multipass_distance(first,beyond));
+  std::list<Point_2> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
index 5b2552410fb..e2c3029b4df 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
@@ -26,10 +26,9 @@
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
-#include <CGAL/multipass_distance.h>
 
 #include <iterator>
-#include <vector>
+#include <list>
 #include <cmath>
 
 namespace CGAL {
@@ -156,8 +155,7 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Point> points;  
-  points.reserve(2 * multipass_distance(first,beyond));
+  std::list<Point> points;  
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
index 2245e76fff6..1be447a36a9 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
@@ -25,8 +25,8 @@
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
 #include <CGAL/linear_least_squares_fitting_points_3.h>
-#include <CGAL/multipass_distance.h>
 
+#include <list>
 #include <iterator>
 
 namespace CGAL {
@@ -81,8 +81,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Point> points;
-  points.reserve(2 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -145,8 +144,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Point> points;
-  points.reserve(2 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
index 787cded68eb..c87fcd3a470 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
@@ -28,7 +28,6 @@
 #include <CGAL/linear_least_squares_fitting_points_3.h>
 #include <CGAL/linear_least_squares_fitting_segments_3.h>
 #include <CGAL/linear_least_squares_fitting_triangles_3.h>
-#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 
@@ -83,8 +82,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Triangle> triangles;
-  triangles.reserve(4 * multipass_distance(first,beyond));
+  std::list<Triangle> triangles;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -119,8 +117,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Segment> segments;
-  segments.reserve(6 * multipass_distance(first,beyond));
+  std::list<Segment> segments;
 
   for(InputIterator it = first;
       it != beyond;
@@ -158,8 +155,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Point> points;
-  points.reserve(4 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -224,8 +220,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Triangle> triangles;
-  triangles.reserve(4 * multipass_distance(first,beyond));
+  std::list<Triangle> triangles;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -260,8 +255,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Segment> segments;
-  segments.reserve(6 * multipass_distance(first,beyond));
+  std::list<Segment> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -298,8 +292,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
 
-  std::vector<Point> points;
-  points.reserve(4 * multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
index 9e6ba28b5f7..7bd3d777d9d 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
@@ -26,7 +26,6 @@
 #include <CGAL/eigen.h>
 #include <CGAL/Linear_algebraCd.h>
 #include <CGAL/PCA_util.h>
-#include <CGAL/multipass_distance.h>
 
 #include <iterator>
 #include <vector>
@@ -202,8 +201,7 @@ linear_least_squares_fitting_2(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Point> points;  
-  points.reserve(3 * multipass_distance(first,beyond));
+  std::list<Point> points;  
   for(InputIterator it = first;
       it != beyond;
       it++)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
index c40d2891a8c..aca731b7191 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
@@ -24,9 +24,8 @@
 #include <CGAL/centroid.h>
 #include <CGAL/eigen.h>
 #include <CGAL/PCA_util.h>
-#include <CGAL/multipass_distance.h>
 
-#include <vector>
+#include <list>
 #include <iterator>
 
 namespace CGAL {
@@ -81,8 +80,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Segment> segments;
-  segments.reserve(3* multipass_distance(first, beyond));
+  std::list<Segment> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -115,8 +113,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
-  std::vector<Point> points;
-  points.reserve(3* multipass_distance(first,beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -180,8 +177,7 @@ linear_least_squares_fitting_3(InputIterator first,
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
   
-  std::vector<Segment> segments;
-  segments.reserve(3* multipass_distance(first, beyond));
+  std::list<Segment> segments;
   for(InputIterator it = first;
       it != beyond;
       it++)
@@ -214,8 +210,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // precondition: at least one element in the container.
   CGAL_precondition(first != beyond);
-  std::vector<Point> points;
-  points.reserve(3* multipass_distance(first, beyond));
+  std::list<Point> points;
   for(InputIterator it = first;
       it != beyond;
       it++)