Merged with trunk and removed unnecessary files

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/witness@934 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: d0ec52d222d22c102e9fe57590882cd0024c82d5

16 files changed, 0 insertions, 7892 deletions

diff --git a/src/Witness_complex/example/Torus_distance.h b/src/Witness_complex/example/Torus_distance.h
deleted file mode 100644
index 5ae127df..00000000
--- a/src/Witness_complex/example/Torus_distance.h
+++ /dev/null
@@ -1,209 +0,0 @@
-#ifndef GUDHI_TORUS_DISTANCE_H_
-#define GUDHI_TORUS_DISTANCE_H_
-
-#include <math.h>
-
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/Epick_d.h>
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::FT FT;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-
-/**
- * \brief Class of distance in a flat torus in dimension D
- *
- */
-class Torus_distance {
-
-public:
-    typedef K::FT    FT;
-    typedef K::Point_d Point_d;
-    typedef Point_d Query_item;
-    typedef typename CGAL::Dynamic_dimension_tag D;
-
-  double box_length = 2;
-
-  FT transformed_distance(Query_item q, Point_d p) const
-  {
-    FT distance = FT(0);
-    FT coord = FT(0);
-    //std::cout << "Hello skitty!\n";
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-	qe = construct_it(q,1), pit = construct_it(p);
-	for(; qit != qe; qit++, pit++)
-          {
-            coord = sqrt(((*qit)-(*pit))*((*qit)-(*pit)));
-            if (coord*coord <= (box_length-coord)*(box_length-coord))
-              distance += coord*coord;
-            else
-              distance += (box_length-coord)*(box_length-coord);
-          }
-        return distance;
-  }
-
-  FT min_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r) const {
-    FT distance = FT(0);
-    FT dist1, dist2;
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-                                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if((*qit) < r.min_coord(i))
-          {
-            dist1 = (r.min_coord(i)-(*qit));
-            dist2 = (box_length - r.max_coord(i)+(*qit));
-            if (dist1 < dist2)
-              distance += dist1*dist1;
-            else
-              distance += dist2*dist2;
-          }
-        else if ((*qit) > r.max_coord(i))
-          {
-            dist1 = (box_length - (*qit)+r.min_coord(i));
-            dist2 = ((*qit) - r.max_coord(i));
-            if (dist1 < dist2)
-              distance += dist1*dist1;
-            else
-              distance += dist2*dist2;
-          }
-      }
-    return distance;
-  }
-
-  FT min_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r,
-                               std::vector<FT>& dists) const {
-    FT distance = FT(0);
-    FT dist1, dist2;
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-	                  	           qe = construct_it(q,1);
-    //std::cout << r.max_coord(0) << std::endl;
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if((*qit) < r.min_coord(i))
-          {
-            dist1 = (r.min_coord(i)-(*qit));
-            dist2 = (box_length - r.max_coord(i)+(*qit));
-            if (dist1 < dist2)
-              {
-                dists[i] = dist1;
-                distance += dist1*dist1;
-              }
-            else
-              {
-                dists[i] = dist2;
-                distance += dist2*dist2;
-                //std::cout << "Good stuff1\n";
-              }
-          }
-        else if ((*qit) > r.max_coord(i))
-          {
-            dist1 = (box_length - (*qit)+r.min_coord(i));
-            dist2 = ((*qit) - r.max_coord(i));
-            if (dist1 < dist2)
-              {
-                dists[i] = dist1;
-                distance += dist1*dist1;
-                //std::cout << "Good stuff2\n";
-              }
-            else
-              {
-                dists[i] = dist2;
-                distance += dist2*dist2;
-              }
-          }
-      };
-    return distance;
-  }
-    
-  FT max_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r) const {
-    FT distance=FT(0);
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-		                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if (box_length <= (r.min_coord(i)+r.max_coord(i)))
-          if ((r.max_coord(i)+r.min_coord(i)-box_length)/FT(2.0) <= (*qit) &&
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-          else
-            distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-        else
-          if ((box_length-r.max_coord(i)-r.min_coord(i))/FT(2.0) <= (*qit) ||
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-          else
-            distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-      }
-    return distance;
-  }
-
-  
-  FT max_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r,
-                               std::vector<FT>& dists) const {
-    FT distance=FT(0);
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-		                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if (box_length <= (r.min_coord(i)+r.max_coord(i)))
-          if ((r.max_coord(i)+r.min_coord(i)-box_length)/FT(2.0) <= (*qit) &&
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            {
-              dists[i] = r.max_coord(i)-(*qit);
-              distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-            }
-          else
-            {
-              dists[i] = sqrt(((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i)));
-              distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-            }
-        else
-          if ((box_length-r.max_coord(i)-r.min_coord(i))/FT(2.0) <= (*qit) ||
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            {
-              dists[i] = sqrt((r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit)));
-              distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-              
-            }
-          else
-            {
-              dists[i] = (*qit)-r.min_coord(i);
-              distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-            }
-      }
-    return distance;
-  }
-
-    inline FT new_distance(FT dist, FT old_off, FT new_off,
-                           int )  const {
-      
-      FT new_dist = dist + (new_off*new_off - old_off*old_off);
-      return new_dist;
-    }
-    
-  inline FT transformed_distance(FT d) const {
-    return d*d;
-  }
-
-  inline FT inverse_of_transformed_distance(FT d) const {
-    return sqrt(d);
-  }
-  
-};
-
-#endif
diff --git a/src/Witness_complex/example/protected_sets/output_tikz.h b/src/Witness_complex/example/protected_sets/output_tikz.h
deleted file mode 100644
index edfd9a5f..00000000
--- a/src/Witness_complex/example/protected_sets/output_tikz.h
+++ /dev/null
@@ -1,67 +0,0 @@
-#ifndef OUTPUT_TIKZ_H
-#define OUTPUT_TIKZ_H
-
-#include <vector>
-#include <string>
-#include <algorithm>
-#include <fstream>
-#include <cmath>
-
-void write_tikz_plot(std::vector<FT> data, std::string filename)
-{
-  int n = data.size();
-  FT vmax = *(std::max_element(data.begin(), data.end()));
-  //std::cout << std::log10(vmax) << " " << std::floor(std::log10(vmax));
-  
-  FT order10 = pow(10,std::floor(std::log10(vmax)));
-  int digit = std::floor( vmax / order10) + 1;
-  if (digit == 4 || digit == 6) digit = 5;
-  if (digit > 6) digit = 10;
-  FT plot_max = digit*order10;
-  std::cout << plot_max << " " << vmax;
-  FT hstep = 10.0/(n-1);
-  FT wstep = 10.0 / plot_max;
-
-  std::cout << "(eps_max-eps_min)/(N-48) = " << (vmax-*data.begin())/(data.size()-48) << "\n";
-  std::ofstream ofs(filename, std::ofstream::out);
-
-  ofs <<
-    "\\documentclass{standalone}\n" <<
-    "\\usepackage[utf8]{inputenc}\n" <<
-    "\\usepackage{amsmath}\n" <<
-    "\\usepackage{tikz}\n\n" <<
-    "\\begin{document}\n" <<
-    "\\begin{tikzpicture}\n";
-  
-  ofs <<  "\\draw[->] (0,0) -- (0,11);" << std::endl <<
-    "\\draw[->] (0,0) -- (11,0);" << std::endl <<
-    "\\foreach \\i in {1,...,10}" << std::endl <<
-    "\\draw (0,\\i) -- (-0.05,\\i);" << std::endl <<
-    "\\foreach \\i in {1,...,10}" << std::endl <<
-    "\\draw (\\i,0) -- (\\i,-0.05);" << std::endl << std::endl <<
-
-    "\\foreach \\i in {1,...,10}" << std::endl <<
-    "\\draw[dashed] (-0.05,\\i) -- (11,\\i);" << std::endl << std::endl <<
-    
-    "\\node at (-0.5,11) {$*$}; " << std::endl <<
-    "\\node at (11,-0.5) {$*$}; " << std::endl <<
-    "\\node at (-0.5,-0.5) {0}; " << std::endl <<
-    "\\node at (-0.5,10) {" << plot_max << "}; " << std::endl <<
-    "%\\node at (10,-0.5) {2}; " << std::endl;
-
-  ofs << "\\draw[red] (0," << wstep*data[0] << ")";
-  for (int i = 1; i < n; ++i)
-    ofs << " -- (" << hstep*i << "," << wstep*data[i] << ")";
-  ofs << ";\n";
-
-  ofs <<
-    "\\end{tikzpicture}\n" <<
-    "\\end{document}";
-  
-  ofs.close();
-
-
-  
-}
-
-#endif
diff --git a/src/Witness_complex/example/protected_sets/protected_sets.h b/src/Witness_complex/example/protected_sets/protected_sets.h
deleted file mode 100644
index ec627808..00000000
--- a/src/Witness_complex/example/protected_sets/protected_sets.h
+++ /dev/null
@@ -1,597 +0,0 @@
-#ifndef PROTECTED_SETS_H
-#define PROTECTED_SETS_H
-
-#include <algorithm>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-#include <CGAL/Kernel_d/Hyperplane_d.h>
-#include <CGAL/Kernel_d/Vector_d.h>
-
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::Vector_d Vector_d;
-typedef K::Oriented_side_d Oriented_side_d;
-typedef K::Has_on_positive_side_d Has_on_positive_side_d;
-typedef K::Sphere_d Sphere_d;
-typedef K::Hyperplane_d Hyperplane_d;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex;
-typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle;
-
-typedef std::vector<Point_d> Point_Vector;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-FT  _sfty = pow(10,-14);
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// AUXILLARY FUNCTIONS
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well 
- *  
- *  W is the initial point vector
- *  chosen_landmark is the index of the chosen point in W
- *  landmarks_ind is the vector of indices of already chosen points in W
- *  delaunay is the Delaunay triangulation
- *  landmark_count is the current number of chosen vertices
- *  torus is true iff you are working on a flat torus [-1,1]^d
- *  OUT: Vertex handle to the newly inserted point
- */
-Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus)
-{
-  if (!torus)
-    {
-      Delaunay_vertex v =delaunay.insert(W[chosen_landmark]);
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      Delaunay_vertex v;
-      for (int i = 0; i < nb_cells; ++i)
-        {
-          std::vector<FT> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1));
-              cell_i /= 3;
-            }
-          v = delaunay.insert(point);
-        }
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-}
-
-/** Small check if the vertex v is in the full cell fc
- */
-
-bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc)
-{
-  for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it)
-    if (*v_it == v)
-      return true;
-  return false;
-}
-
-/** Fill chosen point vector from indices with copies if you are working on a flat torus
- *  
- *  IN:  W is the point vector
- *  OUT: landmarks is the output vector
- *  IN:  landmarks_ind is the vector of indices
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */
-
-void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus)
-{
-  if (!torus)
-    for (unsigned j = 0; j < landmarks_ind.size(); ++j)
-      landmarks.push_back(W[landmarks_ind[j]]);
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      int nbL = landmarks_ind.size();
-      // Fill landmarks
-      for (int i = 0; i < nb_cells-1; ++i)
-        for (int j = 0; j < nbL; ++j)
-          {
-            int cell_i = i;
-            Point_d point;
-            for (int l = 0; l < D; ++l)
-              {
-                point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1));
-                cell_i /= 3;
-              }
-            landmarks.push_back(point);
-          }
-    }
-}
-
-/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices
- *
- *  IN: t is the Delaunay triangulation
- *  OUT: full_cells is the output vector
- */
-
-void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells)
-{
-  // Store vertex indices in a map
-  int ind = 0; //index of a vertex
-  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
-  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-    if (t.is_infinite(v_it))
-      continue;
-    else
-      index_of_vertex[v_it] = ind++;
-  // Write full cells as vectors in full_cells
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      std::vector<int> cell;
-      for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it)
-        cell.push_back(index_of_vertex[*v_it]);
-      full_cells.push_back(cell);
-    }
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// IS VIOLATED TEST
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Check if a newly created cell is protected from old vertices
- *  
- *  t is the Delaunay triangulation
- *  vertices is the vector containing the point to insert and a facet f in t
- *  v1 is the vertex of t, such that f and v1 form a simplex
- *  v2 is the vertex of t, such that f and v2 form another simplex
- *  delta is the protection constant
- *  power_protection is true iff the delta-power protection is used
- */
-
-bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0)
-{
-  assert(vertices.size() == vertices[0].size() ||
-         vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1
-  assert(v1 != v2);
-  if (vertices.size() == vertices[0].size() + 1)
-  // FINITE CASE
-    {
-      Sphere_d cs(vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0]));
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it)) 
-          {
-            //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); 
-            if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-              {
-                FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point());
-                if (!power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-                    return true;
-                if (power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-                    return true;                 
-              }
-          }
-      */
-      // Check if the simplex is thick enough
-      Hyperplane_d tau_h(vertices.begin()+1, vertices.end());
-      Vector_d orth_tau = tau_h.orthogonal_vector();
-      /*
-               p_s1 = Vector_d(*(vertices.begin()), *(vertices.begin()+1));
-      */
-      //std::cout << "||orth_tau|| = " << sqrt(orth_tau.squared_length()) << "\n";
-      FT orth_length = sqrt(orth_tau.squared_length());
-      K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it;
-      // Compute the altitude
-      FT h = 0;
-      for (o_it = orth_tau.cartesian_begin(),
-           p_it = vertices.begin()->cartesian_begin(),
-           s_it = (vertices.begin()+1)->cartesian_begin();
-           o_it != orth_tau.cartesian_end();
-           ++o_it, ++p_it, ++s_it)
-        h += (*o_it)*(*p_it - *s_it)/orth_length;
-      h = fabs(h);
-      // Is the center inside the box?
-      bool inside_the_box = true;
-      for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it)
-        if (*c_it > 1.0 || *c_it < -1.0)
-          {
-            inside_the_box = false; break;
-          }
-      if (inside_the_box && h/r < theta0)
-        return true;
-      if (!t.is_infinite(v1))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-    }
-  else
-  // INFINITE CASE
-    {
-      Delaunay_triangulation::Vertex_iterator v = t.vertices_begin();
-      while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end())
-        v++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE);
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it))
-          if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-            {
-              std::vector<FT> coords;
-              Point_d p = v_it->point();
-              auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-              for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-                coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-              Point_d p_delta = Point_d(coords);
-              bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-              bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-              if (!p_is_inside && p_delta_is_inside)
-                return true;
-            }
-      */
-      if (!t.is_infinite(v1))
-        {
-          std::vector<FT> coords;
-          Point_d p = v1->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          std::vector<FT> coords;
-          Point_d p = v2->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-    }
-  return false;
-}
-  
-/** Auxillary recursive function to check if the point p violates the protection of the cell c and
- *  if there is a violation of an eventual new cell
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  c is the current cell (simplex)
- *  parent_cell is the parent cell (simplex)
- *  index is the index of the facet between c and parent_cell from parent_cell's point of view
- *  D is the dimension of the triangulation
- *  delta is the protection constant
- *  marked_cells is the vector of all visited cells containing p in their circumscribed ball
- *  power_protection is true iff you are working with delta-power protection
- *
- *  OUT: true iff inserting p hasn't produced any violation so far
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  std::vector<Point_d> vertices;
-  if (!t.is_infinite(c))
-    {
-      // if the cell is finite, we look if the protection is violated
-      for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it)
-        vertices.push_back((*v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(ed.transformed_distance(center_cs, vertices[0]));
-      FT dist2 = ed.transformed_distance(center_cs, p);
-      // if the new point is inside the protection ball of a non conflicting simplex
-      if (!power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-          return true;
-      if (power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-          return true;    
-      // if the new point is inside the circumscribing ball : continue violation searching on neighbours
-      //if (dist2 < r*r)
-      //if (dist2 < (5*r+delta)*(5*r+delta))
-      if (dist2 < r*r)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      // if the new point is outside the protection sphere
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is guaranteed to be finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;            
-        }
-    } 
-  else
-    {
-      // Inside of the convex hull is + side. Outside is - side.
-      for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-        if (!t.is_infinite(*vh_it))
-          vertices.push_back((*vh_it)->point());
-      Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin();
-      while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c))
-        v_it++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE);
-      //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point());
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      std::vector<FT> coords;
-      auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-      for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-        coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-      Point_d p_delta = Point_d(coords);
-      bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO);
-      bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-
-      // If we work with power protection, we just ignore any conflicts
-      if (!power_protection && !p_is_inside && p_delta_is_inside)
-        return true;
-      //if the cell is infinite we look at the neighbours regardless
-      if (p_is_inside)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);    
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is finite if the parent cell is finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              if (!t.is_infinite(parent_cell->vertex(i)))
-                vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;
-        }
-    }
-  //c->tds_data().clear_visited();
-  //marked_cells.pop_back();
-  return false;
-}
-
-/** Checks if inserting the point p in t will make conflicts
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  D is the dimension of triangulation
- *  delta is the protection constant
- *  power_protection is true iff you are working with delta-power protection
- *  OUT: true iff inserting p produces a violation of delta-protection.
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  Delaunay_triangulation::Vertex_handle v;
-  Delaunay_triangulation::Face f(t.current_dimension()); 
-  Delaunay_triangulation::Facet ft; 
-  Delaunay_triangulation::Full_cell_handle c; 
-  Delaunay_triangulation::Locate_type lt;
-  std::vector<Full_cell_handle> marked_cells;
-  c = t.locate(p, lt, f, ft, v);
-  bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0);
-  for (Full_cell_handle fc : marked_cells)
-    fc->tds_data().clear();
-  return violation_existing_cells;
-}
-
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!//
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////
-// LANDMARK CHOICE PROCEDURE
-///////////////////////////////////////////////////////////////////////
-
-/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call.
- *
- *  IN:  W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d
- *  IN:  nbP is the size of W
- *  OUT: landmarks is the output vector for the points
- *  OUT: landmarks_ind is the output vector for the indices of the selected points in W
- *  IN:  delta is the constant of protection
- *  OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */ 
-
-void landmark_choice_protected_delaunay(Point_Vector& W, int nbP, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT delta, std::vector<std::vector<int>>& full_cells, bool torus, bool power_protection, FT theta0)
-{
-  bool return_ = true;
-  unsigned D = W[0].size();
-  Torus_distance td;
-  Euclidean_distance ed;
-  Delaunay_triangulation t(D);
-  CGAL::Random rand;
-  int landmark_count = 0;
-  std::list<int> index_list;
-  //      shuffle the list of indexes (via a vector)
-  {
-    std::vector<int> temp_vector;
-    for (int i = 0; i < nbP; ++i)
-      temp_vector.push_back(i);
-    unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
-    std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed));
-    //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end());
-    for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it)
-      index_list.push_front(*it);
-  }
-  if (!torus)
-    for (unsigned pos1 = 0; pos1 < D+1; ++pos1)
-      {
-        std::vector<FT> point;
-        for (unsigned i = 0; i < pos1; ++i)
-          point.push_back(-1);
-        if (pos1 != D)
-          point.push_back(1);
-        for (unsigned i = pos1+1; i < D; ++i)
-          point.push_back(0);
-        assert(point.size() == D);
-        W[index_list.front()] = Point_d(point);
-        insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-        index_list.pop_front();
-      }
-  else if (D == 2)
-    {
-      for (int i = 0; i < 4; ++i)
-        for (int j = 0; j < 2; ++j)
-          {
-            W[index_list.front()] = Point_d(std::vector<FT>{i*0.5, j*1.0});
-            insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-            index_list.pop_front();
-            W[index_list.front()] = Point_d(std::vector<FT>{0.25+i*0.5, 0.5+j});
-            insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-            index_list.pop_front();
-          }
-    }
-  else
-    std::cout << "No torus starter available for dim>2\n";
-  std::list<int>::iterator list_it = index_list.begin();
-  while (list_it != index_list.end())
-    {
-      if (!is_violating_protection(W[*list_it], t, D, delta, power_protection, theta0))
-        {
-          // If no conflicts then insert in every copy of T^3
-
-          insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count, torus);
-          if (return_)
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            index_list.erase(list_it++);
-          /*
-          // PIECE OF CODE FOR DEBUGGING PURPOSES
-          
-          Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count);
-          if (triangulation_is_protected(t, delta))
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            { //THAT'S WHERE SOMETHING'S WRONG
-              t.remove(inserted_v);
-              landmarks_ind.pop_back();
-              landmark_count--;
-              write_delaunay_mesh(t, W[*list_it], is2d);
-              is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore
-            }
-          */
-          //std::cout << "index_list_size() = " << index_list.size() << "\n";
-        }
-      else
-        {
-          list_it++;
-          //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n";
-        }
-      //if (list_it != index_list.end())
-      //  write_delaunay_mesh(t, W[*list_it], is2d);
-    }
-  fill_landmarks(W, landmarks, landmarks_ind, torus);
-  fill_full_cell_vector(t, full_cells);
-  /*
-  if (triangulation_is_protected(t, delta))
-    std::cout << "Triangulation is ok\n";
-  else
-    {
-      std::cout << "Triangulation is BAD!! T_T しくしく!\n";
-    }
-  */
-  //write_delaunay_mesh(t, W[0], is2d);
-  //std::cout << t << std::endl;
-}
-
-#endif
diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp b/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp
deleted file mode 100644
index f3df3f1e..00000000
--- a/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp
+++ /dev/null
@@ -1,610 +0,0 @@
-#ifndef PROTECTED_SETS_H
-#define PROTECTED_SETS_H
-
-#include <algorithm>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-#include <CGAL/Kernel_d/Hyperplane_d.h>
-#include <CGAL/Kernel_d/Vector_d.h>
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::Vector_d Vector_d;
-typedef K::Oriented_side_d Oriented_side_d;
-typedef K::Has_on_positive_side_d Has_on_positive_side_d;
-typedef K::Sphere_d Sphere_d;
-typedef K::Hyperplane_d Hyperplane_d;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex;
-typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle;
-
-typedef std::vector<Point_d> Point_Vector;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-FT  _sfty = pow(10,-14);
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// AUXILLARY FUNCTIONS
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well 
- *  
- *  W is the initial point vector
- *  chosen_landmark is the index of the chosen point in W
- *  landmarks_ind is the vector of indices of already chosen points in W
- *  delaunay is the Delaunay triangulation
- *  landmark_count is the current number of chosen vertices
- *  torus is true iff you are working on a flat torus [-1,1]^d
- *  OUT: Vertex handle to the newly inserted point
- */
-Delaunay_vertex insert_delaunay_landmark_with_copies(Point_d& p, Delaunay_triangulation& delaunay, int& landmark_count, bool torus)
-{
-  if (!torus)
-    {
-      Delaunay_vertex v =delaunay.insert(p);
-      landmark_count++;
-      return v;
-    }
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      Delaunay_vertex v;
-      for (int i = 0; i < nb_cells; ++i)
-        {
-          std::vector<FT> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(p[l] + 2.0*(cell_i%3-1));
-              cell_i /= 3;
-            }
-          v = delaunay.insert(point);
-        }
-      landmark_count++;
-      return v;
-    }
-}
-
-/** Small check if the vertex v is in the full cell fc
- */
-
-bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc)
-{
-  for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it)
-    if (*v_it == v)
-      return true;
-  return false;
-}
-
-/** Fill chosen point vector from indices with copies if you are working on a flat torus
- *  
- *  IN:  W is the point vector
- *  OUT: landmarks is the output vector
- *  IN:  landmarks_ind is the vector of indices
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */
-
-void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus)
-{
-  if (!torus)
-    for (unsigned j = 0; j < landmarks_ind.size(); ++j)
-      landmarks.push_back(W[landmarks_ind[j]]);
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      int nbL = landmarks_ind.size();
-      // Fill landmarks
-      for (int i = 0; i < nb_cells-1; ++i)
-        for (int j = 0; j < nbL; ++j)
-          {
-            int cell_i = i;
-            Point_d point;
-            for (int l = 0; l < D; ++l)
-              {
-                point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1));
-                cell_i /= 3;
-              }
-            landmarks.push_back(point);
-          }
-    }
-}
-
-/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices
- *
- *  IN: t is the Delaunay triangulation
- *  OUT: full_cells is the output vector
- */
-
-void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells)
-{
-  // Store vertex indices in a map
-  int ind = 0; //index of a vertex
-  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
-  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-    if (t.is_infinite(v_it))
-      continue;
-    else
-      index_of_vertex[v_it] = ind++;
-  // Write full cells as vectors in full_cells
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      std::vector<int> cell;
-      for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it)
-        cell.push_back(index_of_vertex[*v_it]);
-      full_cells.push_back(cell);
-    }
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// IS VIOLATED TEST
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Check if a newly created cell is protected from old vertices
- *  
- *  t is the Delaunay triangulation
- *  vertices is the vector containing the point to insert and a facet f in t
- *  v1 is the vertex of t, such that f and v1 form a simplex
- *  v2 is the vertex of t, such that f and v2 form another simplex
- *  delta is the protection constant
- *  power_protection is true iff the delta-power protection is used
- */
-
-bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0)
-{
-  assert(vertices.size() == vertices[0].size() ||
-         vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1
-  assert(v1 != v2);
-  if (vertices.size() == vertices[0].size() + 1)
-  // FINITE CASE
-    {
-      Sphere_d cs(vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0]));
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it)) 
-          {
-            //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); 
-            if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-              {
-                FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point());
-                if (!power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-                    return true;
-                if (power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-                    return true;                 
-              }
-          }
-      */
-      // Check if the simplex is thick enough
-      Hyperplane_d tau_h(vertices.begin()+1, vertices.end());
-      Vector_d orth_tau = tau_h.orthogonal_vector();
-      /*
-               p_s1 = Vector_d(*(vertices.begin()), *(vertices.begin()+1));
-      */
-      //std::cout << "||orth_tau|| = " << sqrt(orth_tau.squared_length()) << "\n";
-      FT orth_length = sqrt(orth_tau.squared_length());
-      K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it;
-      // Compute the altitude
-      FT h = 0;
-      for (o_it = orth_tau.cartesian_begin(),
-           p_it = vertices.begin()->cartesian_begin(),
-           s_it = (vertices.begin()+1)->cartesian_begin();
-           o_it != orth_tau.cartesian_end();
-           ++o_it, ++p_it, ++s_it)
-        h += (*o_it)*(*p_it - *s_it)/orth_length;
-      h = fabs(h);
-      // Is the center inside the box?
-      bool inside_the_box = true;
-      for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it)
-        if (*c_it > 1.0 || *c_it < -1.0)
-          {
-            inside_the_box = false; break;
-          }
-      if (inside_the_box && h/r < theta0)
-        return true;
-      if (!t.is_infinite(v1))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-    }
-  else
-  // INFINITE CASE
-    {
-      Delaunay_triangulation::Vertex_iterator v = t.vertices_begin();
-      while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end())
-        v++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE);
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it))
-          if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-            {
-              std::vector<FT> coords;
-              Point_d p = v_it->point();
-              auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-              for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-                coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-              Point_d p_delta = Point_d(coords);
-              bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-              bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-              if (!p_is_inside && p_delta_is_inside)
-                return true;
-            }
-      */
-      if (!t.is_infinite(v1))
-        {
-          std::vector<FT> coords;
-          Point_d p = v1->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          std::vector<FT> coords;
-          Point_d p = v2->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-    }
-  return false;
-}
-  
-/** Auxillary recursive function to check if the point p violates the protection of the cell c and
- *  if there is a violation of an eventual new cell
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  c is the current cell (simplex)
- *  parent_cell is the parent cell (simplex)
- *  index is the index of the facet between c and parent_cell from parent_cell's point of view
- *  D is the dimension of the triangulation
- *  delta is the protection constant
- *  marked_cells is the vector of all visited cells containing p in their circumscribed ball
- *  power_protection is true iff you are working with delta-power protection
- *
- *  OUT: true iff inserting p hasn't produced any violation so far
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  std::vector<Point_d> vertices;
-  if (!t.is_infinite(c))
-    {
-      // if the cell is finite, we look if the protection is violated
-      for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it)
-        vertices.push_back((*v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(ed.transformed_distance(center_cs, vertices[0]));
-      FT dist2 = ed.transformed_distance(center_cs, p);
-      // if the new point is inside the protection ball of a non conflicting simplex
-      if (!power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-          return true;
-      if (power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-          return true;    
-      // if the new point is inside the circumscribing ball : continue violation searching on neighbours
-      //if (dist2 < r*r)
-      //if (dist2 < (5*r+delta)*(5*r+delta))
-      if (dist2 < r*r)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      // if the new point is outside the protection sphere
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is guaranteed to be finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;            
-        }
-    } 
-  else
-    {
-      // Inside of the convex hull is + side. Outside is - side.
-      for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-        if (!t.is_infinite(*vh_it))
-          vertices.push_back((*vh_it)->point());
-      Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin();
-      while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c))
-        v_it++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE);
-      //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point());
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      std::vector<FT> coords;
-      auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-      for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-        coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-      Point_d p_delta = Point_d(coords);
-      bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO);
-      bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-
-      // If we work with power protection, we just ignore any conflicts
-      if (!power_protection && !p_is_inside && p_delta_is_inside)
-        return true;
-      //if the cell is infinite we look at the neighbours regardless
-      if (p_is_inside)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);    
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is finite if the parent cell is finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              if (!t.is_infinite(parent_cell->vertex(i)))
-                vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;
-        }
-    }
-  //c->tds_data().clear_visited();
-  //marked_cells.pop_back();
-  return false;
-}
-
-/** Checks if inserting the point p in t will make conflicts
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  D is the dimension of triangulation
- *  delta is the protection constant
- *  power_protection is true iff you are working with delta-power protection
- *  OUT: true iff inserting p produces a violation of delta-protection.
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  Delaunay_triangulation::Vertex_handle v;
-  Delaunay_triangulation::Face f(t.current_dimension()); 
-  Delaunay_triangulation::Facet ft; 
-  Delaunay_triangulation::Full_cell_handle c; 
-  Delaunay_triangulation::Locate_type lt;
-  std::vector<Full_cell_handle> marked_cells;
-  c = t.locate(p, lt, f, ft, v);
-  bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0);
-  for (Full_cell_handle fc : marked_cells)
-    fc->tds_data().clear();
-  return violation_existing_cells;
-}
-
-//////////////////////////////////////////////////////////////////////
-// INITIALIZATION
-//////////////////////////////////////////////////////////////////////
-
-void initialize(Search_Tree& W, Delaunay& t, int D, int width, bool torus)
-{
-  if (!torus)
-    std::cout << "Non-toric case is not supported\n";
-  else
-    {
-      if (D == 2)
-        {
-          FT stepx = 2.0/width;
-          FT stepy = sqrt(3)/width;
-          for (int i = 0; i < width; ++i)
-            for (int j = 0; j < floor(2*width/sqrt(3)); ++j)
-              {
-                insert_delaunay_landmark_with_copies(Point_d(step*i,))
-              }
-        }
-      else (D == 3)
-        {
-          
-        }
-      else std::cout << "T^d with d>3 not supported";
-    }
-}
-  
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!//
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////
-// LANDMARK CHOICE PROCEDURE AS IN PAPER
-///////////////////////////////////////////////////////////////////////
-
-/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call.
- *
- *  IN:  W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d
- *  IN:  nbP is the size of W
- *  OUT: landmarks is the output vector for the points
- *  OUT: landmarks_ind is the output vector for the indices of the selected points in W
- *  IN:  delta is the constant of protection
- *  OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */ 
-
-template<class Search_Tree>
-void protected_delaunay_refinement(Search_Tree& W, int nbP, Point_Vector& landmarks, FT delta, bool torus, bool power_protection, FT theta0)
-{
-  bool return_ = true;
-  unsigned D = W[0].size();
-  Torus_distance td;
-  Euclidean_distance ed;
-  Delaunay_triangulation t(D);
-  CGAL::Random rand;
-  int landmark_count = 0;
-  //std::list<int> index_list;
-  //      shuffle the list of indexes (via a vector)
-  // {
-  //   std::vector<int> temp_vector;
-  //   for (int i = 0; i < nbP; ++i)
-  //     temp_vector.push_back(i);
-  //   unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
-  //   std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed));
-  //   //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end());
-  //   for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it)
-  //     index_list.push_front(*it);
-  // }
-  if (torus)
-  if (D == 2)
-    // \T^2
-    {
-      for (int i = 0; i < 4; ++i)
-        for (int j = 0; j < 2; ++j)
-          {
-            W[index_list.front()] = Point_d(std::vector<FT>{i*0.5, j*1.0});
-            insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-            index_list.pop_front();
-            W[index_list.front()] = Point_d(std::vector<FT>{0.25+i*0.5, 0.5+j});
-            insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-            index_list.pop_front();
-          }
-    }
-  else if (D == 3)
-    {
-      
-    }
-    //std::cout << "No torus starter available for dim>2\n";
-  std::list<int>::iterator list_it = index_list.begin();
-  while (list_it != index_list.end())
-    {
-      if (!is_violating_protection(W[*list_it], t, D, delta, power_protection, theta0))
-        {
-          // If no conflicts then insert in every copy of T^3
-
-          insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count, torus);
-          if (return_)
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            index_list.erase(list_it++);
-          /*
-          // PIECE OF CODE FOR DEBUGGING PURPOSES
-          
-          Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count);
-          if (triangulation_is_protected(t, delta))
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            { //THAT'S WHERE SOMETHING'S WRONG
-              t.remove(inserted_v);
-              landmarks_ind.pop_back();
-              landmark_count--;
-              write_delaunay_mesh(t, W[*list_it], is2d);
-              is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore
-            }
-          */
-          //std::cout << "index_list_size() = " << index_list.size() << "\n";
-        }
-      else
-        {
-          list_it++;
-          //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n";
-        }
-      //if (list_it != index_list.end())
-      //  write_delaunay_mesh(t, W[*list_it], is2d);
-    }
-  fill_landmarks(W, landmarks, landmarks_ind, torus);
-  fill_full_cell_vector(t, full_cells);
-  /*
-  if (triangulation_is_protected(t, delta))
-    std::cout << "Triangulation is ok\n";
-  else
-    {
-      std::cout << "Triangulation is BAD!! T_T しくしく!\n";
-    }
-  */
-  //write_delaunay_mesh(t, W[0], is2d);
-  //std::cout << t << std::endl;
-}
-
-#endif
diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper.h b/src/Witness_complex/example/protected_sets/protected_sets_paper.h
deleted file mode 100644
index 61fcc75b..00000000
--- a/src/Witness_complex/example/protected_sets/protected_sets_paper.h
+++ /dev/null
@@ -1,917 +0,0 @@
-#ifndef PROTECTED_SETS_H
-#define PROTECTED_SETS_H
-
-#include <algorithm>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-#include <CGAL/Kernel_d/Hyperplane_d.h>
-#include <CGAL/Kernel_d/Vector_d.h>
-
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Fuzzy_sphere.h>
-
-#include <boost/heap/fibonacci_heap.hpp>
-#include <boost/heap/policies.hpp>
-
-#include "output_tikz.h"
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::Line_d Line_d;
-typedef K::Vector_d Vector_d;
-typedef K::Oriented_side_d Oriented_side_d;
-typedef K::Has_on_positive_side_d Has_on_positive_side_d;
-typedef K::Sphere_d Sphere_d;
-typedef K::Hyperplane_d Hyperplane_d;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex;
-typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle;
-
-typedef std::vector<Point_d> Point_Vector;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-
-FT  _sfty = pow(10,-14);
-
-bool experiment1, experiment2 = false;
-
-/* Experiment 1: epsilon as function on time **********************/
-std::vector<FT> eps_vector;
-
-/* Experiment 2: R/epsilon on delta *******************************/
-std::vector<FT> epsratio_vector;
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// AUXILLARY FUNCTIONS
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well 
- *  
- *  W is the initial point vector
- *  chosen_landmark is the index of the chosen point in W
- *  landmarks_ind is the vector of indices of already chosen points in W
- *  delaunay is the Delaunay triangulation
- *  landmark_count is the current number of chosen vertices
- *  torus is true iff you are working on a flat torus [-1,1]^d
- *  OUT: Vertex handle to the newly inserted point
- */
-Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus)
-{
-  if (!torus)
-    {
-      Delaunay_vertex v =delaunay.insert(W[chosen_landmark]);
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      Delaunay_vertex v;
-      for (int i = 0; i < nb_cells; ++i)
-        {
-          std::vector<FT> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1));
-              cell_i /= 3;
-            }
-          if (i == nb_cells/2)
-            v = delaunay.insert(point); //v = center point
-          else
-            delaunay.insert(point);
-        }
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-}
-
-/** Small check if the vertex v is in the full cell fc
- */
-
-bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc)
-{
-  for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it)
-    if (*v_it == v)
-      return true;
-  return false;
-}
-
-/** Fill chosen point vector from indices with copies if you are working on a flat torus
- *  
- *  IN:  W is the point vector
- *  OUT: landmarks is the output vector
- *  IN:  landmarks_ind is the vector of indices
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */
-
-void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus)
-{
-  if (!torus)
-    for (unsigned j = 0; j < landmarks_ind.size(); ++j)
-      landmarks.push_back(W[landmarks_ind[j]]);
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      int nbL = landmarks_ind.size();
-      // Fill landmarks
-      for (int i = 0; i < nb_cells-1; ++i)
-        for (int j = 0; j < nbL; ++j)
-          {
-            int cell_i = i;
-            Point_d point;
-            for (int l = 0; l < D; ++l)
-              {
-                point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1));
-                cell_i /= 3;
-              }
-            landmarks.push_back(point);
-          }
-    }
-}
-
-/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices
- *
- *  IN: t is the Delaunay triangulation
- *  OUT: full_cells is the output vector
- */
-
-void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells)
-{
-  // Store vertex indices in a map
-  int ind = 0; //index of a vertex
-  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
-  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-    if (t.is_infinite(v_it))
-      continue;
-    else
-      index_of_vertex[v_it] = ind++;
-  // Write full cells as vectors in full_cells
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      std::vector<int> cell;
-      for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it)
-        cell.push_back(index_of_vertex[*v_it]);
-      full_cells.push_back(cell);
-    }
-}
-
-bool sphere_intersects_cube(Point_d& c, FT r)
-{
-  bool in_cube = true;
-  //  int i = 0, D = p.size();
-  for (auto xi = c.cartesian_begin(); xi != c.cartesian_end(); ++xi)
-    // if ((*xi < 1.0 || *xi > -1.0) &&
-    //     (*xi-r < 1.0 || *xi-r > -1.0) &&
-    //     (*xi+r < 1.0 || *xi+r > -1.0))
-
-    if ((*xi-r < -1.0 && *xi+r < -1.0) ||
-        (*xi-r > 1.0  && *xi+r >  1.0 ))
-      {
-        in_cube = false; break;
-      }
-  return in_cube;
-}
-
-/** Recursive function for checking if the simplex is good,
- *  meaning it does not contain a k-face, which is not theta0^(k-1) thick 
- */
-
-bool is_theta0_good(std::vector<Point_d>& vertices, FT theta0)
-{
-  if (theta0 > 1)
-    {
-      std::cout << "Warning! theta0 is set > 1\n";
-      return false;
-    }
-  int D = vertices.size()-1;
-  if (D <= 1)
-    return true; // Edges are always good
-  //******** Circumscribed sphere
-  Euclidean_distance ed;
-  Sphere_d cs(vertices.begin(), vertices.end());
-  FT r = sqrt(cs.squared_radius());
-  for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it)
-    {
-      std::vector<Point_d> facet;
-      for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it)
-        if (f_it != v_it)
-          facet.push_back(*f_it);
-      // Compute the altitude
-
-      if (vertices[0].size() == 3 && D == 2)
-        {
-          //Vector_d l = facet[0] - facet[1];
-          FT orth_length2 = ed.transformed_distance(facet[0],facet[1]);
-          K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it;
-          FT h = 0;
-          // Scalar product = <sp,l>
-          FT scalar = 0;
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            scalar += (*l_it - *s_it)*(*p_it - *s_it);
-          // Gram-Schmidt for one vector
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            {
-              FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2;
-              h += hx*hx;
-            }
-          h = sqrt(h);
-      
-          if (h/(2*r) < pow(theta0, D-1))
-            return false;
-          if (!is_theta0_good(facet, theta0))
-            return false;
-        }
-      else
-        {
-      Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it);
-      Vector_d orth_tau = tau_h.orthogonal_vector();
-      FT orth_length = sqrt(orth_tau.squared_length());
-      K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it;
-      FT h = 0;
-      for (o_it = orth_tau.cartesian_begin(),
-           p_it = v_it->cartesian_begin(),
-           s_it = (facet.begin())->cartesian_begin();
-           o_it != orth_tau.cartesian_end();
-           ++o_it, ++p_it, ++s_it)
-        h += (*o_it)*(*p_it - *s_it)/orth_length;
-      h = fabs(h);
-      if (h/(2*r) < pow(theta0, D-1))
-        return false;
-      if (!is_theta0_good(facet, theta0))
-        return false;
-        }
-    }
-  return true;
-}
-
-
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// IS VIOLATED TEST
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Check if a newly created cell is protected from old vertices
- *  
- *  t is the Delaunay triangulation
- *  vertices is the vector containing the point to insert and a facet f in t
- *  v1 is the vertex of t, such that f and v1 form a simplex
- *  v2 is the vertex of t, such that f and v2 form another simplex
- *  delta is the protection constant
- *  power_protection is true iff the delta-power protection is used
- */
-
-bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0)
-{
-  assert(vertices.size() == vertices[0].size() ||
-         vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1
-  assert(v1 != v2);
-  if (vertices.size() == vertices[0].size() + 1)
-  // FINITE CASE
-    {
-      Sphere_d cs(vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0]));
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it)) 
-          {
-            //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); 
-            if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-              {
-                FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point());
-                if (!power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-                    return true;
-                if (power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-                    return true;                 
-              }
-          }
-      */
-      // Check if the simplex is theta0-good
-      if (!is_theta0_good(vertices, theta0))
-        return true;
-      // Is the center inside the box? (only Euclidean case)
-      // if (!torus)
-      //   {
-      //     bool inside_the_box = true;
-      //     for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it)
-      //       if (*c_it > 1.0 || *c_it < -1.0)
-      //         {
-      //           inside_the_box = false; break;
-      //         }
-      //     if (inside_the_box && h/r < theta0)
-      //       return true;
-      //   }
-      // Check the two vertices (if not infinite)
-      if (!t.is_infinite(v1))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-              return true;
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-              return true;
-        }
-    }
-  else
-  // INFINITE CASE
-    {
-      Delaunay_triangulation::Vertex_iterator v = t.vertices_begin();
-      while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end())
-        v++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE);
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it))
-          if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-            {
-              std::vector<FT> coords;
-              Point_d p = v_it->point();
-              auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-              for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-                coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-              Point_d p_delta = Point_d(coords);
-              bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-              bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-              if (!p_is_inside && p_delta_is_inside)
-                return true;
-            }
-      */
-      if (!t.is_infinite(v1))
-        {
-          std::vector<FT> coords;
-          Point_d p = v1->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          std::vector<FT> coords;
-          Point_d p = v2->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-    }
-  return false;
-}
-  
-/** Auxillary recursive function to check if the point p violates the protection of the cell c and
- *  if there is a violation of an eventual new cell
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  c is the current cell (simplex)
- *  parent_cell is the parent cell (simplex)
- *  index is the index of the facet between c and parent_cell from parent_cell's point of view
- *  D is the dimension of the triangulation
- *  delta is the protection constant
- *  marked_cells is the vector of all visited cells containing p in their circumscribed ball
- *  power_protection is true iff you are working with delta-power protection
- *
- *  OUT: true iff inserting p hasn't produced any violation so far
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  std::vector<Point_d> vertices;
-  if (!t.is_infinite(c))
-    {
-      // if the cell is finite, we look if the protection is violated
-      for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it)
-        vertices.push_back((*v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(ed.transformed_distance(center_cs, vertices[0]));
-      FT dist2 = ed.transformed_distance(center_cs, p);
-      // if the new point is inside the protection ball of a non conflicting simplex
-      if (!power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-          return true;
-      if (power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-          return true;    
-      // if the new point is inside the circumscribing ball : continue violation searching on neighbours
-      //if (dist2 < r*r)
-      //if (dist2 < (5*r+delta)*(5*r+delta))
-      if (dist2 < r*r)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      // if the new point is outside the protection sphere
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is guaranteed to be finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;            
-        }
-    } 
-  else
-    {
-      // Inside of the convex hull is + side. Outside is - side.
-      for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-        if (!t.is_infinite(*vh_it))
-          vertices.push_back((*vh_it)->point());
-      Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin();
-      while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c))
-        v_it++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE);
-      //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point());
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      std::vector<FT> coords;
-      auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-      for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-        coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-      Point_d p_delta = Point_d(coords);
-      bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO);
-      bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-
-      // If we work with power protection, we just ignore any conflicts
-      if (!power_protection && !p_is_inside && p_delta_is_inside)
-        return true;
-      //if the cell is infinite we look at the neighbours regardless
-      if (p_is_inside)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);    
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0))
-                return true;
-            }
-        }
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is finite if the parent cell is finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              if (!t.is_infinite(parent_cell->vertex(i)))
-                vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;
-        }
-    }
-  //c->tds_data().clear_visited();
-  //marked_cells.pop_back();
-  return false;
-}
-
-/** Checks if inserting the point p in t will make conflicts
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  D is the dimension of triangulation
- *  delta is the protection constant
- *  power_protection is true iff you are working with delta-power protection
- *  OUT: true iff inserting p produces a violation of delta-protection.
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0)
-{
-  Euclidean_distance ed;
-  Delaunay_triangulation::Vertex_handle v;
-  Delaunay_triangulation::Face f(t.current_dimension()); 
-  Delaunay_triangulation::Facet ft; 
-  Delaunay_triangulation::Full_cell_handle c; 
-  Delaunay_triangulation::Locate_type lt;
-  std::vector<Full_cell_handle> marked_cells;
-  //c = t.locate(p, lt, f, ft, v);
-  c = t.locate(p);
-  bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0);
-  for (Full_cell_handle fc : marked_cells)
-    fc->tds_data().clear();
-  return violation_existing_cells;
-}
-
-
-////////////////////////////////////////////////////////////////////////
-// INITIALIZATION
-////////////////////////////////////////////////////////////////////////
-
-// Query for a sphere near a cite in all copies of a torus
-// OUT points_inside
-void torus_search(Tree& treeW, int D, Point_d cite, FT r, std::vector<int>& points_inside)
-{
-  int nb_cells = pow(3, D);
-  Delaunay_vertex v;
-  for (int i = 0; i < nb_cells; ++i)
-    {
-      std::vector<FT> cite_copy;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          cite_copy.push_back(cite[l] + 2.0*(cell_i%3-1));
-          cell_i /= 3;
-        }
-      Fuzzy_sphere fs(cite_copy, r, 0, treeW.traits());
-      treeW.search(std::insert_iterator<std::vector<int>>(points_inside, points_inside.end()), fs);
-    }
-}
-
-  
-void initialize_torus(Point_Vector& W, Tree& treeW, Delaunay_triangulation& t, FT epsilon, std::vector<int>& landmarks_ind, int& landmark_count)
-{
-  int D = W[0].size();
-  if (D == 2)
-    {
-      int xw = 6, yw = 4;
-      // Triangular lattice close to regular triangles h=0.866a ~ 0.875a   : 48p
-      for (int i = 0; i < xw; ++i)
-        for (int j = 0; j < yw; ++j)
-          {
-            Point_d cite1(std::vector<FT>{2.0/xw*i, 1.0/yw*j});
-            std::vector<int> points_inside;
-            torus_search(treeW, D, cite1, epsilon, points_inside);
-            assert(points_inside.size() > 0);
-            insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                 landmarks_ind, t, landmark_count, true);
-            Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 1.0/yw*(j+0.5)});
-            points_inside.clear();
-            torus_search(treeW, D, cite2, epsilon, points_inside);
-            assert(points_inside.size() > 0);
-            insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                 landmarks_ind, t, landmark_count, true);            
-          }
-    }
-  else if (D == 3)
-    {
-      int wd = 3;
-      // Body-centered cubic lattice : 54p
-      for (int i = 0; i < wd; ++i)
-        for (int j = 0; j < wd; ++j)
-          for (int k = 0; k < wd; ++k)
-            {
-              Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k});
-              std::vector<int> points_inside;
-              torus_search(treeW, D, cite1, epsilon, points_inside);
-              assert(points_inside.size() > 0);
-              insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                   landmarks_ind, t, landmark_count, true);
-              Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)});
-              points_inside.clear();
-              torus_search(treeW, D, cite2, epsilon, points_inside);
-              assert(points_inside.size() > 0);
-              insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                   landmarks_ind, t, landmark_count, true);
-            }
-    }
-}
-  
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!//
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-
-// Struct for R_max_heap elements
-
-struct R_max_handle
-{
-  FT value;
-  Point_d center;
-  
-  R_max_handle(FT value_, Point_d c): value(value_), center(c)
-  {}
-};
-
-struct R_max_compare
-{
-  bool operator()(const R_max_handle& rmh1, const R_max_handle& rmh2) const
-  {
-    return rmh1.value < rmh2.value;
-  }
-};
-
-// typedef boost::heap::fibonacci_heap<R_max_handle, boost::heap::compare<R_max_compare>> Heap;
-
-// void make_heap(Delaunay_triangulation& t, Heap& R_max_heap)
-// {
-//   R_max_heap.clear();
-//   for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) 
-//     {
-//       if (t.is_infinite(fc_it))
-//         continue;
-//       Point_Vector vertices;
-//       for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-//         vertices.push_back((*fc_v_it)->point());
-//       Sphere_d cs( vertices.begin(), vertices.end());
-//       Point_d csc = cs.center();
-//       FT r = sqrt(cs.squared_radius());
-//       // A ball is in the heap, if it intersects the cube
-//       bool accepted = sphere_intersects_cube(csc, sqrt(r)); 
-//       if (!accepted)
-//         continue;
-//       R_max_heap.push(R_max_handle(r, fc_it, csc));
-//     }
-// }
-
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-// SAMPLING RADIUS 
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-R_max_handle sampling_radius(Delaunay_triangulation& t)
-{
-  FT epsilon2 = 0;
-  Point_d final_center;
-  Point_d control_point;
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin()));
-      if (epsilon2 < r2)
-        {
-          epsilon2 = r2;
-          final_center = csc;         
-          control_point = (*vertices.begin());
-        }
-    }
-  return R_max_handle(sqrt(epsilon2), final_center);
-}
-
-///////////////////////////////////////////////////////////////////////
-// LANDMARK CHOICE PROCEDURE
-///////////////////////////////////////////////////////////////////////
-
-/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call.
- *
- *  IN:  W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d
- *  IN:  nbP is the size of W
- *  OUT: landmarks is the output vector for the points
- *  OUT: landmarks_ind is the output vector for the indices of the selected points in W
- *  IN:  delta is the constant of protection
- *  OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */ 
-
-void protected_delaunay(Point_Vector& W,
-                        //Point_Vector& landmarks,
-                        std::vector<int>& landmarks_ind,
-                        FT delta,
-                        FT epsilon,
-                        FT alpha,
-                        FT theta0,
-                        //std::vector<std::vector<int>>& full_cells,
-                        bool torus,
-                        bool power_protection
-                        )
-{
-  //bool return_ = true;
-  unsigned D = W[0].size();
-  int nbP = W.size();
-  Torus_distance td;
-  Euclidean_distance ed;
-  Delaunay_triangulation t(D);
-  CGAL::Random rand;
-  int landmark_count = 0;
-  std::list<int> index_list;
-  //****************** Kd Tree W
-  STraits traits(&(W[0]));
-  Tree treeW(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nbP),
-         typename Tree::Splitter(),
-         traits);
-  //      shuffle the list of indexes (via a vector)
-  {
-    std::vector<int> temp_vector;
-    for (int i = 0; i < nbP; ++i)
-      temp_vector.push_back(i);
-    unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
-    std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed));
-    //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end());
-    for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it)
-      index_list.push_front(*it);
-  }
-  //******************** Initialize point set
-  if (!torus)
-    for (unsigned pos1 = 0; pos1 < D+1; ++pos1)
-      {
-        std::vector<FT> point;
-        for (unsigned i = 0; i < pos1; ++i)
-          point.push_back(-1);
-        if (pos1 != D)
-          point.push_back(1);
-        for (unsigned i = pos1+1; i < D; ++i)
-          point.push_back(0);
-        assert(point.size() == D);
-        W[index_list.front()] = Point_d(point);
-        insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-        index_list.pop_front();
-      }
-  else
-    initialize_torus(W, treeW, t, epsilon, landmarks_ind, landmark_count);
-  //std::cout << "Size of treeW: " << treeW.size() << "\n";
-  //std::cout << "Size of t: " << t.number_of_vertices() << "\n";
-  //******************* Initialize heap for R_max
-  //Heap R_max_heap;
-  //make_heap(t, R_max_heap);
-
-  
-  R_max_handle rh = sampling_radius(t);
-  FT epsilon0 = rh.value; 
-  if (experiment1) eps_vector.push_back(pow(1/rh.value,D));
-  //******************** Iterative algorithm
-  std::vector<int> candidate_points;
-  torus_search(treeW, D,
-               rh.center,
-               alpha*rh.value,
-               candidate_points);
-  std::list<int>::iterator list_it;
-  std::vector<int>::iterator cp_it = candidate_points.begin();
-  while (cp_it != candidate_points.end())
-    {
-      if (!is_violating_protection(W[*cp_it], t, D, delta, power_protection, theta0))
-        {
-          insert_delaunay_landmark_with_copies(W, *cp_it, landmarks_ind, t, landmark_count, torus);
-          //make_heap(t, R_max_heap);
-          rh = sampling_radius(t);
-          if (experiment1) eps_vector.push_back(pow(1/rh.value,D));
-          //std::cout << "rhvalue = " << rh.value << "\n";
-          //std::cout << "D = " << 
-          candidate_points.clear();
-          torus_search(treeW, D,
-                       rh.center,
-                       alpha*rh.value,
-                       candidate_points);
-          /*
-          // PIECE OF CODE FOR DEBUGGING PURPOSES
-          
-          Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count);
-          if (triangulation_is_protected(t, delta))
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            { //THAT'S WHERE SOMETHING'S WRONG
-              t.remove(inserted_v);
-              landmarks_ind.pop_back();
-              landmark_count--;
-              write_delaunay_mesh(t, W[*list_it], is2d);
-              is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore
-            }
-          */
-          //std::cout << "index_list_size() = " << index_list.size() << "\n";
-        }
-      else
-        {
-          cp_it++;
-          //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n";
-        }
-      //if (list_it != index_list.end())
-      //  write_delaunay_mesh(t, W[*list_it], is2d);
-    }
-  if (experiment2) epsratio_vector.push_back(rh.value/epsilon0);
-  std::cout << "The iteration ended when cp_count = " << candidate_points.size() << "\n";
-  std::cout << "alphaRmax = " << alpha*rh.value << "\n";
-  std::cout << "epsilon' = " << rh.value << "\n";
-  std::cout << "nbL = " << landmarks_ind.size() << "\n";
-  //fill_landmarks(W, landmarks, landmarks_ind, torus);
-  //fill_full_cell_vector(t, full_cells);
-  /*
-  if (triangulation_is_protected(t, delta))
-    std::cout << "Triangulation is ok\n";
-  else
-    {
-      std::cout << "Triangulation is BAD!! T_T しくしく!\n";
-    }
-  */
-  //write_delaunay_mesh(t, W[0], is2d);
-  //std::cout << t << std::endl;
-}
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Series of experiments
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-void start_experiments(Point_Vector& W, FT theta0, std::vector<int>& landmarks_ind, FT epsilon)
-{
-  // Experiment 1
-  experiment1 = true;
-  protected_delaunay(W, landmarks_ind, 0.1*epsilon, epsilon, 0.5, 0, true, true);
-  write_tikz_plot(eps_vector,"epstime.tikz");
-  experiment1 = false;
-
-  // Experiment 2
-  // experiment2 = true;
-  // for (FT delta = 0; delta < epsilon; delta += 0.1*epsilon)
-  //   protected_delaunay(W, landmarks_ind, delta, epsilon, 0.5, 0, true, true);
-  // write_tikz_plot(epsratio_vector,"epsratio_delta.tikz");
-  // experiment2 = false;
-
-}
-  
-#endif
diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper2.h b/src/Witness_complex/example/protected_sets/protected_sets_paper2.h
deleted file mode 100644
index 04b5e3bc..00000000
--- a/src/Witness_complex/example/protected_sets/protected_sets_paper2.h
+++ /dev/null
@@ -1,1384 +0,0 @@
-#ifndef PROTECTED_SETS_H
-#define PROTECTED_SETS_H
-
-#include <algorithm>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-#include <CGAL/Kernel_d/Hyperplane_d.h>
-#include <CGAL/Kernel_d/Vector_d.h>
-
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Fuzzy_sphere.h>
-
-#include <boost/heap/fibonacci_heap.hpp>
-#include <boost/heap/policies.hpp>
-
-#include "output_tikz.h"
-#include "../output.h"
-#include "../generators.h"
-
-#include <CGAL/point_generators_d.h>
-
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::Line_d Line_d;
-typedef K::Vector_d Vector_d;
-typedef K::Oriented_side_d Oriented_side_d;
-typedef K::Has_on_positive_side_d Has_on_positive_side_d;
-typedef K::Sphere_d Sphere_d;
-typedef K::Hyperplane_d Hyperplane_d;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex;
-typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle;
-
-typedef std::vector<Point_d> Point_Vector;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
-
-
-FT  _sfty = pow(10,-14);
-
-bool experiment1, experiment2, experiment3, experiment5 = false;
-
-/* Experiment 1: epsilon as function on time **********************/
-std::vector<FT> eps_vector;
-
-/* Experiment 2: R/epsilon on alpha *******************************/
-std::vector<FT> epsratio_vector;
-std::vector<FT> epsslope_vector;
-
-/* Experiment 3: theta on delta ***********************************/
-std::vector<FT> thetamin_vector; FT curr_theta;
-std::vector<FT> gammamin_vector;
-
-/* Statistical data ***********************************************/
-int refused_case1, refused_case2, refused_bad, refused_centers1, refused_centers2;
-
-void initialize_statistics()
-{
-  refused_case1 = 0;
-  refused_case2 = 0;
-  refused_bad   = 0;
-  refused_centers1 = 0;
-  refused_centers2 = 0;
-}
-
-void print_statistics()
-{
-  std::cout << " * Old simplex not protected: " << refused_case1 << "\n";
-  std::cout << " * New simplex not protected: " << refused_case2 << "\n";
-  std::cout << " * New simplex not good:      " << refused_bad << "\n";
-  std::cout << " * New-old centers too close:      " << refused_centers1 << "\n";
-  std::cout << " * New-new centers too close:      " << refused_centers2 << "\n";
-}
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// AUXILLARY FUNCTIONS
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well 
- *  
- *  W is the initial point vector
- *  chosen_landmark is the index of the chosen point in W
- *  landmarks_ind is the vector of indices of already chosen points in W
- *  delaunay is the Delaunay triangulation
- *  landmark_count is the current number of chosen vertices
- *  torus is true iff you are working on a flat torus [-1,1]^d
- *  OUT: Vertex handle to the newly inserted point
- */
-Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus)
-{
-  if (!torus)
-    {
-      Delaunay_vertex v =delaunay.insert(W[chosen_landmark]);
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      Delaunay_vertex v;
-      for (int i = 0; i < nb_cells; ++i)
-        {
-          std::vector<FT> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1));
-              cell_i /= 3;
-            }
-          if (i == nb_cells/2)
-            v = delaunay.insert(point); //v = center point
-          else
-            delaunay.insert(point);
-        }
-      landmarks_ind.push_back(chosen_landmark);
-      landmark_count++;
-      return v;
-    }
-}
-
-/** Small check if the vertex v is in the full cell fc
- */
-
-bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc)
-{
-  for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it)
-    if (*v_it == v)
-      return true;
-  return false;
-}
-
-/** Fill chosen point vector from indices with copies if you are working on a flat torus
- *  
- *  IN:  W is the point vector
- *  OUT: landmarks is the output vector
- *  IN:  landmarks_ind is the vector of indices
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */
-
-void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus)
-{
-  if (!torus)
-    for (unsigned j = 0; j < landmarks_ind.size(); ++j)
-      landmarks.push_back(W[landmarks_ind[j]]);
-  else
-    {
-      int D = W[0].size();
-      int nb_cells = pow(3, D);
-      int nbL = landmarks_ind.size();
-      // Fill landmarks
-      for (int i = 0; i < nb_cells-1; ++i)
-        for (int j = 0; j < nbL; ++j)
-          {
-            int cell_i = i;
-            Point_d point;
-            for (int l = 0; l < D; ++l)
-              {
-                point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1));
-                cell_i /= 3;
-              }
-            landmarks.push_back(point);
-          }
-    }
-}
-
-/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices
- *
- *  IN: t is the Delaunay triangulation
- *  OUT: full_cells is the output vector
- */
-
-void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells)
-{
-  // Store vertex indices in a map
-  int ind = 0; //index of a vertex
-  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
-  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-    if (t.is_infinite(v_it))
-      continue;
-    else
-      index_of_vertex[v_it] = ind++;
-  // Write full cells as vectors in full_cells
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      std::vector<int> cell;
-      for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it)
-        cell.push_back(index_of_vertex[*v_it]);
-      full_cells.push_back(cell);
-    }
-}
-
-bool sphere_intersects_cube(Point_d& c, FT r)
-{
-  bool in_cube = true;
-  //  int i = 0, D = p.size();
-  for (auto xi = c.cartesian_begin(); xi != c.cartesian_end(); ++xi)
-    // if ((*xi < 1.0 || *xi > -1.0) &&
-    //     (*xi-r < 1.0 || *xi-r > -1.0) &&
-    //     (*xi+r < 1.0 || *xi+r > -1.0))
-
-    if ((*xi-r < -1.0 && *xi+r < -1.0) ||
-        (*xi-r > 1.0  && *xi+r >  1.0 ))
-      {
-        in_cube = false; break;
-      }
-  return in_cube;
-}
-
-/** Recursive function for checking if the simplex is good,
- *  meaning it does not contain a k-face, which is not theta0^(k-1) thick 
- */
-
-bool is_theta0_good(std::vector<Point_d>& vertices, FT theta0)
-{
-  if (theta0 > 1)
-    {
-      std::cout << "Warning! theta0 is set > 1\n";
-      return false;
-    }
-  int D = vertices.size()-1;
-  if (D <= 1)
-    return true; // Edges are always good
-  //******** Circumscribed sphere
-  Euclidean_distance ed;
-  Sphere_d cs(vertices.begin(), vertices.end());
-  FT r = sqrt(cs.squared_radius());
-  for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it)
-    {
-      std::vector<Point_d> facet;
-      for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it)
-        if (f_it != v_it)
-          facet.push_back(*f_it);
-      // Compute the altitude
-
-      if (vertices[0].size() == 3 && D == 2)
-        {
-          //Vector_d l = facet[0] - facet[1];
-          FT orth_length2 = ed.transformed_distance(facet[0],facet[1]);
-          K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it;
-          FT h = 0;
-          // Scalar product = <sp,l>
-          FT scalar = 0;
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            scalar += (*l_it - *s_it)*(*p_it - *s_it);
-          // Gram-Schmidt for one vector
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            {
-              FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2;
-              h += hx*hx;
-            }
-          h = sqrt(h);
-      
-          if (h/(2*r) < pow(theta0, D-1))
-            return false;
-          if (!is_theta0_good(facet, theta0))
-            return false;
-        }
-      else
-        {
-          Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it);
-          Vector_d orth_tau = tau_h.orthogonal_vector();
-          FT orth_length = sqrt(orth_tau.squared_length());
-          K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it;
-          FT h = 0;
-          for (o_it = orth_tau.cartesian_begin(),
-                 p_it = v_it->cartesian_begin(),
-                 s_it = (facet.begin())->cartesian_begin();
-               o_it != orth_tau.cartesian_end();
-               ++o_it, ++p_it, ++s_it)
-            h += (*o_it)*(*p_it - *s_it)/orth_length;
-          h = fabs(h);
-          if (experiment3 && thetamin_vector[thetamin_vector.size()-1] > pow(h/(2*r), 1.0/(D-1)))
-            {
-              thetamin_vector[thetamin_vector.size()-1] = pow(h/(2*r), 1.0/(D-1));
-              //std::cout << "theta=" << h/(2*r) << ", ";
-            }
-          if (h/(2*r) < pow(theta0, D-1))
-              return false;
-          if (!is_theta0_good(facet, theta0))
-            return false;
-        }
-    }
-  return true;
-}
-
-/** Recursive function for checking the goodness of a simplex,
- *  meaning it does not contain a k-face, which is not theta0^(k-1) thick 
- */
-
-FT theta(std::vector<Point_d>& vertices)
-{
-  FT curr_value = 1.0;
-  int D = vertices.size()-1;
-  if (D <= 1)
-    return 1; // Edges are always good
-  //******** Circumscribed sphere
-  Euclidean_distance ed;
-  Sphere_d cs(vertices.begin(), vertices.end());
-  FT r = sqrt(cs.squared_radius());
-  for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it)
-    {
-      std::vector<Point_d> facet;
-      for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it)
-        if (f_it != v_it)
-          facet.push_back(*f_it);
-      // Compute the altitude
-      curr_value = std::min(curr_value, theta(facet)); // Check the corresponding facet
-      if (vertices[0].size() == 3 && D == 2)
-        {
-          //Vector_d l = facet[0] - facet[1];
-          FT orth_length2 = ed.transformed_distance(facet[0],facet[1]);
-          K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it;
-          FT h = 0;
-          // Scalar product = <sp,l>
-          FT scalar = 0;
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            scalar += (*l_it - *s_it)*(*p_it - *s_it);
-          // Gram-Schmidt for one vector
-          for (p_it = v_it->cartesian_begin(),
-               s_it = facet[0].cartesian_begin(),
-               l_it = facet[1].cartesian_begin();
-               p_it != v_it->cartesian_end();
-               ++l_it, ++p_it, ++s_it)
-            {
-              FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2;
-              h += hx*hx;
-            }
-          h = sqrt(h);
-          curr_value = std::min(curr_value, std::pow(h/(2*r), 1.0/(D-1)));
-        }
-      else
-        {
-          Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it);
-          Vector_d orth_tau = tau_h.orthogonal_vector();
-          FT orth_length = sqrt(orth_tau.squared_length());
-          K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it;
-          FT h = 0;
-          for (o_it = orth_tau.cartesian_begin(),
-                 p_it = v_it->cartesian_begin(),
-                 s_it = (facet.begin())->cartesian_begin();
-               o_it != orth_tau.cartesian_end();
-               ++o_it, ++p_it, ++s_it)
-            h += (*o_it)*(*p_it - *s_it)/orth_length;
-          h = fabs(h);
-          curr_value = std::min(curr_value, pow(h/(2*r), 1.0/(D-1)));
-        }
-    }
-  return curr_value;
-}
-
-// Doubling in a way 1->2->5->10
-void double_round(int& i)
-{
-  FT order10 = pow(10,std::floor(std::log10(i)));
-  int digit = std::floor( i / order10);
-  std::cout << digit;
-  if (digit == 1)
-    i *= 2;
-  else if (digit == 2)
-    i = 5*i/2;
-  else if (digit == 5)
-    i *= 2;
-  else
-    std::cout << "digit not correct. digit = " << digit << std::endl;
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// IS VIOLATED TEST
-////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-/** Check if a newly created cell is protected from old vertices
- *  
- *  t is the Delaunay triangulation
- *  vertices is the vector containing the point to insert and a facet f in t
- *  v1 is the vertex of t, such that f and v1 form a simplex
- *  v2 is the vertex of t, such that f and v2 form another simplex
- *  delta is the protection constant
- *  power_protection is true iff the delta-power protection is used
- */
-
-bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta0, bool power_protection, FT theta0, FT gamma0)
-{
-  assert(vertices.size() == vertices[0].size() ||
-         vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1
-  assert(v1 != v2);
-  if (vertices.size() == vertices[0].size() + 1)
-  // FINITE CASE
-    {
-      Sphere_d cs(vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0]));
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it)) 
-          {
-            //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); 
-            if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-              {
-                FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point());
-                if (!power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta))
-                    return true;
-                if (power_protection)
-                  if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) 
-                    return true;                 
-              }
-          }
-      */
-      // Is the center inside the box? (only Euclidean case)
-      // if (!torus)
-      //   {
-      //     bool inside_the_box = true;
-      //     for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it)
-      //       if (*c_it > 1.0 || *c_it < -1.0)
-      //         {
-      //           inside_the_box = false; break;
-      //         }
-      //     if (inside_the_box && h/r < theta0)
-      //       return true;
-      //   }
-      // Check the two vertices (if not infinite)
-      if (!t.is_infinite(v1))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0))
-              { refused_case2++; return true;}
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+r*r*delta0*delta0) 
-              { refused_case2++; return true;}
-          // Check if the centers are not too close
-          std::vector<Point_d> sigma(vertices);
-          sigma[0] = v1->point();
-          Sphere_d cs_sigma(sigma.begin(), sigma.end());
-          Point_d csc_sigma = cs_sigma.center();
-          FT r_sigma = sqrt(cs_sigma.squared_radius());
-          FT dcc = sqrt(Euclidean_distance().transformed_distance(center_cs, csc_sigma));
-          if (experiment3 && dcc/r < gammamin_vector[gammamin_vector.size()-1])
-            gammamin_vector[gammamin_vector.size()-1] = dcc/r;
-          if (experiment3 && dcc/r_sigma < gammamin_vector[gammamin_vector.size()-1])
-            gammamin_vector[gammamin_vector.size()-1] = dcc/r_sigma;
-          if (dcc < r*gamma0 || dcc < r_sigma*gamma0)
-            { refused_centers1++; return true; }
-        }
-      if (!t.is_infinite(v2))
-        {
-          FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point());
-          if (!power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0))
-              { refused_case2++; return true;}
-          if (power_protection)
-            if (dist2 >= r*r-_sfty && dist2 <= r*r+r*r*delta0*delta0) 
-              { refused_case2++; return true;}
-          // Check if the centers are not too close
-          std::vector<Point_d> sigma(vertices);
-          sigma[0] = v2->point();
-          Sphere_d cs_sigma(sigma.begin(), sigma.end());
-          Point_d csc_sigma = cs_sigma.center();
-          FT r_sigma = sqrt(cs_sigma.squared_radius());
-          FT dcc = sqrt(Euclidean_distance().transformed_distance(center_cs, csc_sigma));
-          if (experiment3 && dcc/r < gammamin_vector[gammamin_vector.size()-1])
-            gammamin_vector[gammamin_vector.size()-1] = dcc/r;
-          if (experiment3 && dcc/r_sigma < gammamin_vector[gammamin_vector.size()-1])
-            gammamin_vector[gammamin_vector.size()-1] = dcc/r_sigma;
-          if (dcc < r*gamma0 || dcc < r_sigma*gamma0)
-            { refused_centers1++; return true; }
-        }
-      // Check if the simplex is theta0-good
-      if (!is_theta0_good(vertices, theta0))
-        { refused_bad++; return true;}
-      
-    }
-  else
-  // INFINITE CASE
-    {
-      Delaunay_triangulation::Vertex_iterator v = t.vertices_begin();
-      while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end())
-        v++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE);
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      /*
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        if (!t.is_infinite(v_it))
-          if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end())
-            {
-              std::vector<FT> coords;
-              Point_d p = v_it->point();
-              auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-              for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-                coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length()));
-              Point_d p_delta = Point_d(coords);
-              bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-              bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-              if (!p_is_inside && p_delta_is_inside)
-                return true;
-            }
-      */
-      if (!t.is_infinite(v1))
-        {
-          std::vector<FT> coords;
-          Point_d p = v1->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-      if (!t.is_infinite(v2))
-        {
-          std::vector<FT> coords;
-          Point_d p = v2->point();
-          auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-          for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-            coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length()));
-          Point_d p_delta = Point_d(coords);
-          bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p);
-          bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-          if (!power_protection && !p_is_inside && p_delta_is_inside)
-            return true;
-        }
-    }
-  return false;
-}
-  
-/** Auxillary recursive function to check if the point p violates the protection of the cell c and
- *  if there is a violation of an eventual new cell
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  c is the current cell (simplex)
- *  parent_cell is the parent cell (simplex)
- *  index is the index of the facet between c and parent_cell from parent_cell's point of view
- *  D is the dimension of the triangulation
- *  delta is the protection constant
- *  marked_cells is the vector of all visited cells containing p in their circumscribed ball
- *  power_protection is true iff you are working with delta-power protection
- *
- *  OUT: true iff inserting p hasn't produced any violation so far
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta0, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0, FT gamma0)
-{
-  Euclidean_distance ed;
-  std::vector<Point_d> vertices;
-  if (!t.is_infinite(c))
-    {
-      // if the cell is finite, we look if the protection is violated
-      for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it)
-        vertices.push_back((*v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d center_cs = cs.center();
-      FT r = sqrt(ed.transformed_distance(center_cs, vertices[0]));
-      FT dist2 = ed.transformed_distance(center_cs, p);
-      // if the new point is inside the protection ball of a non conflicting simplex
-      if (!power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0))
-          { refused_case1++; return true;}
-      if (power_protection)
-        if (dist2 >= r*r-_sfty && dist2 <= r*r+delta0*delta0*r*r) 
-          { refused_case1++; return true;}    
-      // if the new point is inside the circumscribing ball : continue violation searching on neighbours
-      //if (dist2 < r*r)
-      //if (dist2 < (5*r+delta)*(5*r+delta))
-      if (dist2 < r*r)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta0, marked_cells, power_protection, theta0, gamma0))
-                return true;
-            }
-        }
-      // if the new point is outside the protection sphere
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is guaranteed to be finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta0, power_protection, theta0, gamma0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;            
-        }
-    } 
-  else
-    {
-      // Inside of the convex hull is + side. Outside is - side.
-      for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-        if (!t.is_infinite(*vh_it))
-          vertices.push_back((*vh_it)->point());
-      Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin();
-      while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c))
-        v_it++;
-      Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE);
-      //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point());
-      Vector_d orth_v = facet_plane.orthogonal_vector();
-      std::vector<FT> coords;
-      auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin();
-      for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i)
-        coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length()));
-      Point_d p_delta = Point_d(coords);
-      bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO);
-      bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta);
-
-      // If we work with power protection, we just ignore any conflicts
-      if (!power_protection && !p_is_inside && p_delta_is_inside)
-        return true;
-      //if the cell is infinite we look at the neighbours regardless
-      if (p_is_inside)
-        {
-          c->tds_data().mark_visited();
-          marked_cells.push_back(c);    
-          for (int i = 0; i < D+1; ++i)
-            {
-              Full_cell_handle next_c = c->neighbor(i);
-              if (next_c->tds_data().is_clear() &&
-                  is_violating_protection(p, t, next_c, c, i, D, delta0, marked_cells, power_protection, theta0, gamma0))
-                return true;
-            }
-        }
-      else
-        {
-          // facet f is on the border of the conflict zone : check protection of simplex {p,f}
-          // the new simplex is finite if the parent cell is finite
-          vertices.clear(); vertices.push_back(p);
-          for (int i = 0; i < D+1; ++i)
-            if (i != index)
-              if (!t.is_infinite(parent_cell->vertex(i)))
-                vertices.push_back(parent_cell->vertex(i)->point());
-          Delaunay_vertex vertex_to_check = t.infinite_vertex();
-          for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it)
-            if (!vertex_is_in_full_cell(*vh_it, parent_cell))
-              {
-                vertex_to_check = *vh_it; break;
-              }
-          if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta0, power_protection, theta0, gamma0)) 
-          //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) 
-            return true;
-        }
-    }
-  //c->tds_data().clear_visited();
-  //marked_cells.pop_back();
-  return false;
-}
-
-/** Checks if inserting the point p in t will make conflicts
- *
- *  p is the point to insert
- *  t is the current triangulation
- *  D is the dimension of triangulation
- *  delta is the protection constant
- *  power_protection is true iff you are working with delta-power protection
- *  OUT: true iff inserting p produces a violation of delta-protection.
- */
-
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta0, bool power_protection, FT theta0, FT gamma0)
-{
-  Euclidean_distance ed;
-  Delaunay_triangulation::Vertex_handle v;
-  Delaunay_triangulation::Face f(t.current_dimension()); 
-  Delaunay_triangulation::Facet ft; 
-  Delaunay_triangulation::Full_cell_handle c; 
-  Delaunay_triangulation::Locate_type lt;
-  std::vector<Full_cell_handle> marked_cells;
-  //c = t.locate(p, lt, f, ft, v);
-  c = t.locate(p);
-  bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta0, marked_cells, power_protection, theta0, gamma0);
-  for (Full_cell_handle fc : marked_cells)
-    fc->tds_data().clear();
-  return violation_existing_cells;
-}
-
-
-////////////////////////////////////////////////////////////////////////
-// INITIALIZATION
-////////////////////////////////////////////////////////////////////////
-
-// Query for a sphere near a cite in all copies of a torus
-// OUT points_inside
-void torus_search(Tree& treeW, int D, Point_d cite, FT r, std::vector<int>& points_inside)
-{
-  int nb_cells = pow(3, D);
-  Delaunay_vertex v;
-  for (int i = 0; i < nb_cells; ++i)
-    {
-      std::vector<FT> cite_copy;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          cite_copy.push_back(cite[l] + 2.0*(cell_i%3-1));
-          cell_i /= 3;
-        }
-      Fuzzy_sphere fs(cite_copy, r, 0, treeW.traits());
-      treeW.search(std::insert_iterator<std::vector<int>>(points_inside, points_inside.end()), fs);
-    }
-}
-
-  
-void initialize_torus(Point_Vector& W, Tree& treeW, Delaunay_triangulation& t, FT epsilon, std::vector<int>& landmarks_ind, int& landmark_count, std::vector<bool>& point_taken)
-{
-  initialize_statistics();
-  int D = W[0].size();
-  if (D == 2)
-    {
-      int xw = 6, yw = 4;
-      // Triangular lattice close to regular triangles h=0.866a ~ 0.875a   : 48p
-      for (int i = 0; i < xw; ++i)
-        for (int j = 0; j < yw; ++j)
-          {
-            Point_d cite1(std::vector<FT>{2.0/xw*i, 2.0/yw*j});
-            std::vector<int> points_inside;
-            torus_search(treeW, D, cite1, epsilon, points_inside);
-            //std::cout << "i=" << i << ", j=" << j << " "; print_vector(points_inside); std::cout << "\n";
-            std::vector<int>::iterator p_it = points_inside.begin();
-            while (p_it != points_inside.end() && point_taken[*p_it])
-              ++p_it;
-            assert(p_it != points_inside.end());
-            //W[*p_it] = cite1;  // debug purpose
-            insert_delaunay_landmark_with_copies(W, *p_it,
-                                                 landmarks_ind, t, landmark_count, true);
-            point_taken[*p_it] = true;
-
-            Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 2.0/yw*(j+0.5)});
-            points_inside.clear();
-            torus_search(treeW, D, cite2, epsilon, points_inside);
-            //std::cout << "i=" << i << ", j=" << j << " "; print_vector(points_inside); std::cout << "\n";
-            p_it = points_inside.begin();
-            while (p_it != points_inside.end() && point_taken[*p_it])
-              ++p_it;
-            assert(p_it != points_inside.end());
-            //W[*p_it] = cite2;  // debug purpose
-            insert_delaunay_landmark_with_copies(W, *p_it,
-                                                 landmarks_ind, t, landmark_count, true);
-            point_taken[*p_it] = true;            
-          }
-    }
-  else if (D == 3)
-    {
-      int wd = 3;
-      // Body-centered cubic lattice : 54p
-      for (int i = 0; i < wd; ++i)
-        for (int j = 0; j < wd; ++j)
-          for (int k = 0; k < wd; ++k)
-            {
-              Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k});
-              std::vector<int> points_inside;
-              torus_search(treeW, D, cite1, epsilon, points_inside);
-              std::vector<int>::iterator p_it = points_inside.begin();
-              while (p_it != points_inside.end() && point_taken[*p_it])
-                ++p_it;
-              assert(p_it != points_inside.end());
-              insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                   landmarks_ind, t, landmark_count, true);
-              point_taken[*p_it] = true;
-              
-              Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)});
-              points_inside.clear();
-              torus_search(treeW, D, cite2, epsilon, points_inside);
-              p_it = points_inside.begin();
-              while (p_it != points_inside.end() && point_taken[*p_it])
-                ++p_it;
-              assert(p_it != points_inside.end());
-              insert_delaunay_landmark_with_copies(W, *(points_inside.begin()),
-                                                   landmarks_ind, t, landmark_count, true);
-              point_taken[*p_it] = true;
-            }
-    }
-  //write_mesh
-}
-  
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!//
-///////////////////////////////////////////////////////////////////////
-///////////////////////////////////////////////////////////////////////
-
-// Struct for R_max_heap elements
-
-struct R_max_handle
-{
-  FT value;
-  Point_d center;
-  
-  R_max_handle(FT value_, Point_d c): value(value_), center(c)
-  {}
-};
-
-struct R_max_compare
-{
-  bool operator()(const R_max_handle& rmh1, const R_max_handle& rmh2) const
-  {
-    return rmh1.value < rmh2.value;
-  }
-};
-
-// typedef boost::heap::fibonacci_heap<R_max_handle, boost::heap::compare<R_max_compare>> Heap;
-
-// void make_heap(Delaunay_triangulation& t, Heap& R_max_heap)
-// {
-//   R_max_heap.clear();
-//   for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) 
-//     {
-//       if (t.is_infinite(fc_it))
-//         continue;
-//       Point_Vector vertices;
-//       for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-//         vertices.push_back((*fc_v_it)->point());
-//       Sphere_d cs( vertices.begin(), vertices.end());
-//       Point_d csc = cs.center();
-//       FT r = sqrt(cs.squared_radius());
-//       // A ball is in the heap, if it intersects the cube
-//       bool accepted = sphere_intersects_cube(csc, sqrt(r)); 
-//       if (!accepted)
-//         continue;
-//       R_max_heap.push(R_max_handle(r, fc_it, csc));
-//     }
-// }
-
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-// SAMPLING RADIUS 
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-R_max_handle sampling_radius(Delaunay_triangulation& t)
-{
-  FT epsilon2 = 0;
-  Point_d final_center;
-  Point_d control_point;
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin()));
-      if (epsilon2 < r2)
-        {
-          epsilon2 = r2;
-          final_center = csc;         
-          control_point = (*vertices.begin());
-        }
-    }
-  return R_max_handle(sqrt(epsilon2), final_center);
-}
-
-FT sampling_fatness(Delaunay_triangulation& t)
-{
-  FT curr_theta = 1.0;
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      FT theta_f = theta(vertices);
-      curr_theta = std::min(curr_theta, theta_f);
-      //std::cout << "theta(sigma) = " << theta_f << "\n";
-    }
-  return curr_theta;
-}
-
-// Generate an epsilon sample for a given epsilon
-void generate_epsilon_sample_torus(Point_Vector& W, FT epsilon, int dim, Delaunay_triangulation& t)
-{
-  W.clear();
-  t.clear();
-  int point_count = 0;
-  std::vector<int> point_ind;
-  // std::vector<FT> coords;
-  FT curr_eps = 2*dim;
-  // Initialize
-  // for (int i = 0; i < dim; ++i)
-  //   coords.push_back(-1);
-  // R_max_handle rmh(2*sqrt(dim), Point_d(coords));
-  // int N = dim; std::floor(std::pow(1/epsilon,dim));
-  // std::cout << N << "\n";
-  typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator;
-  Random_cube_iterator rp(dim, 1.0);
-  W.push_back(*rp++);
-  insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true);
-  curr_eps = sampling_radius(t).value;      
-  while (curr_eps > epsilon)
-    {
-      
-      W.push_back(*rp++);
-      insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true);
-      
-      Point_d c = sampling_radius(t).center;
-      W.push_back(c);
-      insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true);
-      curr_eps = sampling_radius(t).value;
-      
-      std::cout << "curr_eps = " << curr_eps << "\n";
-    }
-  // Iterate and insert in a torus
-  // while (rmh.value > epsilon)
-  //   {
-  //     W.push_back(rmh.center);
-  //     insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true);
-  //     rmh = sampling_radius(t);
-  //     //std::cout << rmh.value;
-  //   }
-}
-
-///////////////////////////////////////////////////////////////////////
-// LANDMARK CHOICE PROCEDURE
-///////////////////////////////////////////////////////////////////////
-
-/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call.
- *
- *  IN:  W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d
- *  IN:  nbP is the size of W
- *  OUT: landmarks is the output vector for the points
- *  OUT: landmarks_ind is the output vector for the indices of the selected points in W
- *  IN:  delta is the constant of protection
- *  OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation
- *  IN:  torus is true iff you are working on a flat torus [-1,1]^d
- */ 
-
-void protected_delaunay(Point_Vector& W,
-                        //Point_Vector& landmarks,
-                        std::vector<int>& landmarks_ind,
-                        FT alpha,
-                        FT epsilon,
-                        FT delta0,
-                        FT theta0,
-                        FT gamma0,
-                        //std::vector<std::vector<int>>& full_cells,
-                        bool torus,
-                        bool power_protection
-                        )
-{
-  //bool return_ = true;
-  unsigned D = W[0].size();
-  int nbP = W.size();
-  //FT beta = 1/(1-alpha);
-  //FT Ad = pow((4*alpha + 8*beta)/alpha, D);
-  //FT theta0 = 1/Ad;
-  //FT delta0 = pow(1/Ad,D);
-  Torus_distance td;
-  Euclidean_distance ed;
-  Delaunay_triangulation t(D);
-  std::vector<bool> point_taken(nbP,false);
-  CGAL::Random rand;
-  int landmark_count = 0;
-  std::list<int> index_list;
-  //****************** Kd Tree W
-  STraits traits(&(W[0]));
-  Tree treeW(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nbP),
-         typename Tree::Splitter(),
-         traits);
-  //      shuffle the list of indexes (via a vector)
-  {
-    std::vector<int> temp_vector;
-    for (int i = 0; i < nbP; ++i)
-      temp_vector.push_back(i);
-    unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
-    std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed));
-    //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end());
-    for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it)
-      index_list.push_front(*it);
-  }
-  //******************** Initialize point set
-  if (!torus)
-    for (unsigned pos1 = 0; pos1 < D+1; ++pos1)
-      {
-        std::vector<FT> point;
-        for (unsigned i = 0; i < pos1; ++i)
-          point.push_back(-1);
-        if (pos1 != D)
-          point.push_back(1);
-        for (unsigned i = pos1+1; i < D; ++i)
-          point.push_back(0);
-        assert(point.size() == D);
-        W[index_list.front()] = Point_d(point);
-        insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus);
-        index_list.pop_front();
-      }
-  else
-    initialize_torus(W, treeW, t, epsilon, landmarks_ind, landmark_count, point_taken);
-  //std::cout << "Size of treeW: " << treeW.size() << "\n";
-  //std::cout << "Size of t: " << t.number_of_vertices() << "\n";
-  //******************* Initialize heap for R_max
-  //Heap R_max_heap;
-  //make_heap(t, R_max_heap);
-
-  
-  R_max_handle rh = sampling_radius(t);
-  FT epsilon0 = rh.value; 
-  if (experiment1) eps_vector.push_back(pow(1/rh.value,D));
-  //******************** Iterative algorithm
-  std::vector<int> candidate_points;
-  torus_search(treeW, D,
-               rh.center,
-               alpha*rh.value,
-               candidate_points);
-  std::list<int>::iterator list_it;
-  std::vector<int>::iterator cp_it = candidate_points.begin();
-  while (cp_it != candidate_points.end())
-    {
-      if (!point_taken[*cp_it] && !is_violating_protection(W[*cp_it], t, D, delta0, power_protection, theta0, gamma0))
-        {
-          Delaunay_vertex v = insert_delaunay_landmark_with_copies(W, *cp_it, landmarks_ind, t, landmark_count, torus);
-          {
-            // Simple check if the new cells don't have centers too close one to another
-            std::vector<Full_cell_handle> inc_cells;
-            std::back_insert_iterator<std::vector<Full_cell_handle>> out(inc_cells);
-            t.tds().incident_full_cells(v, out);
-
-            std::vector<Sphere_d> spheres;
-            for (auto i_it = inc_cells.begin(); i_it != inc_cells.end(); ++i_it)
-              {
-                std::vector<Point_d> vertices;
-                for (auto v_it = (*i_it)->vertices_begin(); v_it != (*i_it)->vertices_end(); ++v_it)
-                  vertices.push_back((*v_it)->point());
-                spheres.push_back(Sphere_d(vertices.begin(), vertices.end()));
-              }
-            for (auto s_it = spheres.begin(); s_it != spheres.end(); ++s_it)
-              for (auto t_it = s_it+1; t_it != spheres.end(); ++t_it)
-                {
-                  FT ddc2 = ed.transformed_distance(s_it->center(),t_it->center());
-                  if (ddc2 < gamma0*gamma0*s_it->squared_radius() ||
-                      ddc2 < gamma0*gamma0*t_it->squared_radius())
-                    { refused_centers2++; }
-                }
-          }
-            
-          //std::cout << *cp_it << ",\n";
-          //make_heap(t, R_max_heap);
-          point_taken[*cp_it] = true;
-          rh = sampling_radius(t);
-          if (experiment1) eps_vector.push_back(pow(1/rh.value,D));
-          //std::cout << "rhvalue = " << rh.value << "\n";
-          //std::cout << "D = " << 
-          candidate_points.clear();
-          torus_search(treeW, D,
-                       rh.center,
-                       alpha*rh.value,
-                       candidate_points);
-          cp_it = candidate_points.begin();
-          /*
-          // PIECE OF CODE FOR DEBUGGING PURPOSES
-          
-          Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count);
-          if (triangulation_is_protected(t, delta))
-            {
-              index_list.erase(list_it);
-              list_it = index_list.begin();
-            }
-          else
-            { //THAT'S WHERE SOMETHING'S WRONG
-              t.remove(inserted_v);
-              landmarks_ind.pop_back();
-              landmark_count--;
-              write_delaunay_mesh(t, W[*list_it], is2d);
-              is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore
-            }
-          */
-          //std::cout << "index_list_size() = " << index_list.size() << "\n";
-        }
-      else
-        {
-          cp_it++;
-          //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n";
-        }
-      //if (list_it != index_list.end())
-      //  write_delaunay_mesh(t, W[*list_it], is2d);
-    }
-  
-  if (experiment2) epsratio_vector.push_back(rh.value/epsilon0);
-  if (experiment2) epsslope_vector.push_back( (pow(1/rh.value,D)-pow(1/epsilon0,D))/(landmarks_ind.size() - 48) );
-  std::cout << "The iteration ended when cp_count = " << candidate_points.size() << "\n";
-  std::cout << "alphaRmax = " << alpha*rh.value << "\n";
-  std::cout << "epsilon' = " << rh.value << "\n";
-  std::cout << "nbL = " << landmarks_ind.size() << "\n";
-  print_statistics();
-  //print_vector(landmarks_ind); std::cout << std::endl;
-  //std::sort(landmarks_ind.begin(), landmarks_ind.end());
-  print_vector(landmarks_ind); std::cout << std::endl;
-  if (experiment3) thetamin_vector[thetamin_vector.size()-1] = sampling_fatness(t);
-  std::cout << "theta = " << sampling_fatness(t) << "\n";
-  //fill_landmarks(W, landmarks, landmarks_ind, torus);
-  //fill_full_cell_vector(t, full_cells);
-  /*
-  if (triangulation_is_protected(t, delta))
-    std::cout << "Triangulation is ok\n";
-  else
-    {
-      std::cout << "Triangulation is BAD!! T_T しくしく!\n";
-    }
-  */
-  write_delaunay_mesh(t, W[0], true);
-  //std::cout << t << std::endl;
-}
-
-void run_experiment5(Point_Vector& W,
-                     int D,
-                     FT alpha,
-                     FT epsilon,
-                     FT delta0,
-                     FT theta0,
-                     FT gamma0,
-                     //std::vector<std::vector<int>>& full_cells,
-                     bool torus,
-                     bool power_protection
-                     )
-{
-  // INITIALIZATION
-  Delaunay_triangulation t(D);
-  std::vector<int> landmarks_ind;
-  int landmark_count = 0;
-  initialize_statistics();
-  if (D == 2)
-    {
-      int xw = 6, yw = 4;
-      // Triangular lattice close to regular triangles h=0.866a ~ 0.875a   : 48p
-      for (int i = 0; i < xw; ++i)
-        for (int j = 0; j < yw; ++j)
-          {
-            Point_d cite1(std::vector<FT>{2.0/xw*i, 2.0/yw*j});
-            W.push_back(cite1);  // debug purpose
-            insert_delaunay_landmark_with_copies(W, W.size()-1,
-                                                 landmarks_ind, t, landmark_count, true);
-
-            Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 2.0/yw*(j+0.5)});
-            W.push_back(cite2);  // debug purpose
-            insert_delaunay_landmark_with_copies(W, W.size()-1,
-                                                 landmarks_ind, t, landmark_count, true);
-          }
-    }
-  else if (D == 3)
-    {
-      int wd = 3;
-      // Body-centered cubic lattice : 54p
-      for (int i = 0; i < wd; ++i)
-        for (int j = 0; j < wd; ++j)
-          for (int k = 0; k < wd; ++k)
-            {
-              Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k});
-              W.push_back(cite1);  // debug purpose
-              insert_delaunay_landmark_with_copies(W, W.size()-1,
-                                                   landmarks_ind, t, landmark_count, true);
-
-              Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)});
-              W.push_back(cite2);  // debug purpose
-              insert_delaunay_landmark_with_copies(W, W.size()-1,
-                                                   landmarks_ind, t, landmark_count, true);
-            }
-    }
-
-  // ITERATIONS
-  R_max_handle rh = sampling_radius(t);
-  Point_d rp = *(Random_point_iterator(D, alpha*rh.value));
-  int death_count = 0;
-  std::cout << "death count " << death_count << " rp = " << rp << "\n";
-  while (death_count < 100)
-    {
-      std::vector<FT> coords;
-      for (auto c_it = rh.center.cartesian_begin(),
-           r_it = rp.cartesian_begin();
-           c_it != rh.center.cartesian_end();
-           ++c_it, ++r_it)
-        coords.push_back(*c_it + *r_it);
-      Point_d new_p(coords);
-      if (!is_violating_protection(new_p, t, D, delta0, power_protection, theta0, gamma0))
-        {
-          W.push_back(new_p);
-          insert_delaunay_landmark_with_copies(W, W.size()-1, landmarks_ind, t, landmark_count, torus);
-          rh = sampling_radius(t);
-          rp = *(Random_point_iterator(D, alpha*rh.value));
-          death_count = 0;
-          std::cout << "death count " << death_count << " rp = " << rp << "\n";
-        }
-      else
-        {
-          rp = *(Random_point_iterator(D, alpha*rh.value));
-          death_count++;
-          std::cout << "death count " << death_count << " rp = " << rp << "\n";
-        }
-      //Point_d new_p = (*rp++) + Vector_d;
-    }
-}
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Series of experiments
-///////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-void start_experiments(Point_Vector& W, FT alpha, std::vector<int>& landmarks_ind, FT epsilon)
-{
-  int experiment_no = 1;
-  FT delta0 = 0.1;
-  FT theta0 = 0.1;
-  FT gamma0 = 0.01;
-  std::string suffix;
-  //std::cout << "ようこそジプシー我が神秘の部屋へ:\n";
-  while (experiment_no != 0)
-    {
-      std::cout << "Enter experiment no (0 to exit): ";
-      std::cin >> experiment_no;
-      switch (experiment_no)
-        {
-        case 1:
-          // Experiment 1
-          experiment1 = true;         
-          eps_vector = {};
-          std::cout << "Enter delta0: "; std::cin >> delta0;
-          std::cout << "Enter theta0: "; std::cin >> theta0;
-          std::cout << "Enter gamma0: "; std::cin >> gamma0;
-          protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true);
-          write_tikz_plot(eps_vector,"epstime.tikz");
-          experiment1 = false;
-          break;
-          
-        case 2:
-          // Experiment 2
-          suffix = "";
-          experiment2 = true;
-          epsratio_vector = {0};
-          epsslope_vector = {0};
-          std::cout << "File name suffix: ";
-          std::cin >> suffix;
-          for (FT alpha = 0.01; alpha < 0.999; alpha += 0.01)
-            {
-              landmarks_ind.clear();
-              std::cout << "Test for alpha = " << alpha << "\n";
-              protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true);
-            }
-          write_tikz_plot(epsratio_vector,"epsratio_alpha." + suffix + ".tex");
-          write_tikz_plot(epsslope_vector,"epsslope_alpha." + suffix + ".tex");
-          experiment2 = false;
-          break;
-
-        case 3:
-          // Experiment 3
-          experiment3 = true;
-          thetamin_vector = {};
-          gammamin_vector = {};
-          theta0 = 0;
-          gamma0 = 0;
-          for (FT delta0 = 0; delta0 < 0.999; delta0 += 0.05)
-            {
-              landmarks_ind.clear();
-              thetamin_vector.push_back(1.0); //0.7489 fatness of the initialization
-              gammamin_vector.push_back(10);
-              std::cout << "Test for delta0 = " << delta0 << "\n";
-              protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true);
-            }
-          write_tikz_plot(thetamin_vector,"thetamin_delta.tex");
-          write_tikz_plot(gammamin_vector,"gammamin_delta.tex");
-          experiment3 = false;
-          break;
-
-        // case 4:
-        //   // Experiment 4
-        //   {
-        //     int dim;
-        //     std::cout << "Enter dimension: ";
-        //     std::cin >> dim;
-        //     Delaunay_triangulation t(dim);
-        //     // for (FT eps = 0.7; eps < 1.1; eps += 0.1)
-        //   //     {
-        //   //       generate_epsilon_sample_torus(W, eps, dim, t);
-        //   //       for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        //   //         {
-        //   //           if (t.is_infinite(v_it))
-        //   //             continue;
-        //   //           bool in_cube = true; 
-        //   //           for (auto xi = v_it->cartesian_begin(); xi != v_it->cartesian_end(); ++xi)
-        //   //             if (*xi > 1.0 || *xi < -1.0)
-        //   //               {
-        //   //                 in_cube = false; break;
-        //   //               }
-        //   //           if (!in_cube)
-        //   //             continue;
-        //   //           for (auto t.tds().incident_full_cells())
-        //   //         }
-        //   //       std::cout << "eps = " << eps << ", real epsilon = " << sampling_radius(t).value << "\n";
-        //   //     }
-        //   // }
-        //   break;
-
-
-        case 5:
-          // Experiment 5
-          experiment5 = true;
-          //     std::cout << "Enter dimension: ";
-          //     std::cin >> dim;
-
-          landmarks_ind.clear();
-          W.clear();
-          run_experiment5(W,  alpha, epsilon, delta0, theta0, gamma0, true, true);
-          experiment5 = false;
-          break;
-        }
-
-    }
-
-}
-  
-#endif
diff --git a/src/Witness_complex/example/witness_complex_cube.cpp b/src/Witness_complex/example/witness_complex_cube.cpp
deleted file mode 100644
index e448c55d..00000000
--- a/src/Witness_complex/example/witness_complex_cube.cpp
+++ /dev/null
@@ -1,590 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-// Avoiding the max arity issue with CGAL
-#ifndef BOOST_PARAMETER_MAX_ARITY
-# define BOOST_PARAMETER_MAX_ARITY 12
-#endif
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <algorithm>
-#include <set>
-#include <iterator>
-#include <chrono>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-#include "Torus_distance.h" 
-#include "generators.h"
-#include "output.h"
-//#include "protected_sets/protected_sets.h"
-#include "protected_sets/protected_sets_paper2.h"
-
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-#include <CGAL/Kernel_d/Hyperplane_d.h>
-#include <CGAL/enum.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Random.h>
-#include <CGAL/Timer.h>
-#include <CGAL/Delaunay_triangulation.h>
-
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-typedef K::Vector_d Vector_d;
-typedef K::Oriented_side_d Oriented_side_d;
-typedef K::Has_on_positive_side_d Has_on_positive_side_d;
-
-//typedef CGAL::Point_d<K> Point_d;
-typedef K::FT FT;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-//typedef K::Equal_d Equal_d;
-//typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex;
-typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle;
-//typedef CGAL::Sphere_d<K> Sphere_d;
-typedef K::Sphere_d Sphere_d;
-typedef K::Hyperplane_d Hyperplane_d;
-
-/*//////////////////////////////////////
- * GLOBAL VARIABLES ********************
- *//////////////////////////////////////
-
-//NA bool toric=false;
-bool power_protection = true;
-bool grid_points = true;
-bool is2d = true;
-//FT  _sfty = pow(10,-14);
-bool torus = false;
-
-
-bool triangulation_is_protected(Delaunay_triangulation& t, FT delta)
-{
-  std::cout << "Start protection verification\n";
-  Euclidean_distance ed;
-  // Fill the map Vertices -> Numbers
-  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
-  int ind = 0;
-  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-    {
-      if (t.is_infinite(v_it))
-        continue;
-      index_of_vertex[v_it] = ind++;
-    }
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    if (!t.is_infinite(fc_it))
-      {
-        std::vector<Point_d> vertices;
-        for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-          vertices.push_back((*fc_v_it)->point());                
-        Sphere_d cs( vertices.begin(), vertices.end());
-        Point_d center_cs = cs.center();
-        FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(0)->point()));
-        for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-          if (!t.is_infinite(v_it))
-          //check if vertex belongs to the face
-            if (!vertex_is_in_full_cell(v_it, fc_it))
-              {
-                FT dist2 = ed.transformed_distance(center_cs, v_it->point());
-                //if the new point is inside the protection ball of a non conflicting simplex
-                //std::cout << "Dist^2 = " << dist2 << " (r+delta)*(r+delta) = " << (r+delta)*(r+delta) << " r^2 = " << r*r <<"\n";
-                if (!power_protection)
-                  if (dist2 <= (r+delta)*(r+delta) && dist2 >= r*r)
-                    {
-                      write_delaunay_mesh(t, v_it->point(), is2d);
-                      // Output the problems
-                      std::cout << "Problematic vertex " << index_of_vertex[v_it] << " ";
-                      std::cout << "Problematic cell ";
-                      for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it)
-                        if (!t.is_infinite(*vh_it))
-                          std::cout << index_of_vertex[*vh_it] << " ";
-                      std::cout << "\n";
-                      std::cout << "r^2 = " << r*r << ", d^2 = " << dist2 << ", (r+delta)^2 = " << (r+delta)*(r+delta) << "\n";
-                      return false;
-                    }
-                if (power_protection)
-                  if (dist2 <= r*r+delta*delta && dist2 >= r*r)
-                    {
-                      write_delaunay_mesh(t, v_it->point(), is2d);
-                      std::cout << "Problematic vertex " << *v_it << " ";
-                      std::cout << "Problematic cell " << *fc_it << "\n";
-                      std::cout << "r^2 = " << r*r << ", d^2 = " << dist2 << ", r^2+delta^2 = " << r*r+delta*delta << "\n";
-                      return false;
-                    }
-              }
-      } 
-  return true;
-}
-
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-// SAMPLING RADIUS 
-//////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-FT sampling_radius(Delaunay_triangulation& t, FT epsilon0)
-{
-  FT epsilon2 = 0;
-  Point_d control_point;
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin()));
-      if (epsilon2 < r2)
-        {
-          epsilon2 = r2;
-          control_point = (*vertices.begin());
-        }
-    }
-  if (epsilon2 < epsilon0*epsilon0)
-    {
-      std::cout << "ACHTUNG! E' < E\n";
-      std::cout << "eps = " << epsilon0 << " eps' = " << sqrt(epsilon2) << "\n";
-      write_delaunay_mesh(t, control_point, is2d);
-    }
-  return sqrt(epsilon2);
-}
-
-FT point_sampling_radius_by_delaunay(Point_Vector& points, FT epsilon0)
-{
-  Delaunay_triangulation t(points[0].size());
-  t.insert(points.begin(), points.end());
-  return sampling_radius(t, epsilon0);
-}
-
-// A little script to make a tikz histogram of epsilon distribution
-// Returns the average epsilon
-FT epsilon_histogram(Delaunay_triangulation& t, int n)
-{
-  FT epsilon_max = 0; //sampling_radius(t,0);
-  FT sum_epsilon = 0;
-  int count_simplices = 0;
-  std::vector<int> histo(n+1, 0);
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    {
-      if (t.is_infinite(fc_it))
-        continue;
-      Point_Vector vertices;
-      for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-        vertices.push_back((*fc_v_it)->point());
-      Sphere_d cs( vertices.begin(), vertices.end());
-      Point_d csc = cs.center();
-      bool in_cube = true; 
-      for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi)
-        if (*xi > 1.0 || *xi < -1.0)
-          {
-            in_cube = false; break;
-          }
-      if (!in_cube)
-        continue;
-      FT r = sqrt(Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin())));
-      if (r > epsilon_max)
-        epsilon_max = r;
-      sum_epsilon += r;
-      count_simplices++;
-      histo[floor(r/epsilon_max*n)]++;
-    }
-  std::ofstream ofs ("histogram.tikz", std::ofstream::out);
-  FT barwidth = 20.0/n;
-  int max_value = *(std::max_element(histo.begin(), histo.end()));
-  std::cout << max_value << std::endl;
-  FT ten_power = pow(10, ceil(log10(max_value)));
-  FT max_histo = ten_power;
-  if (max_value/ten_power < 2)
-    max_histo = 0.2*ten_power;
-  if (max_value/ten_power < 5)
-    max_histo = 0.5*ten_power;  
-  std::cout << ceil(log10(max_value)) << std::endl << max_histo << std::endl;
-  FT unitht = max_histo/10.0;
-
-  ofs << "\\draw[->] (0,0) -- (0,11);\n" <<
-    "\\draw[->] (0,0) -- (21,0);\n" <<
-    "\\foreach \\i in {1,...,10}\n" <<
-    "\\draw (0,\\i) -- (-0.1,\\i);\n" <<
-    "\\foreach \\i in {1,...,20}\n" <<
-    "\\draw (\\i,0) -- (\\i,-0.1);\n" <<
- 
-    "\\node at (-1,11) {$\\epsilon$};\n" << 
-    "\\node at (22,-1) {$\\epsilon/\\epsilon_{max}$};\n" << 
-    "\\node at (-0.5,-0.5) {0};\n" << 
-    "\\node at (-0.5,10) {" << max_histo << "};\n" << 
-    "\\node at (20,-0.5) {1};\n";
-    
-
-  for (int i = 0; i < n; ++i)
-    ofs << "\\draw (" << barwidth*i << "," << histo[i]/unitht << ") -- ("
-        << barwidth*(i+1) << "," << histo[i]/unitht << ") -- ("
-  << barwidth*(i+1) << ",0) -- (" << barwidth*i << ",0) -- cycle;\n";
-  
-  ofs.close();
-
-  //return sum_epsilon/count_simplices;
-  return epsilon_max;
-}
-
-FT epsilon_histogram_by_delaunay(Point_Vector& points, int n)
-{
-  Delaunay_triangulation t(points[0].size());
-  t.insert(points.begin(), points.end());
-  return epsilon_histogram(t, n);
-}
-
-
-int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<std::vector<int>>& full_cells)
-{
-  //******************** Preface: origin point
-  int D = W[0].size();
-  std::vector<FT> orig_vector;
-  for (int i=0; i<D; i++)
-    orig_vector.push_back(0);
-  Point_d origin(orig_vector);
-
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  Euclidean_distance ed;
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-  std::vector<Point_d> landmarks_ext;
-  int nb_cells = 1;
-  for (int i = 0; i < D; ++i)
-    nb_cells *= 3;
-  for (int i = 0; i < nb_cells; ++i)
-      for (int k = 0; k < nbL; ++k)
-        {
-          std::vector<double> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(landmarks[k][l] + 2.0*((cell_i%3)-1.0));
-              cell_i /= 3;
-            }
-          landmarks_ext.push_back(point);
-        }
-  write_points("landmarks/initial_landmarks",landmarks_ext);
-  STraits traits(&(landmarks_ext[0]));
-  std::vector< std::vector <int> > WL(nbP);
-
-  //********************** Neighbor search in a Kd tree
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nb_cells*nbL),
-         typename Tree::Splitter(),
-         traits);
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  for (int i = 0; i < nbP; i++)
-    {
-      Point_d& w = W[i];
-      ////Search D+1 nearest neighbours from the tree of landmarks L
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks_ext[0])) );
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          if (std::find(WL[i].begin(), WL[i].end(), (it->first)%nbL) == WL[i].end())
-            WL[i].push_back((it->first)%nbL);
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-    }
-  std::string out_file = "wl_result";
-  //write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  witnessComplex.witness_complex(WL);
-
-  //******************** Verifying if all full cells are in the complex
-
-  int in=0, not_in=0;
-  for (auto cell : full_cells)
-    {
-      //print_vector(cell);
-      if (witnessComplex.find(cell) != witnessComplex.null_simplex())
-        in++;
-      else
-        not_in++;
-    }
-  std::cout << "Out of all the cells in Delaunay triangulation:\n" << in << " are in the witness complex\n" <<
-    not_in << " are not.\n";
-  
-  //******************** Making a set of bad link landmarks
-  
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  //std::cout << "Bad links around ";
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  for (auto u: witnessComplex.complex_vertex_range())
-    {
-       if (!witnessComplex.has_good_link(u, count_bad, count_good))
-         {
-           count_badlinks++;
-           Point_d& l = landmarks[u];
-           Fuzzy_sphere fs(l, sqrt(lambda)*3, 0, traits);
-           std::vector<int> curr_perturb;
-           L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs);
-           for (int i: curr_perturb)
-             perturbL.insert(i%nbL);
-       }
-    }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  
-  //*********************** Perturb bad link landmarks  
-  /*
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/8);
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          while (K().squared_distance_d_object()(*rp,origin) < lambda/256)
-            rp++;
-          FT coord = landmarks[u][i] + (*rp)[i];
-          if (coord > 1)
-            point.push_back(coord-1);
-          else if (coord < -1)
-            point.push_back(coord+1);
-          else
-            point.push_back(coord);
-        }
-      landmarks[u] = Point_d(point);
-    }
-  std::cout << "lambda=" << lambda << std::endl;
-  */
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  
-  //write_edges("landmarks/edges", witnessComplex, landmarks);
-  /*
-  return count_badlinks;
-  */
-  return 0;
-}
-
-int main (int argc, char * const argv[])
-{
-  power_protection = true;//false;
-  grid_points = false;//true;
-  torus = true;
-  
-  if (argc != 4)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " nbP dim delta\n";
-      return 0;
-    }
-  int nbP       = atoi(argv[1]);
-  int dim       = atoi(argv[2]);
-  double theta0 = atof(argv[3]);
-  //double delta  = atof(argv[3]);
-
-  is2d = (dim == 2);
-  
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  if (grid_points)
-    {
-      generate_points_grid(point_vector, (int)pow(nbP, 1.0/dim), dim, torus);
-      nbP = (int)pow((int)pow(nbP, 1.0/dim), dim);
-    }
-  else
-    generate_points_random_box(point_vector, nbP, dim);
-  FT epsilon = point_sampling_radius_by_delaunay(point_vector, 0);
-  //FT epsilon = epsilon_histogram_by_delaunay(point_vector,50);
-  std::cout << "Initial epsilon = " << epsilon << std::endl;
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  //write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  CGAL::Timer timer;
-
-  int n = 1;
-  std::vector<FT> values(n,0);
-  std::vector<FT> time(n,0);
-
-  //FT step = 0.001;
-  //FT delta = 0.01*epsilon;
-  //FT alpha = 0.5;
-  //FT step = atof(argv[3]);
-
-  start_experiments(point_vector, theta0, chosen_landmarks, epsilon);
-    
-  // for (int i = 0; i < n; i++)
-  // //for (int i = 0; bl > 0; i++)
-  //   {
-  //     //std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n";
-  //     //double delta = pow(10, -(1.0*i)/2);
-  //     //delta = step*i*epsilon;
-  //     //theta0 = step*i;
-  //     std::cout << "delta/epsilon = " << delta/epsilon << std::endl;
-  //     std::cout << "theta0 = " << theta0 << std::endl;
-  //     // Averaging the result
-  //     int sum_values = 0;
-  //     int nb_iterations = 1;
-  //     std::vector<std::vector<int>> full_cells;
-  //     for (int i = 0; i < nb_iterations; ++i)
-  //       {
-  //         //L = {};
-  //         chosen_landmarks = {};
-  //         //full_cells = {};
-  //         //timer.start();
-  //         //protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta, epsilon, alpha, theta0, full_cells, torus, power_protection);
-  //         protected_delaunay(point_vector, chosen_landmarks, delta, epsilon, alpha, theta0, torus, power_protection);
-  //         //timer.stop();
-  //         sum_values += chosen_landmarks.size();
-  //       }
-  //     //FT epsilon2 = point_sampling_radius_by_delaunay(L, epsilon);
-  //     //std::cout << "Final epsilon = " << epsilon2  << ". Ratio = " << epsilon2/epsilon << std::endl;
-  //     //write_points("landmarks/initial_landmarks",L);
-  //     //std::cout << "delta/epsilon' = " << delta/epsilon2 << std::endl;
-  //     FT nbL = (sum_values*1.0)/nb_iterations;
-  //     //values[i] = pow((1.0*nbL)/nbP, -1.0/dim);
-  //     values[i] = (1.0*nbL)/nbP;
-  //     std::cout << "Number of landmarks = " << nbL << ", time= " << timer.time() << "s"<< std::endl;
-  //     //landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells);
-  //     time[i] = timer.time();
-  //     timer.reset();
-  //     //write_points("landmarks/landmarks0",L);
-  //   }
-  
-  // // OUTPUT A PLOT
-  // FT hstep = 20.0/(n-1);
-  // FT wstep = 10.0;
-
-  // std::ofstream ofs("N'Nplot.tikz", std::ofstream::out);
-  // ofs << "\\draw[red] (0," << wstep*values[0] << ")";
-  // for (int i = 1; i < n; ++i)
-  //   ofs << " -- (" << hstep*i << "," << wstep*values[i] << ")";
-  // ofs << ";\n";
-  // ofs.close();
-  /*
-  wstep = 0.1;
-  ofs = std::ofstream("time.tikz", std::ofstream::out);
-  ofs << "\\draw[red] (0," << wstep*time[0] << ")";
-  for (int i = 1; i < n; ++i)
-    ofs << " -- (" << hstep*i << "," << wstep*time[i] << ")";
-  ofs << ";\n";
-  ofs.close();
-  
-  
-  std::vector<std::vector<int>> full_cells;
-  timer.start();
-  landmark_choice_protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta, full_cells);
-  timer.stop();
-  FT epsilon2 = point_sampling_radius_by_delaunay(L);
-  std::cout << "Final epsilon = " << epsilon2  << ". Ratio = " << epsilon/epsilon2 << std::endl;
-  write_points("landmarks/initial_landmarks",L);
-  int nbL = chosen_landmarks.size();
-  std::cout << "Number of landmarks = " << nbL << ", time= " << timer.time() << "s"<< std::endl;
-  //landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells);
-  timer.reset();
-  */
-}
diff --git a/src/Witness_complex/example/witness_complex_cubic_systems.cpp b/src/Witness_complex/example/witness_complex_cubic_systems.cpp
deleted file mode 100644
index 2f4ee1cb..00000000
--- a/src/Witness_complex/example/witness_complex_cubic_systems.cpp
+++ /dev/null
@@ -1,547 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <algorithm>
-#include <set>
-#include <iterator>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-#include <unistd.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-#include "Torus_distance.h" 
-
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Random.h>
-#include <CGAL/Delaunay_triangulation.h>
-
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-//typedef CGAL::Cartesian_d<double> K;
-//typedef CGAL::Point_d<K> Point_d;
-typedef K::FT FT;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-//typedef K::Equal_d Equal_d;
-//typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator;
-typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator;
-typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef CGAL::Sphere_d<K> Sphere_d;
-
-bool toric=false;
-
-
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , Point_Vector & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      Point_d p(point.begin(), point.end());
-      if (point.size() != 1)
-        points.push_back(p);
-    }
-  in_file.close();
-}
-
-void generate_points_random_box(Point_Vector& W, int nbP, int dim)
-{
-  /*
-  Random_cube_iterator rp(dim, 1);
-  for (int i = 0; i < nbP; i++)
-    {
-      std::vector<double> point;
-      for (auto it = rp->cartesian_begin(); it != rp->cartesian_end(); ++it)
-        point.push_back(*it);
-      W.push_back(Point_d(point));
-      rp++;
-    }
-  */
-  Random_cube_iterator rp(dim, 1.0);
-  for (int i = 0; i < nbP; i++)
-    {
-      W.push_back(*rp++);
-    }
-}
-
-
-void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto l: w)
-        ofs << l << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-
-void write_points( std::string file_name, std::vector< Point_d > & points)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : points)
-    {
-      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
-        ofs << *it << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto u: witness_complex.complex_vertex_range())
-    for (auto v: witness_complex.complex_vertex_range())
-      {
-        typeVectorVertex edge = {u,v};
-        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
-          {
-            for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n";
-            for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n\n\n";
-          }
-      }
-  ofs.close();
-}
-
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  int chosen_landmark;
-  Point_d* p;
-  CGAL::Random rand;
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::count(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=0);
-      //rand++;
-      //std::cout << "Chose " << chosen_landmark << std::endl;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-
-void aux_fill_grid(Point_Vector& W, int& width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool> & curr_pattern)
-{
-  int D = W[0].size();
-  int nb_points = 1;
-  for (int i = 0; i < D; ++i)
-    nb_points *= width;
-  for (int i = 0; i < nb_points; ++i)
-    {
-      std::vector<double> point;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          if (curr_pattern[l])
-            point.push_back(-1.0+(2.0/width)*(cell_i%width)+(1.0/width));
-          else
-            point.push_back(-1.0+(2.0/width)*(cell_i%width));
-          cell_i /= width;
-        }
-      landmarks.push_back(Point_d(point));
-      landmarks_ind.push_back(0);//landmarks_ind.push_back(W.size());
-      //std::cout << "Added point " << W.size() << std::endl;;
-      //W.push_back(Point_d(point));
-    }
-}
-  
-void aux_put_halves(Point_Vector& W, int& width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool>& curr_pattern, std::vector<bool>::iterator curr_pattern_it, std::vector<bool>::iterator bool_it, std::vector<bool>::iterator bool_end)
-{
-  if (curr_pattern_it != curr_pattern.end())
-    {
-      if (bool_it != bool_end)
-        {
-          *curr_pattern_it = false;
-          aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern_it+1, bool_it, bool_end);
-          *curr_pattern_it = true;
-          aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern_it+1, bool_it+1, bool_end);
-        }
-    }
-  else
-    if (*bool_it)
-      {
-        std::cout << "Filling the pattern ";
-        for (bool b: curr_pattern)
-          if (b) std::cout << '1';
-          else   std::cout << '0';
-        std::cout << "\n";
-        aux_fill_grid(W, width, landmarks, landmarks_ind, curr_pattern);
-      }  
-}
-
-void landmark_choice_cs(Point_Vector& W, int width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool>& face_centers)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  //int chosen_landmark;
-  CGAL::Random rand;
-  //To speed things up check the last true in the code and put it as the finishing condition
-  unsigned last_true = face_centers.size()-1;
-  while (!face_centers[last_true] && last_true != 0)
-    last_true--;
-  //Recursive procedure to understand where we put +1/2 in centers' coordinates
-  std::vector<bool> curr_pattern(W[0].size(), false);
-  aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern.begin(), face_centers.begin(), face_centers.begin()+(last_true+1));
-  std::cout << "The number of landmarks is: " << landmarks.size() << std::endl;
-
- }
-
-int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  //******************** Preface: origin point
-  int D = W[0].size();
-  std::vector<FT> orig_vector;
-  for (int i=0; i<D; i++)
-    orig_vector.push_back(0);
-  Point_d origin(orig_vector);
-
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  int nbL = landmarks.size();
-  Euclidean_distance ed;
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-  std::vector<Point_d> landmarks_ext;
-  int nb_cells = 1;
-  for (int i = 0; i < D; ++i)
-    nb_cells *= 3;
-  for (int i = 0; i < nb_cells; ++i)
-      for (int k = 0; k < nbL; ++k)
-        {
-          std::vector<double> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(landmarks[k][l] + 2.0*((cell_i%3)-1.0));
-              cell_i /= 3;
-            }
-          landmarks_ext.push_back(point);
-        }
-  write_points("landmarks/initial_landmarks",landmarks_ext);
-  STraits traits(&(landmarks_ext[0]));
-  std::vector< std::vector <int> > WL(nbP);
-
-  //********************** Neighbor search in a Kd tree
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nb_cells*nbL),
-         typename Tree::Splitter(),
-         traits);
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  for (int i = 0; i < nbP; i++)
-    {
-      Point_d& w = W[i];
-      ////Search D+1 nearest neighbours from the tree of landmarks L
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks_ext[0])) );
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          if (std::find(WL[i].begin(), WL[i].end(), (it->first)%nbL) == WL[i].end())
-            WL[i].push_back((it->first)%nbL);
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-    }
-  std::string out_file = "wl_result";
-  write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  witnessComplex.witness_complex(WL);
-
-  //******************** Making a set of bad link landmarks
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  //std::cout << "Bad links around ";
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  for (auto u: witnessComplex.complex_vertex_range())
-    {
-      if (!witnessComplex.has_good_link(u, count_bad, count_good, D))
-         {
-           count_badlinks++;
-           Point_d& l = landmarks[u];
-           Fuzzy_sphere fs(l, sqrt(lambda)*3, 0, traits);
-           std::vector<int> curr_perturb;
-           L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs);
-           for (int i: curr_perturb)
-             perturbL.insert(i%nbL);
-       }
-    }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  
-  //*********************** Perturb bad link landmarks  
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/8);
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          while (K().squared_distance_d_object()(*rp,origin) < lambda/256)
-            rp++;
-          FT coord = landmarks[u][i] + (*rp)[i];
-          if (coord > 1)
-            point.push_back(coord-1);
-          else if (coord < -1)
-            point.push_back(coord+1);
-          else
-            point.push_back(coord);
-        }
-      landmarks[u] = Point_d(point);
-    }
-  std::cout << "lambda=" << lambda << std::endl;
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  write_edges("landmarks/edges", witnessComplex, landmarks);
-  return count_badlinks;
-}
-
-void exaustive_search(Point_Vector& W, int width)
-{
-  int D = W[0].size()+1;
-  int nb_points = pow(2,D);
-  std::vector<bool> face_centers(D, false);
-  int bl = 0; //Bad links
-  std::vector<std::vector<bool>> good_patterns;
-  for (int i = 0; i < nb_points; ++i)
-    {
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          if (cell_i%2 == 0)
-            face_centers[l] = false;
-          else
-            face_centers[l] = true;
-          cell_i /= 2;
-        }
-      std::cout << "**Current pattern ";
-      for (bool b: face_centers)
-        if (b) std::cout << '1';
-        else   std::cout << '0';
-      std::cout << "\n";
-      Point_Vector landmarks;
-      std::vector<int> landmarks_ind;
-      Point_Vector W_copy(W);
-      landmark_choice_cs(W_copy, width, landmarks, landmarks_ind, face_centers);
-      if (landmarks.size() != 0)
-        {
-          bl = landmark_perturbation(W_copy, landmarks, landmarks_ind);
-          if ((1.0*bl)/landmarks.size() < 0.5)
-            good_patterns.push_back(face_centers);
-        }
-    }
-  std::cout << "The following patterns worked: ";
-  for (std::vector<bool> pattern : good_patterns)
-    {
-      std::cout << "[";
-      for (bool b: pattern)
-        if (b) std::cout << '1';
-        else   std::cout << '0';
-      std::cout << "] ";
-    }
-  std::cout << "\n";        
-}
-
-int main (int argc, char * const argv[])
-{
-  unsigned nbP       = atoi(argv[1]);
-  unsigned width     = atoi(argv[2]);
-  unsigned dim       = atoi(argv[3]);
-  std::string code   = (std::string) argv[4];
-  bool e_option = false;
-  int c;
-  if (argc != 5)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << "witness_complex_cubic_systems nbP width dim code || witness_complex_systems -e nbP width dim\n"
-                << "where nbP stands for the number of witnesses, width for the width of the grid, dim for dimension "
-                << "and code is a sequence of (dim+1) symbols 0 and 1 representing if we take the centers of k-dimensional faces of the cubic system depending if it is 0 or 1."
-                << "-e stands for the 'exaustive' option";
-      return 0;
-    }
-  while ((c = getopt (argc, argv, "e::")) != -1)
-    switch(c)
-      {
-      case 'e' :
-        e_option  = true;
-        nbP       = atoi(argv[2]);
-        width     = atoi(argv[3]);
-        dim       = atoi(argv[4]);
-        break;
-      default  :
-        nbP       = atoi(argv[1]);
-        width     = atoi(argv[2]);
-        dim       = atoi(argv[3]);
-        code   = (std::string) argv[4];
-      }
-  Point_Vector point_vector;
-  generate_points_random_box(point_vector, nbP, dim);
-  
-  // Exaustive search
-  if (e_option)
-    {
-      std::cout << "Start exaustive search!\n";
-      exaustive_search(point_vector, width);
-      return 0;
-    }
-  // Search with a specific cubic system
-  std::vector<bool> face_centers;
-  if (code.size() != dim+1)
-    {
-      std::cerr << "The code should contain (dim+1) symbols";
-      return 1;
-    }
-  for (char c: code)
-    if (c == '0')
-      face_centers.push_back(false);
-    else
-      face_centers.push_back(true);
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  
-  landmark_choice_cs(point_vector, width, L, chosen_landmarks, face_centers);
-  
-  int nbL = width; //!!!!!!!!!!!!!
-  int bl = nbL, curr_min = bl;
-  write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  //for (int i = 0; i < 1; i++)
-  for (int i = 0; bl > 0; i++)
-    {
-      std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n";
-      bl=landmark_perturbation(point_vector, L, chosen_landmarks);
-      if (bl < curr_min)
-        curr_min=bl;
-      write_points("landmarks/landmarks0",L);
-    }
-  
-}
diff --git a/src/Witness_complex/example/witness_complex_epsilon.cpp b/src/Witness_complex/example/witness_complex_epsilon.cpp
deleted file mode 100644
index 7f8b985f..00000000
--- a/src/Witness_complex/example/witness_complex_epsilon.cpp
+++ /dev/null
@@ -1,55 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <vector>
-
-#include <CGAL/Epick_d.h>
-#include <CGAL/enum.h>
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d                                 Point_d;
-typedef K::FT                                      FT;
-typedef K::Hyperplane_d                            Hyperplane_d;
-typedef K::Has_on_positive_side_d                  Has_on_positive_side_d;
-
-int main ()
-{
-  std::vector<Point_d> vertices;
-  Point_d v1(std::vector<FT>({-1,1}));
-  Point_d v2(std::vector<FT>({1,-1}));
-  vertices.push_back(v1);
-  vertices.push_back(v2);
-  Point_d p(std::vector<FT>({-1,-1}));
-  Hyperplane_d hp(vertices.begin(), vertices.end());
-  //Hyperplane_d hp(vertices.begin(), vertices.end(), p, CGAL::ON_POSITIVE_SIDE);
-  if (Has_on_positive_side_d()(hp, p))
-    std::cout << "OK\n";
-  else
-    std::cout << "NOK\n";
-  CGAL::Oriented_side side_p = K::Oriented_side_d()(hp, p);
-  if (side_p == CGAL::ZERO)
-    std::cout << "Point (-1,-1) is on the line passing through (-1,1) and (1,-1)";
-  CGAL::Oriented_side side_v2 = K::Oriented_side_d()(hp, v2);
-  if (side_v2 != CGAL::ZERO)
-    std::cout << "Point (1,-1) is not on the line passing through (-1,1) and (1,-1)";
-}
diff --git a/src/Witness_complex/example/witness_complex_flat_torus.cpp b/src/Witness_complex/example/witness_complex_flat_torus.cpp
deleted file mode 100644
index 49383154..00000000
--- a/src/Witness_complex/example/witness_complex_flat_torus.cpp
+++ /dev/null
@@ -1,851 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <algorithm>
-#include <set>
-#include <iterator>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-//#include <boost/filesystem.hpp> 
-
-//#include <CGAL/Delaunay_triangulation.h>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Random.h>
-
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-//typedef CGAL::Cartesian_d<double> K;
-//typedef CGAL::Point_d<K> Point_d;
-typedef K::FT FT;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-/**
- * \brief Class of distance in a flat torus in dimension D
- *
- */
-//class Torus_distance : public Euclidean_distance {
-/*
-  class Torus_distance {
-
-public:
-    typedef K::FT    FT;
-    typedef K::Point_d Point_d;
-    typedef Point_d Query_item;
-    typedef typename CGAL::Dynamic_dimension_tag D;
-
-  double box_length = 2;
-
-  FT transformed_distance(Query_item q, Point_d p) const
-  {
-    FT distance = FT(0);
-    FT coord = FT(0);
-    //std::cout << "Hello skitty!\n";
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-	qe = construct_it(q,1), pit = construct_it(p);
-	for(; qit != qe; qit++, pit++)
-          {
-            coord = sqrt(((*qit)-(*pit))*((*qit)-(*pit)));
-            if (coord*coord <= (box_length-coord)*(box_length-coord))
-              distance += coord*coord;
-            else
-              distance += (box_length-coord)*(box_length-coord);
-          }
-        return distance;
-  }
-
-  FT min_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r) const {
-    FT distance = FT(0);
-    FT dist1, dist2;
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-                                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if((*qit) < r.min_coord(i))
-          {
-            dist1 = (r.min_coord(i)-(*qit));
-            dist2 = (box_length - r.max_coord(i)+(*qit));
-            if (dist1 < dist2)
-              distance += dist1*dist1;
-            else
-              distance += dist2*dist2;
-          }
-        else if ((*qit) > r.max_coord(i))
-          {
-            dist1 = (box_length - (*qit)+r.min_coord(i));
-            dist2 = ((*qit) - r.max_coord(i));
-            if (dist1 < dist2)
-              distance += dist1*dist1;
-            else
-              distance += dist2*dist2;
-          }
-      }
-    return distance;
-  }
-
-  FT min_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r,
-                               std::vector<FT>& dists) const {
-    FT distance = FT(0);
-    FT dist1, dist2;
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-	                  	           qe = construct_it(q,1);
-    //std::cout << r.max_coord(0) << std::endl;
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if((*qit) < r.min_coord(i))
-          {
-            dist1 = (r.min_coord(i)-(*qit));
-            dist2 = (box_length - r.max_coord(i)+(*qit));
-            if (dist1 < dist2)
-              {
-                dists[i] = dist1;
-                distance += dist1*dist1;
-              }
-            else
-              {
-                dists[i] = dist2;
-                distance += dist2*dist2;
-                //std::cout << "Good stuff1\n";
-              }
-          }
-        else if ((*qit) > r.max_coord(i))
-          {
-            dist1 = (box_length - (*qit)+r.min_coord(i));
-            dist2 = ((*qit) - r.max_coord(i));
-            if (dist1 < dist2)
-              {
-                dists[i] = dist1;
-                distance += dist1*dist1;
-                //std::cout << "Good stuff2\n";
-              }
-            else
-              {
-                dists[i] = dist2;
-                distance += dist2*dist2;
-              }
-          }
-      };
-    return distance;
-  }
-    
-  FT max_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r) const {
-    FT distance=FT(0);
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-		                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if (box_length <= (r.min_coord(i)+r.max_coord(i)))
-          if ((r.max_coord(i)+r.min_coord(i)-box_length)/FT(2.0) <= (*qit) &&
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-          else
-            distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-        else
-          if ((box_length-r.max_coord(i)-r.min_coord(i))/FT(2.0) <= (*qit) ||
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-          else
-            distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-      }
-    return distance;
-  }
-
-  
-  FT max_distance_to_rectangle(const Query_item& q,
-                               const CGAL::Kd_tree_rectangle<FT,D>& r,
-                               std::vector<FT>& dists) const {
-    FT distance=FT(0);
-    typename K::Construct_cartesian_const_iterator_d construct_it=Traits_base().construct_cartesian_const_iterator_d_object();
-    typename K::Cartesian_const_iterator_d qit = construct_it(q),
-		                           qe = construct_it(q,1);
-    for(unsigned int i = 0;qit != qe; i++, qit++)
-      {
-        if (box_length <= (r.min_coord(i)+r.max_coord(i)))
-          if ((r.max_coord(i)+r.min_coord(i)-box_length)/FT(2.0) <= (*qit) &&
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            {
-              dists[i] = r.max_coord(i)-(*qit);
-              distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-            }
-          else
-            {
-              dists[i] = sqrt(((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i)));
-              distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-            }
-        else
-          if ((box_length-r.max_coord(i)-r.min_coord(i))/FT(2.0) <= (*qit) ||
-              (*qit) <= (r.min_coord(i)+r.max_coord(i))/FT(2.0))
-            {
-              dists[i] = sqrt((r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit)));
-              distance += (r.max_coord(i)-(*qit))*(r.max_coord(i)-(*qit));
-              
-            }
-          else
-            {
-              dists[i] = (*qit)-r.min_coord(i);
-              distance += ((*qit)-r.min_coord(i))*((*qit)-r.min_coord(i));
-            }
-      }
-    return distance;
-  }
-
-    inline FT new_distance(FT dist, FT old_off, FT new_off,
-                           int )  const {
-      
-      FT new_dist = dist + (new_off*new_off - old_off*old_off);
-      return new_dist;
-    }
-    
-  inline FT transformed_distance(FT d) const {
-    return d*d;
-  }
-
-  inline FT inverse_of_transformed_distance(FT d) const {
-    return sqrt(d);
-  }
-  
-};
-*/
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-//typedef K::Equal_d Equal_d;
-//typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator;
-typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator;
-typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
-
-bool toric=false;
-
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , Point_Vector & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      Point_d p(point.begin(), point.end());
-      if (point.size() != 1)
-        points.push_back(p);
-    }
-  in_file.close();
-}
-
-void generate_points_grid(Point_Vector& W, int width, int D)
-{
-  int nb_points = 1;
-  for (int i = 0; i < D; ++i)
-    nb_points *= width;
-  for (int i = 0; i < nb_points; ++i)
-    {
-      std::vector<double> point;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          point.push_back((2.0/width)*(cell_i%width));
-          cell_i /= width;
-        }
-      W.push_back(point);
-    }
-}
-
-void generate_points_random_box(Point_Vector& W, int nbP, int dim)
-{
-  /*
-  Random_cube_iterator rp(dim, 1);
-  for (int i = 0; i < nbP; i++)
-    {
-      std::vector<double> point;
-      for (auto it = rp->cartesian_begin(); it != rp->cartesian_end(); ++it)
-        point.push_back(*it);
-      W.push_back(Point_d(point));
-      rp++;
-    }
-  */
-  Random_cube_iterator rp(dim, 1.0);
-  for (int i = 0; i < nbP; i++)
-    {
-      W.push_back(*rp++);
-    }
-}
-
-/* NOT TORUS RELATED
- */
-void generate_points_sphere(Point_Vector& W, int nbP, int dim)
-{
-  CGAL::Random_points_on_sphere_d<Point_d> rp(dim,1);
-  for (int i = 0; i < nbP; i++)
-    W.push_back(*rp++);
-}
-/*
-void read_points_to_tree (std::string file_name, Tree& tree)
-{
-  //I assume here that tree is empty
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-   while( getline ( in_file , line ) )
-    {
-      std::vector<double> coords;
-      std::istringstream iss( line );
-      while(iss >> x) { coords.push_back(x); }
-      if (coords.size() != 1)
-        {
-          Point_d point(coords.begin(), coords.end());
-          tree.insert(point);
-        }
-    }
-  in_file.close();
-}
-*/
-
-void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto l: w)
-        ofs << l << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-
-std::vector<Point_d> convert_to_torus(std::vector< Point_d>& points)
-{
-  std::vector< Point_d > points_torus;
-  for (auto p: points)
-    {
-      FT theta = M_PI*p[0];
-      FT phi = M_PI*p[1];
-      std::vector<FT> p_torus;
-      p_torus.push_back((1+0.2*cos(theta))*cos(phi));
-      p_torus.push_back((1+0.2*cos(theta))*sin(phi));
-      p_torus.push_back(0.2*sin(theta));
-      points_torus.push_back(Point_d(p_torus));
-    }
-  return points_torus;
-}
-
-void write_points_torus( std::string file_name, std::vector< Point_d > & points)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  std::vector<Point_d> points_torus = convert_to_torus(points);
-  for (auto w : points_torus)
-    {
-      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
-        ofs << *it << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void write_points( std::string file_name, std::vector< Point_d > & points)
-{
-  if (toric) write_points_torus(file_name, points);
-  else
-    {
-      std::ofstream ofs (file_name, std::ofstream::out);
-      for (auto w : points)
-        {
-          for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
-            ofs << *it << " ";
-          ofs << "\n";
-        }
-      ofs.close();
-    }
-}
-
-
-void write_edges_torus(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  Point_Vector l_torus = convert_to_torus(landmarks);
-  for (auto u: witness_complex.complex_vertex_range())
-    for (auto v: witness_complex.complex_vertex_range())
-      {
-        typeVectorVertex edge = {u,v};
-        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
-          {
-            for (auto it = l_torus[u].cartesian_begin(); it != l_torus[u].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n";
-            for (auto it = l_torus[v].cartesian_begin(); it != l_torus[v].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n\n\n";
-          }
-    }
-  ofs.close();
-}
-
-void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  if (toric) write_edges_torus(file_name, witness_complex, landmarks);
-  else
-    {
-      for (auto u: witness_complex.complex_vertex_range())
-        for (auto v: witness_complex.complex_vertex_range())
-          {
-            typeVectorVertex edge = {u,v};
-            if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
-              {
-                for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
-                  ofs << *it << " ";
-                ofs << "\n";
-                for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
-                  ofs << *it << " ";
-                ofs << "\n\n\n";
-              }
-          }
-      ofs.close();
-    }
-}
-
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  int chosen_landmark;
-  Point_d* p;
-  CGAL::Random rand;
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::find(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=landmarks_ind.end());
-      //rand++;
-      //std::cout << "Chose " << chosen_landmark << std::endl;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-
-/** \brief Choose landmarks on a body-central cubic system
- */
-void landmark_choice_bcc(Point_Vector &W, int nbP, int width, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  int D = W[0].size();
-  int nb_points = 1;
-  for (int i = 0; i < D; ++i)
-    nb_points *= width;
-  for (int i = 0; i < nb_points; ++i)
-    {
-      std::vector<double> point;
-      std::vector<double> cpoint;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          point.push_back(-1.0+(2.0/width)*(cell_i%width));
-          cpoint.push_back(-1.0+(2.0/width)*(cell_i%width)+(1.0/width));
-          cell_i /= width;
-        }
-      landmarks.push_back(point);
-      landmarks.push_back(cpoint);
-      landmarks_ind.push_back(2*i);
-      landmarks_ind.push_back(2*i+1);
-    }
-  std::cout << "The number of landmarks is: " << landmarks.size() << std::endl;
-}
-
-
-int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  //********************Preface: origin point
-  int D = W[0].size();
-  std::vector<FT> orig_vector;
-  for (int i=0; i<D; i++)
-    orig_vector.push_back(0);
-  Point_d origin(orig_vector);
-  //Distance dist;
-  //dist.transformed_distance(0,1);
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  int nbL = landmarks.size();
-  //Point_Vector landmarks_ = landmarks;
-  Euclidean_distance ed;
-  //Equal_d ed;
-  //Point_d p1(std::vector<FT>({0.8,0.8})), p2(std::vector<FT>({0.1,0.1}));
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-  //std::cout << "Lambda=" << lambda << std::endl;
-    //FT lambda = 0.1;//Euclidean_distance();
-  std::vector<Point_d> landmarks_ext;
-  int nb_cells = 1;
-  for (int i = 0; i < D; ++i)
-    nb_cells *= 3;
-  for (int i = 0; i < nb_cells; ++i)
-      for (int k = 0; k < nbL; ++k)
-        {
-          std::vector<double> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(landmarks[k][l] + 2.0*((cell_i%3)-1.0));
-              cell_i /= 3;
-            }
-          landmarks_ext.push_back(point);
-        }
-  write_points("landmarks/initial_landmarks",landmarks_ext);
-  STraits traits(&(landmarks_ext[0]));
-  std::vector< std::vector <int> > WL(nbP);
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nb_cells*nbL),
-         typename Tree::Splitter(),
-         traits);
-  /*Tree2 L2(boost::counting_iterator<std::ptrdiff_t>(0),
-           boost::counting_iterator<std::ptrdiff_t>(nbL),
-           typename Tree::Splitter(),
-           STraits(&(landmarks[0])));
-  */
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  //std::cout << "Size of the tree is " << L.size() << std::endl;
-  for (int i = 0; i < nbP; i++)
-    {
-      //std::cout << "Entered witness number " << i << std::endl;
-      Point_d& w = W[i];
-      //std::cout << "Safely constructed a point\n";
-      ////Search D+1 nearest neighbours from the tree of landmarks L
-      /*
-      if (w[0]>0.95)
-        std::cout << i << std::endl;
-      */
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               //CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])) );
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks_ext[0])) );
-      //std::cout << "Safely found nearest landmarks\n";
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          //Point_etiquette_map::iterator itm = L_i.find(it->first);
-          //assert(itm != L_i.end());
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          if (std::find(WL[i].begin(), WL[i].end(), (it->first)%nbL) == WL[i].end())
-            WL[i].push_back((it->first)%nbL);
-          //std::cout << "ITFIRST " << it->first << std::endl;
-          //std::cout << i << " " << it->first << ": " << it->second << std::endl; 
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          //std::cout << "'";
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-    }
-  //std::cout << "\n";
-  
-  std::string out_file = "wl_result";
-  write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  witnessComplex.witness_complex(WL);
-  /*
-  if (witnessComplex.is_witness_complex(WL))
-    std::cout << "!!YES. IT IS A WITNESS COMPLEX!!\n";
-  else
-    std::cout << "??NO. IT IS NOT A WITNESS COMPLEX??\n";    
-  */
-  //******************** Making a set of bad link landmarks
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  //std::cout << "Bad links around ";
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  for (auto u: witnessComplex.complex_vertex_range())
-    {
-      //std::cout << "Vertex " << u << " ";
-      if (!witnessComplex.has_good_link(u, count_bad, count_good))
-      {
-        //std::cout << "Landmark " << u << " start!" << std::endl;
-        //perturbL.insert(u);
-        count_badlinks++;
-        //std::cout << u << " ";
-        Point_d& l = landmarks[u];
-        Fuzzy_sphere fs(l, sqrt(lambda), 0, traits);
-        std::vector<int> curr_perturb;
-        L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs);
-        for (int i: curr_perturb)
-          perturbL.insert(i%nbL);
-        //L.search(std::inserter(perturbL,perturbL.begin()),fs);
-        //L.search(std::ostream_iterator<int>(std::cout,"\n"),fs);
-        //std::cout << "PerturbL size is " << perturbL.size() << std::endl;
-      }
-    }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  //std::cout << "landmark[0][0] before" << landmarks[0][0] << std::endl;
-  //*********************** Perturb bad link landmarks
-  
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/8);
-      //std::cout << landmarks[u] << std::endl;
-      
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          while (K().squared_distance_d_object()(*rp,origin) < lambda/256)
-            rp++;
-          //FT coord = W[landmarks_ind[u]][i] + (*rp)[i];
-          FT coord = landmarks[u][i] + (*rp)[i];
-          if (coord > 1)
-            point.push_back(coord-1);
-          else if (coord < -1)
-            point.push_back(coord+1);
-          else
-            point.push_back(coord);
-        }
-      landmarks[u] = Point_d(point);
-      //std::cout << landmarks[u] << std::endl;
-    }
-  
-  //std::cout << "landmark[0][0] after" << landmarks[0][0] << std::endl;
-  std::cout << "lambda=" << lambda << std::endl;
-
-  //std::cout << "WL size" << WL.size() << std::endl;
-  /*
-  std::cout << "L:" << std::endl;
-  for (int i = 0; i < landmarks.size(); i++)
-      std::cout << landmarks[i] << std::endl;
-  */
-  
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  /*
-  i = sprintf(buffer,"badlinks.txt");
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.write_bad_links(ofs);
-      ofs.close();
-    }
-  */
-  write_edges("landmarks/edges", witnessComplex, landmarks);
-  //std::cout << Distance().transformed_distance(Point_d(std::vector<double>({0.1,0.1})), Point_d(std::vector<double>({1.9,1.9}))) << std::endl;
-  return count_badlinks;
-}
-
-
-int main (int argc, char * const argv[])
-{
-  
-  if (argc != 4)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " nbP nbL dim\n";
-      return 0;
-    }
-  /*
-  boost::filesystem::path p;
-  for (; argc > 2; --argc, ++argv)
-    p /= argv[1];
-  */
-  
-  int nbP       = atoi(argv[1]);
-  int nbL       = atoi(argv[2]);
-  int dim       = atoi(argv[3]);
-  //clock_t start, end;
-  //Construct the Simplex Tree
-  //Witness_complex<> witnessComplex;
- 
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  //read_points_cust(file_name, point_vector);
-  //generate_points_random_box(point_vector, nbP, dim);
-  generate_points_grid(point_vector, (int)pow(nbP, 1.0/dim), dim);
-  //nbP = (int)(pow((int)pow(nbP, 1.0/dim), dim));
-  /*
-  for (auto &p: point_vector)
-    {
-      assert(std::count(point_vector.begin(),point_vector.end(),p) == 1);
-    }
-  */
-  //std::cout << "Successfully read the points\n";
-  //witnessComplex.setNbL(nbL);
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  //int nbP = point_vector.size();
-  //std::vector<std::vector< int > > WL(nbP);
-  //std::set<int> L;
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  //Point_etiquette_map L_i;
-  //start = clock();
-  //witnessComplex.landmark_choice_by_furthest_points(point_vector, point_vector.size(), WL);
-  bool ok=false;
-  while (!ok)
-    {
-      ok = true;
-      L = {};
-      chosen_landmarks = {};
-      landmark_choice(point_vector, nbP, nbL, L, chosen_landmarks);
-      
-      //int width = (int)pow(nbL, 1.0/dim); landmark_choice_bcc(point_vector, nbP, width, L, chosen_landmarks);
-      for (auto i: chosen_landmarks)
-        {
-          ok = ok && (std::count(chosen_landmarks.begin(),chosen_landmarks.end(),i) == 1);
-          if (!ok) break;
-        }
-      
-    }
-  int bl = nbL, curr_min = bl;
-  write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  for (int i = 0; i < 1; i++)
-    //for (int i = 0; bl > 0; i++)
-    {
-      std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n";
-      bl=landmark_perturbation(point_vector, L, chosen_landmarks);
-      if (bl < curr_min)
-        curr_min=bl;
-      write_points("landmarks/landmarks0",L);
-    }
-  //end = clock();
-  
-  /*
-  std::cout << "Landmark choice took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  */
-  
-  /*
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
-  std::ofstream ofs2(out_file, std::ofstream::out);
-  witnessComplex.write_bad_links(ofs2);
-  ofs2.close();
-  */
-}
diff --git a/src/Witness_complex/example/witness_complex_from_off.cpp b/src/Witness_complex/example/witness_complex_from_off.cpp
deleted file mode 100644
index 948f09a8..00000000
--- a/src/Witness_complex/example/witness_complex_from_off.cpp
+++ /dev/null
@@ -1,184 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <sys/types.h>
-#include <sys/stat.h>
-
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-
-using namespace Gudhi;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-typedef std::vector< std::vector <double> > Point_Vector;
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , std::vector< std::vector< double > > & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      if (point.size() != 1)
-        points.push_back(point);
-    }
-  in_file.close();
-}
-
-/**
- * \brief Rock age method of reading off file
- *
- */
-inline void
-off_reader_cust ( std::string file_name , std::vector< std::vector< double > > & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  // Line OFF. No need in it
-  if (!getline(in_file, line))
-    {
-      std::cerr << "No line OFF\n";
-      return;
-    }
-  // Line with 3 numbers. No need
-  if (!getline(in_file, line))
-    {
-      std::cerr << "No line with 3 numbers\n";
-      return;
-    }
-  // Reading points
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      points.push_back(point);
-    }
-  in_file.close();
-}
-
-int main (int argc, char * const argv[])
-{
-    if (argc != 3)
-      {
-          std::cerr << "Usage: " << argv[0]
-    << " path_to_point_file nbL \n";
-    return 0;
-  }
-  std::string file_name   = argv[1];
-  int nbL       = atoi(argv[2]);
-  
-  clock_t start, end;
-  //Construct the Simplex Tree
-  Witness_complex<> witnessComplex;
-
-  /*
-  std::cout << "Let the carnage begin!\n";
-  start = clock();
-  Point_Vector point_vector;
-  off_reader_cust(file_name, point_vector);
-  std::cout << "Successfully read the points\n";
-  witnessComplex.setNbL(nbL);
-  witnessComplex.witness_complex_from_points(point_vector);
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  char buffer[100];
-  int i = sprintf(buffer,"%s_%s_result.txt",argv[1],argv[2]);
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  */
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  off_reader_cust(file_name, point_vector);
-  //std::cout << "Successfully read the points\n";
-  witnessComplex.setNbL(nbL);
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  std::vector<std::vector< int > > WL;
-  std::set<int> L;
-  start = clock();
-  //witnessComplex.landmark_choice_by_furthest_points(point_vector, point_vector.size(), WL);
-  witnessComplex.landmark_choice_by_random_points(point_vector, point_vector.size(), L);
-  witnessComplex.nearest_landmarks(point_vector,L,WL);
-  end = clock();
-  std::cout << "Landmark choice took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  // Write the WL matrix in a file
-  mkdir("output", S_IRWXU);
-  const size_t last_slash_idx = file_name.find_last_of("/");
-  if (std::string::npos != last_slash_idx)
-    {
-      file_name.erase(0, last_slash_idx + 1);
-    }
-  std::string out_file = "output/"+file_name+"_"+argv[2]+".wl";
-  //write_wl(out_file,WL);
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
-  std::ofstream ofs2(out_file, std::ofstream::out);
-  witnessComplex.write_bad_links(ofs2);
-  ofs2.close();
-}
diff --git a/src/Witness_complex/example/witness_complex_from_wl_matrix.cpp b/src/Witness_complex/example/witness_complex_from_wl_matrix.cpp
deleted file mode 100644
index 614bb945..00000000
--- a/src/Witness_complex/example/witness_complex_from_wl_matrix.cpp
+++ /dev/null
@@ -1,148 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-//#include <boost/filesystem.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-typedef std::vector< std::vector <double> > Point_Vector;
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , std::vector< std::vector< double > > & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      if (point.size() != 1)
-        points.push_back(point);
-    }
-  in_file.close();
-}
-
-void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto l: w)
-        ofs << l << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void read_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  int x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< int > witness;
-      std::istringstream iss( line );
-      while(iss >> x) { witness.push_back(x); }
-      WL.push_back(witness);
-    }
-  in_file.close();
-
-}
-
-int main (int argc, char * const argv[])
-{
-  if (argc != 2)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " path_to_point_file \n";
-      return 0;
-    }
-  /*
-  boost::filesystem::path p;
-
-  for (; argc > 2; --argc, ++argv)
-    p /= argv[1];
-  */
-  std::string file_name   = argv[1];
-  //int nbL       = atoi(argv[2]);
-  
-  clock_t start, end;
-  //Construct the Simplex Tree
-  Witness_complex<> witnessComplex;
- 
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  read_points_cust(file_name, point_vector);
-  //std::cout << "Successfully read the points\n";
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  std::vector<std::vector< int > > WL;
-  read_wl(file_name,WL);
-  witnessComplex.setNbL(WL[0].size());
-  // Write the WL matrix in a file
-  std::string out_file;
-  write_wl(out_file,WL);
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-}
diff --git a/src/Witness_complex/example/witness_complex_knn_landmarks.cpp b/src/Witness_complex/example/witness_complex_knn_landmarks.cpp
deleted file mode 100644
index c45bc0c1..00000000
--- a/src/Witness_complex/example/witness_complex_knn_landmarks.cpp
+++ /dev/null
@@ -1,210 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-#include "generators.h"
-#include "output.h"
-//#include <boost/filesystem.hpp>
-
-//#include <CGAL/Delaunay_triangulation.h>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::FT FT;
-typedef K::Point_d Point_d;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-
-typedef std::vector<Point_d> Point_Vector;
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-void landmark_choice_to_tree(Point_Vector &W, int nbP, Point_etiquette_map &L_i, int nbL, std::vector< std::vector <int> > &WL)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  std::vector<Point_d> landmarks;
-  int chosen_landmark;
-  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
-  Point_d* p;
-  srand(24660);
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-          chosen_landmark = rand()%nbP;
-          p = &W[chosen_landmark];
-          //L_i.emplace(chosen_landmark,i);
-          //  }
-      landmarks.push_back(*p);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nbL),
-         typename Tree::Splitter(),
-         STraits((Point_d*)&(landmarks[0])));
-  /*}
-
-
-void d_nearest_landmarks(Point_Vector &W, Tree &L, Point_etiquette_map &L_i, std::vector< std::vector <int> > &WL)
-{*/
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  std::cout << "Size of the tree is " << L.size() << std::endl;
-//int nbP = W.size();
-  int D = W[0].size();
-  for (int i = 0; i < nbP; i++)
-    {
-      //std::cout << "Entered witness number " << i << std::endl;
-      Point_d& w = W[i];
-      //std::cout << "Safely constructed a point\n";
-      //Search D+1 nearest neighbours from the tree of landmarks L 
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,CGAL::Euclidean_distance<Traits_base>>((Point_d*)&(landmarks[0])) );
-      //std::cout << "Safely found nearest landmarks\n";
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          //Point_etiquette_map::iterator itm = L_i.find(it->first);
-          //assert(itm != L_i.end());
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          WL[i].push_back(it->first);
-          //std::cout << i << " " << it->first << ": " << it->second << std::endl; 
-        }
-    }
-}
-
-int main (int argc, char * const argv[])
-{
-  if (argc != 3)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " path_to_point_file nbL \n";
-      return 0;
-    }
-  /*
-  boost::filesystem::path p;
-
-  for (; argc > 2; --argc, ++argv)
-    p /= argv[1];
-  */
-  std::string file_name   = argv[1];
-  int nbL       = atoi(argv[2]);
-  
-  clock_t start, end;
-  //Construct the Simplex Tree
-  Witness_complex<> witnessComplex;
- 
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  read_points_cust(file_name, point_vector);
-  //std::cout << "Successfully read the points\n";
-  witnessComplex.setNbL(nbL);
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  int nbP = point_vector.size();
-  std::vector<std::vector< int > > WL(nbP);
-  //std::set<int> L;
-  Tree L;
-  Point_etiquette_map L_i;
-  start = clock();
-  //witnessComplex.landmark_choice_by_furthest_points(point_vector, point_vector.size(), WL);
-  landmark_choice_to_tree(point_vector, nbP, L_i, nbL, WL);
-  //d_nearest_landmarks(point_vector, L, L_i, WL);
-  end = clock();
-  std::cout << "Landmark choice took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  // Write the WL matrix in a file
-  mkdir("output", S_IRWXU);
-  const size_t last_slash_idx = file_name.find_last_of("/");
-  if (std::string::npos != last_slash_idx)
-    {
-      file_name.erase(0, last_slash_idx + 1);
-    }
-  std::string out_file = "output/"+file_name+"_"+argv[2]+".wl";
-  write_wl(out_file,WL);
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  /*
-  char buffer[100];
-  int i = sprintf(buffer,"%s_%s_result.txt",argv[1],argv[2]);
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  */
-
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
-  std::ofstream ofs2(out_file, std::ofstream::out);
-  //witnessComplex.write_bad_links(ofs2);
-  ofs2.close();
-}
diff --git a/src/Witness_complex/example/witness_complex_perturbations.cpp b/src/Witness_complex/example/witness_complex_perturbations.cpp
deleted file mode 100644
index f78bcdab..00000000
--- a/src/Witness_complex/example/witness_complex_perturbations.cpp
+++ /dev/null
@@ -1,462 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <set>
-#include <iterator>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-//#include <boost/filesystem.hpp> 
-
-//#include <CGAL/Delaunay_triangulation.h>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Origin.h>
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::FT FT;
-typedef K::Point_d Point_d;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-//typedef K::Equal_d Equal_d;
-typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , Point_Vector & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      Point_d p(point.begin(), point.end());
-      if (point.size() != 1)
-        points.push_back(p);
-    }
-  in_file.close();
-}
-
-/*
-void read_points_to_tree (std::string file_name, Tree& tree)
-{
-  //I assume here that tree is empty
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-   while( getline ( in_file , line ) )
-    {
-      std::vector<double> coords;
-      std::istringstream iss( line );
-      while(iss >> x) { coords.push_back(x); }
-      if (coords.size() != 1)
-        {
-          Point_d point(coords.begin(), coords.end());
-          tree.insert(point);
-        }
-    }
-  in_file.close();
-}
-*/
-
-void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto l: w)
-        ofs << l << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void write_points( std::string file_name, std::vector< Point_d > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
-        ofs << *it << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void write_edges_gnuplot(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto u: witness_complex.complex_vertex_range())
-    for (auto v: witness_complex.complex_vertex_range())
-      {
-        typeVectorVertex edge = {u,v};
-        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
-          {
-            for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n";
-            for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n\n\n";
-          }
-    }
-  ofs.close();
-}
-    
-
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-/*
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  //std::vector<Point_d> landmarks;
-  int chosen_landmark;
-  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
-  Point_d* p;
-  srand(24660);
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      chosen_landmark = rand()%nbP;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-*/
-
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  //std::vector<Point_d> landmarks;
-  int chosen_landmark = 0;
-  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
-  Point_d* p;
-  CGAL::Random rand;
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      do chosen_landmark = rand.uniform_int(0,nbP);
-      while (std::find(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark) != landmarks_ind.end());
-          //rand++;
-      //std::cout << "Chose " << chosen_landmark << std::endl;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-
-
-int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  int nbL = landmarks.size();
-  //Point_Vector landmarks_ = landmarks;
-  Euclidean_distance ed;
-  //Equal_d ed;
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-    //FT lambda = 0.1;//Euclidean_distance();
-  std::vector< std::vector <int> > WL(nbP);
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nbL),
-         typename Tree::Splitter(),
-         STraits(&(landmarks[0])));
-  /*Tree2 L2(boost::counting_iterator<std::ptrdiff_t>(0),
-           boost::counting_iterator<std::ptrdiff_t>(nbL),
-           typename Tree::Splitter(),
-           STraits(&(landmarks[0])));
-  */
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  //std::cout << "Size of the tree is " << L.size() << std::endl;
-  int D = W[0].size();
-  clock_t start, end;
-  start = clock();  
-  for (int i = 0; i < nbP; i++)
-    {
-      //std::cout << "Entered witness number " << i << std::endl;
-      Point_d& w = W[i];
-      //std::cout << "Safely constructed a point\n";
-      ////Search D+1 nearest neighbours from the tree of landmarks L 
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,CGAL::Euclidean_distance<Traits_base>>(&(landmarks[0])) );
-      //std::cout << "Safely found nearest landmarks\n";
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          //Point_etiquette_map::iterator itm = L_i.find(it->first);
-          //assert(itm != L_i.end());
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          WL[i].push_back(it->first);
-          //std::cout << "ITFIRST " << it->first << std::endl;
-          //std::cout << i << " " << it->first << ": " << it->second << std::endl; 
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          //std::cout << "'";
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-      //std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-      }
-  //std::cout << "\n";
-  end = clock();
-  std::cout << "WL matrix construction on " << nbL << " landmarks took " << (double)(end-start)/CLOCKS_PER_SEC << "s.\n";
-  
-
-  std::string out_file = "wl_result";
-  //write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  end = clock();
-  std::cout << "Witness complex construction on " << nbL << " landmarks took " << (double)(end-start)/CLOCKS_PER_SEC << "s.\n";
-  //******************** Making a set of bad link landmarks
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  //std::cout << "Bad links around ";
-  for (auto u: witnessComplex.complex_vertex_range())
-    if (!witnessComplex.has_good_link(u, count_bad, count_good))
-      {
-        //std::cout << "Landmark " << u << " start!" << std::endl;
-        //perturbL.insert(u);
-        count_badlinks++;
-        //std::cout << u << " ";
-        Point_d& l = landmarks[u];
-        Fuzzy_sphere fs(l, sqrt(lambda)*2, 0, STraits(&(landmarks[0])));
-        L.search(std::insert_iterator<std::set<int>>(perturbL,perturbL.begin()),fs);
-        //L.search(std::inserter(perturbL,perturbL.begin()),fs);
-        //L.search(std::ostream_iterator<int>(std::cout,"\n"),fs);
-        //std::cout << "PerturbL size is " << perturbL.size() << std::endl;
-      }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "Bad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  //std::cout << "landmark[0][0] before" << landmarks[0][0] << std::endl;
-  //*********************** Perturb bad link landmarks
-  
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/4);
-      //std::cout << landmarks[u] << std::endl;
-      
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          point.push_back(W[landmarks_ind[u]][i] + (*rp)[i]);
-        }
-      landmarks[u] = Point_d(point);
-      //std::cout << landmarks[u] << std::endl;
-    }
-  
-  //std::cout << "landmark[0][0] after" << landmarks[0][0] << std::endl;
-  std::cout << "lambda=" << lambda << std::endl;
-  // Write the WL matrix in a file
- 
-  /*
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  */
-  //witnessComplex.write_badlinks("badlinks");
-  //write_edges_gnuplot("landmarks/edges", witnessComplex, landmarks);
-  return count_badlinks;
-}
-
-
-int main (int argc, char * const argv[])
-{
-  if (argc != 3)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " path_to_point_file nbL \n";
-      return 0;
-    }
-  /*
-  boost::filesystem::path p;
-
-  for (; argc > 2; --argc, ++argv)
-    p /= argv[1];
-  */
-  std::string file_name   = argv[1];
-  int nbL       = atoi(argv[2]);
-  
-  //clock_t start, end;
-  //Construct the Simplex Tree
-  //Witness_complex<> witnessComplex;
- 
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  read_points_cust(file_name, point_vector);
-  //std::cout << "Successfully read the points\n";
-  //witnessComplex.setNbL(nbL);
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  int nbP = point_vector.size();
-  //std::vector<std::vector< int > > WL(nbP);
-  //std::set<int> L;
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  //Point_etiquette_map L_i;
-  //start = clock();
-  //witnessComplex.landmark_choice_by_furthest_points(point_vector, point_vector.size(), WL);
-  landmark_choice(point_vector, nbP, nbL, L, chosen_landmarks);
-  int bl = 1;
-
-  mkdir("landmarks", S_IRWXU);
-  const size_t last_slash_idx = file_name.find_last_of("/");
-  if (std::string::npos != last_slash_idx)
-    {
-      file_name.erase(0, last_slash_idx + 1);
-    }
-  write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  //for (int i = 0; bl != 0; i++)
-  for (int i = 0; i < 1; i++)
-    {
-      std::cout << "========== Start iteration " << i << " ========\n";
-      bl = landmark_perturbation(point_vector, L, chosen_landmarks);
-      std::ostringstream os(std::ostringstream::ate);;
-      os << "landmarks/landmarks0";
-      write_points(os.str(),L);
-    }
-  //end = clock();
-  
-  /*
-  std::cout << "Landmark choice took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  */
-  
-  /*
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
-  std::ofstream ofs2(out_file, std::ofstream::out);
-  witnessComplex.write_bad_links(ofs2);
-  ofs2.close();
-  */
-}
diff --git a/src/Witness_complex/example/witness_complex_protected_delaunay.cpp b/src/Witness_complex/example/witness_complex_protected_delaunay.cpp
deleted file mode 100644
index 77a167a5..00000000
--- a/src/Witness_complex/example/witness_complex_protected_delaunay.cpp
+++ /dev/null
@@ -1,604 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <algorithm>
-#include <set>
-#include <iterator>
-#include <chrono>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-#include "Torus_distance.h" 
-
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-#include <CGAL/Kernel_d/Sphere_d.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Random.h>
-#include <CGAL/Delaunay_triangulation.h>
-
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::Point_d Point_d;
-//typedef CGAL::Cartesian_d<double> K;
-//typedef CGAL::Point_d<K> Point_d;
-typedef K::FT FT;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-//typedef K::Equal_d Equal_d;
-//typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator;
-typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator;
-typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
-
-typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
-typedef Delaunay_triangulation::Facet Facet;
-typedef CGAL::Sphere_d<K> Sphere_d;
-
-bool toric=false;
-
-
-/**
- * \brief Customized version of read_points
- * which takes into account a possible nbP first line
- *
- */
-inline void
-read_points_cust ( std::string file_name , Point_Vector & points)
-{  
-  std::ifstream in_file (file_name.c_str(),std::ios::in);
-  if(!in_file.is_open())
-    {
-      std::cerr << "Unable to open file " << file_name << std::endl;
-      return;
-    }
-  std::string line;
-  double x;
-  while( getline ( in_file , line ) )
-    {
-      std::vector< double > point;
-      std::istringstream iss( line );
-      while(iss >> x) { point.push_back(x); }
-      Point_d p(point.begin(), point.end());
-      if (point.size() != 1)
-        points.push_back(p);
-    }
-  in_file.close();
-}
-
-void generate_points_grid(Point_Vector& W, int width, int D)
-{
-  int nb_points = 1;
-  for (int i = 0; i < D; ++i)
-    nb_points *= width;
-  for (int i = 0; i < nb_points; ++i)
-    {
-      std::vector<double> point;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-          point.push_back(0.01*(cell_i%width));
-          cell_i /= width;
-        }
-      W.push_back(point);
-    }
-}
-
-void generate_points_random_box(Point_Vector& W, int nbP, int dim)
-{
-  /*
-  Random_cube_iterator rp(dim, 1);
-  for (int i = 0; i < nbP; i++)
-    {
-      std::vector<double> point;
-      for (auto it = rp->cartesian_begin(); it != rp->cartesian_end(); ++it)
-        point.push_back(*it);
-      W.push_back(Point_d(point));
-      rp++;
-    }
-  */
-  Random_cube_iterator rp(dim, 1.0);
-  for (int i = 0; i < nbP; i++)
-    {
-      W.push_back(*rp++);
-    }
-}
-
-
-void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : WL)
-    {
-      for (auto l: w)
-        ofs << l << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-
-void write_points( std::string file_name, std::vector< Point_d > & points)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto w : points)
-    {
-      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
-        ofs << *it << " ";
-      ofs << "\n";
-    }
-  ofs.close();
-}
-
-void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
-{
-  std::ofstream ofs (file_name, std::ofstream::out);
-  for (auto u: witness_complex.complex_vertex_range())
-    for (auto v: witness_complex.complex_vertex_range())
-      {
-        typeVectorVertex edge = {u,v};
-        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
-          {
-            for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n";
-            for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
-              ofs << *it << " ";
-            ofs << "\n\n\n";
-          }
-      }
-  ofs.close();
-}
-
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  int chosen_landmark;
-  Point_d* p;
-  CGAL::Random rand;
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::count(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=0);
-      //rand++;
-      //std::cout << "Chose " << chosen_landmark << std::endl;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-
-void insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count)
-{
-  int D = W[0].size();
-  int nb_cells = pow(3, D);
-  for (int i = 0; i < nb_cells; ++i)
-    {
-      std::vector<FT> point;
-      int cell_i = i;
-      for (int l = 0; l < D; ++l)
-        {
-                point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1));
-                cell_i /= 3;
-        }
-      delaunay.insert(point);
-    }
-  landmarks_ind.push_back(chosen_landmark);
-  landmark_count++;
-}
-
-
-
-
-////////////////////////////////////////////////////////////////////////
-// OLD CODE VVVVVVVV
-////////////////////////////////////////////////////////////////////////
-
-
-/*
-bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta)
-{
-  Euclidean_distance ed;
-  Delaunay_triangulation::Vertex_handle v;
-  Delaunay_triangulation::Face f(t.current_dimension()); 
-  Delaunay_triangulation::Facet ft; 
-  Delaunay_triangulation::Full_cell_handle c; 
-  Delaunay_triangulation::Locate_type lt;
-  c = t.locate(p, lt, f, ft, v);
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    if (!t.is_infinite(fc_it))
-      {
-        std::vector<Point_d> vertices;
-        for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it)
-          vertices.push_back((*v_it)->point());
-        Sphere_d cs(D, vertices.begin(), vertices.end());
-        Point_d center_cs = cs.center();
-        FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(1)->point()));
-        FT dist2 = ed.transformed_distance(center_cs, p);
-        //if the new point is inside the protection ball of a non conflicting simplex
-        if (dist2 >= r*r && dist2 <= (r+delta)*(r+delta)) 
-          return true;
-      }
-  return false;
-}
-
-bool triangulation_is_protected(Delaunay_triangulation& t, FT delta)
-{
-  Euclidean_distance ed;
-  int D = t.current_dimension();
-  for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
-    if (!t.is_infinite(fc_it))
-      for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
-        {
-          //check if vertex belongs to the face
-          bool belongs = false;
-          for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-            if (v_it == *fc_v_it)
-              {
-                belongs = true;
-                break;
-              }
-          if (!belongs)
-            {
-              std::vector<Point_d> vertices;
-              for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it)
-                vertices.push_back((*fc_v_it)->point());
-              Sphere_d cs(D, vertices.begin(), vertices.end());
-              Point_d center_cs = cs.center();
-              FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(1)->point()));
-              FT dist2 = ed.transformed_distance(center_cs, v_it->point());
-              //if the new point is inside the protection ball of a non conflicting simplex
-              if (dist2 <= (r+delta)*(r+delta)) 
-                return false;
-            }
-        }
-  return true;
-}
-
-void fill_landmark_copies(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  int D = W[0].size();
-  int nb_cells = pow(3, D);
-  int nbL = landmarks_ind.size();
-  // Fill landmarks
-  for (int i = 0; i < nb_cells-1; ++i)
-    for (int j = 0; j < nbL; ++j)
-      {
-        int cell_i = i;
-        Point_d point;
-        for (int l = 0; l < D; ++l)
-          {
-            point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1));
-            cell_i /= 3;
-          }
-        landmarks.push_back(point);
-      }
-}
-
-void landmark_choice_by_delaunay(Point_Vector& W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT delta)
-{
-  int D = W[0].size();
-  Delaunay_triangulation t(D);
-  CGAL::Random rand;
-  int chosen_landmark;
-  int landmark_count = 0;
-  for (int i = 0; i <= D+1; ++i)
-    {
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::count(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=0);
-      insert_delaunay_landmark_with_copies(W, chosen_landmark, landmarks_ind, t, landmark_count);
-    }
-  while (landmark_count < nbL)
-    {      
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::count(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=0);      
-      // If no conflicts then insert in every copy of T^3
-      if (!is_violating_protection(W[chosen_landmark], t, D, delta))
-        insert_delaunay_landmark_with_copies(W, chosen_landmark, landmarks_ind, t, landmark_count);
-    }
-  fill_landmark_copies(W, landmarks, landmarks_ind);
-}
-
-
-void landmark_choice_protected_delaunay(Point_Vector& W, int nbP, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT delta)
-{
-  int D = W[0].size();
-  Torus_distance td;
-  Euclidean_distance ed;
-  Delaunay_triangulation t(D);
-  CGAL::Random rand;
-  int landmark_count = 0;
-  std::list<int> index_list;
-  //      shuffle the list of indexes (via a vector)
-  {
-    std::vector<int> temp_vector;
-    for (int i = 0; i < nbP; ++i)
-      temp_vector.push_back(i);
-    unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
-    std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed));
-    for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it)
-      index_list.push_front(*it);
-  }
-  //      add the first D+1 vertices to form one non-empty cell 
-  for (int i = 0; i <= D+1; ++i)
-    {
-      insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count);
-      index_list.pop_front();
-    }
-  //      add other vertices if they don't violate protection
-  std::list<int>::iterator list_it = index_list.begin();
-  while (list_it != index_list.end())
-    if (!is_violating_protection(W[*list_it], t, D, delta))
-      {
-          // If no conflicts then insert in every copy of T^3      
-          insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count);
-          index_list.erase(list_it);
-          list_it = index_list.begin();
-        }
-    else
-      list_it++;
-  fill_landmark_copies(W, landmarks, landmarks_ind);
-}
-
-
-int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  //******************** Preface: origin point
-  int D = W[0].size();
-  std::vector<FT> orig_vector;
-  for (int i=0; i<D; i++)
-    orig_vector.push_back(0);
-  Point_d origin(orig_vector);
-
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  Euclidean_distance ed;
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-  std::vector<Point_d> landmarks_ext;
-  int nb_cells = 1;
-  for (int i = 0; i < D; ++i)
-    nb_cells *= 3;
-  for (int i = 0; i < nb_cells; ++i)
-      for (int k = 0; k < nbL; ++k)
-        {
-          std::vector<double> point;
-          int cell_i = i;
-          for (int l = 0; l < D; ++l)
-            {
-              point.push_back(landmarks[k][l] + 2.0*((cell_i%3)-1.0));
-              cell_i /= 3;
-            }
-          landmarks_ext.push_back(point);
-        }
-  write_points("landmarks/initial_landmarks",landmarks_ext);
-  STraits traits(&(landmarks_ext[0]));
-  std::vector< std::vector <int> > WL(nbP);
-
-  //********************** Neighbor search in a Kd tree
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nb_cells*nbL),
-         typename Tree::Splitter(),
-         traits);
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  for (int i = 0; i < nbP; i++)
-    {
-      Point_d& w = W[i];
-      ////Search D+1 nearest neighbours from the tree of landmarks L
-      K_neighbor_search search(L, w, D+1, FT(0), true,
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks_ext[0])) );
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          if (std::find(WL[i].begin(), WL[i].end(), (it->first)%nbL) == WL[i].end())
-            WL[i].push_back((it->first)%nbL);
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-    }
-  std::string out_file = "wl_result";
-  write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  witnessComplex.witness_complex(WL);
-
-  //******************** Making a set of bad link landmarks
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  //std::cout << "Bad links around ";
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  for (auto u: witnessComplex.complex_vertex_range())
-    {
-       if (!witnessComplex.has_good_link(u, count_bad, count_good))
-         {
-           count_badlinks++;
-           Point_d& l = landmarks[u];
-           Fuzzy_sphere fs(l, sqrt(lambda)*3, 0, traits);
-           std::vector<int> curr_perturb;
-           L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs);
-           for (int i: curr_perturb)
-             perturbL.insert(i%nbL);
-       }
-    }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  
-  //*********************** Perturb bad link landmarks  
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/8);
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          while (K().squared_distance_d_object()(*rp,origin) < lambda/256)
-            rp++;
-          FT coord = landmarks[u][i] + (*rp)[i];
-          if (coord > 1)
-            point.push_back(coord-1);
-          else if (coord < -1)
-            point.push_back(coord+1);
-          else
-            point.push_back(coord);
-        }
-      landmarks[u] = Point_d(point);
-    }
-  std::cout << "lambda=" << lambda << std::endl;
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  write_edges("landmarks/edges", witnessComplex, landmarks);
-  return count_badlinks;
-}
-
-
-int main (int argc, char * const argv[])
-{
-  if (argc != 5)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " nbP nbL dim delta\n";
-      return 0;
-    }
-  int nbP       = atoi(argv[1]);
-  int nbL       = atoi(argv[2]);
-  int dim       = atoi(argv[3]);
-  FT delta      = atof(argv[4]);
-  
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  generate_points_random_box(point_vector, nbP, dim);
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  bool ok=false;
-  while (!ok)
-    {
-      ok = true;
-      L = {};
-      chosen_landmarks = {};
-      //landmark_choice_by_delaunay(point_vector, nbP, nbL, L, chosen_landmarks, delta);
-      landmark_choice_protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta);
-      nbL = chosen_landmarks.size();
-      std::cout << "Number of landmarks is " << nbL << std::endl;
-      //int width = (int)pow(nbL, 1.0/dim); landmark_choice_bcc(point_vector, nbP, width, L, chosen_landmarks);
-      for (auto i: chosen_landmarks)
-        {
-          ok = ok && (std::count(chosen_landmarks.begin(),chosen_landmarks.end(),i) == 1);
-          if (!ok) break;
-        }
-      
-    }
-  int bl = nbL, curr_min = bl;
-  write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  //for (int i = 0; i < 1; i++)
-  for (int i = 0; bl > 0; i++)
-    {
-      std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n";
-      bl=landmark_perturbation(point_vector, nbL, L, chosen_landmarks);
-      if (bl < curr_min)
-        curr_min=bl;
-      write_points("landmarks/landmarks0",L);
-    }
-  
-}
-*/
diff --git a/src/Witness_complex/example/witness_complex_sphere.cpp b/src/Witness_complex/example/witness_complex_sphere.cpp
deleted file mode 100644
index bf3015fa..00000000
--- a/src/Witness_complex/example/witness_complex_sphere.cpp
+++ /dev/null
@@ -1,457 +0,0 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
- *    Author(s):       Siargey Kachanovich
- *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
- *
- *    This program is free software: you can redistribute it and/or modify
- *    it under the terms of the GNU General Public License as published by
- *    the Free Software Foundation, either version 3 of the License, or
- *    (at your option) any later version.
- *
- *    This program is distributed in the hope that it will be useful,
- *    but WITHOUT ANY WARRANTY; without even the implied warranty of
- *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *    GNU General Public License for more details.
- *
- *    You should have received a copy of the GNU General Public License
- *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
- */
-
-#include <iostream>
-#include <fstream>
-#include <ctime>
-#include <utility>
-#include <algorithm>
-#include <set>
-#include <iterator>
-
-#include <sys/types.h>
-#include <sys/stat.h>
-//#include <stdlib.h>
-
-//#include "gudhi/graph_simplicial_complex.h"
-#include "gudhi/Witness_complex.h"
-#include "gudhi/reader_utils.h"
-#include "generators.h"
-#include "output.h"
-//#include <boost/filesystem.hpp> 
-
-//#include <CGAL/Delaunay_triangulation.h>
-#include <CGAL/Cartesian_d.h>
-#include <CGAL/Search_traits.h>
-#include <CGAL/Search_traits_adapter.h>
-#include <CGAL/property_map.h>
-#include <CGAL/Epick_d.h>
-#include <CGAL/Orthogonal_k_neighbor_search.h>
-#include <CGAL/Kd_tree.h>
-#include <CGAL/Euclidean_distance.h>
-
-#include <CGAL/Kernel_d/Vector_d.h>
-#include <CGAL/point_generators_d.h>
-#include <CGAL/constructions_d.h>
-#include <CGAL/Fuzzy_sphere.h>
-#include <CGAL/Random.h>
-
-
-#include <boost/tuple/tuple.hpp>
-#include <boost/iterator/zip_iterator.hpp>
-#include <boost/iterator/counting_iterator.hpp>
-#include <boost/range/iterator_range.hpp>
-
-using namespace Gudhi;
-//using namespace boost::filesystem;
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef K::FT FT;
-typedef K::Point_d Point_d;
-typedef CGAL::Search_traits<
-  FT, Point_d,
-  typename K::Cartesian_const_iterator_d,
-  typename K::Construct_cartesian_const_iterator_d> Traits_base;
-typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
-//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
-
-typedef CGAL::Search_traits_adapter<
-  std::ptrdiff_t, Point_d*, Traits_base> STraits;
-//typedef K TreeTraits;
-//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
-//typedef CGAL::Kd_tree<STraits> Kd_tree;
-typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search;
-typedef K_neighbor_search::Tree Tree;
-typedef K_neighbor_search::Distance Distance;
-typedef K_neighbor_search::iterator KNS_iterator;
-typedef K_neighbor_search::iterator KNS_range;
-typedef boost::container::flat_map<int, int> Point_etiquette_map;
-typedef CGAL::Kd_tree<STraits> Tree2;
-
-typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
-
-typedef std::vector<Point_d> Point_Vector;
-
-//typedef K::Equal_d Equal_d;
-
-bool toric=false;
-
-std::vector<Point_d> convert_to_torus(std::vector< Point_d>& points)
-{
-  std::vector< Point_d > points_torus;
-  for (auto p: points)
-    {
-      FT theta = M_PI*p[0];
-      FT phi = M_PI*p[1];
-      std::vector<FT> p_torus;
-      p_torus.push_back((1+0.2*cos(theta))*cos(phi));
-      p_torus.push_back((1+0.2*cos(theta))*sin(phi));
-      p_torus.push_back(0.2*sin(theta));
-      points_torus.push_back(Point_d(p_torus));
-    }
-  return points_torus;
-}
-
-/** Function that chooses landmarks from W and place it in the kd-tree L.
- *  Note: nbL hould be removed if the code moves to Witness_complex
- */
-void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  std::cout << "Enter landmark choice to kd tree\n";
-  //std::vector<Point_d> landmarks;
-  int chosen_landmark;
-  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
-  Point_d* p;
-  CGAL::Random rand;
-  for (int i = 0; i < nbL; i++)
-    {
-      //      while (!res.second)
-      //  {
-      do chosen_landmark = rand.get_int(0,nbP);
-      while (std::find(landmarks_ind.begin(), landmarks_ind.end(), chosen_landmark) != landmarks_ind.end());
-      //rand++;
-      //std::cout << "Chose " << chosen_landmark << std::endl;
-      p = &W[chosen_landmark];
-      //L_i.emplace(chosen_landmark,i);
-      //  }
-      landmarks.push_back(*p);
-      landmarks_ind.push_back(chosen_landmark);
-      //std::cout << "Added landmark " << chosen_landmark << std::endl;
-    }
- }
-
-/** \brief A test with 600cell, the generalisation of icosaedre in 4d
- */
-void landmark_choice_600cell(Point_Vector&W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  assert(W[0].size() == 4); //4-dimensionality required
-  FT phi = (1+sqrt(5))/2;
-  FT phi_1 = FT(1)/phi;
-  std::vector<FT> p;
-  // 16 vertices
-  for (FT a = -0.5; a < 1; a += 1)
-    for (FT b = -0.5; b < 1; b += 1)
-      for (FT c = -0.5; c < 1; c += 1)
-        for (FT d = -0.5; d < 1; d += 1)
-          landmarks.push_back(Point_d(std::vector<FT>({a,b,c,d})));
-  // 8 vertices
-  for (FT a = -0.5; a < 1; a += 1)
-    {
-      landmarks.push_back(Point_d(std::vector<FT>({a,0,0,0})));
-      landmarks.push_back(Point_d(std::vector<FT>({0,a,0,0})));
-      landmarks.push_back(Point_d(std::vector<FT>({0,0,a,0})));
-      landmarks.push_back(Point_d(std::vector<FT>({0,0,0,a})));
-    }
-  // 96 vertices
-  for (FT a = -phi/2; a < phi; a += phi)
-    for (FT b = -0.5; b < 1; b += 1)
-      for (FT c = -phi_1/2; c < phi_1; c += phi_1)
-        {
-          landmarks.push_back(Point_d(std::vector<FT>({a,b,c,0})));
-          landmarks.push_back(Point_d(std::vector<FT>({b,a,0,c})));
-          landmarks.push_back(Point_d(std::vector<FT>({c,0,a,b})));
-          landmarks.push_back(Point_d(std::vector<FT>({0,c,b,a})));
-          landmarks.push_back(Point_d(std::vector<FT>({a,c,0,b})));
-          landmarks.push_back(Point_d(std::vector<FT>({a,0,b,c})));
-          landmarks.push_back(Point_d(std::vector<FT>({c,b,0,a})));
-          landmarks.push_back(Point_d(std::vector<FT>({0,b,a,c})));
-          landmarks.push_back(Point_d(std::vector<FT>({b,0,c,a})));
-          landmarks.push_back(Point_d(std::vector<FT>({0,a,c,b})));
-          landmarks.push_back(Point_d(std::vector<FT>({b,c,a,0})));
-          landmarks.push_back(Point_d(std::vector<FT>({c,a,b,0})));
-        }
-  for (int i = 0; i < 120; ++i)
-    landmarks_ind.push_back(i);
-}
-
-int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
-{
-  //********************Preface: origin point
-  clock_t start, end;
-  int D = W[0].size();
-  std::vector<FT> orig_vector;
-  for (int i=0; i<D; i++)
-    orig_vector.push_back(0);
-  Point_d origin(orig_vector);
-  //Distance dist;
-  //dist.transformed_distance(0,1);
-  //******************** Constructing a WL matrix
-  int nbP = W.size();
-  int nbL = landmarks.size();
-  Euclidean_distance ed;
-  FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]);
-  //std::cout << "Lambda=" << lambda << std::endl;
-    //FT lambda = 0.1;//Euclidean_distance();
-  STraits traits(&(landmarks[0]));
-  std::vector< std::vector <int> > WL(nbP);
-  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
-         boost::counting_iterator<std::ptrdiff_t>(nbL),
-         typename Tree::Splitter(),
-         traits);
-  /*Tree2 L2(boost::counting_iterator<std::ptrdiff_t>(0),
-           boost::counting_iterator<std::ptrdiff_t>(nbL),
-           typename Tree::Splitter(),
-           STraits(&(landmarks[0])));
-  */
-  std::cout << "Enter (D+1) nearest landmarks\n";
-  //std::cout << "Size of the tree is " << L.size() << std::endl;
-  start = clock();
-  for (int i = 0; i < nbP; i++)
-    {
-      //std::cout << "Entered witness number " << i << std::endl;
-      Point_d& w = W[i];
-      //std::cout << "Safely constructed a point\n";
-      ////Search D+1 nearest neighbours from the tree of landmarks L
-      /*
-      if (w[0]>0.95)
-        std::cout << i << std::endl;
-      */
-      K_neighbor_search search(L, w, D, FT(0), true,
-                               //CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])) );
-                               CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])) );
-      //std::cout << "Safely found nearest landmarks\n";
-      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
-        {
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          //Point_etiquette_map::iterator itm = L_i.find(it->first);
-          //assert(itm != L_i.end());
-          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
-          WL[i].push_back(it->first);
-          //std::cout << "ITFIRST " << it->first << std::endl;
-          //std::cout << i << " " << it->first << ": " << it->second << std::endl; 
-        }
-      if (i == landmarks_ind[WL[i][0]])
-        {
-          //std::cout << "'";
-          FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]);
-          if (dist < lambda)
-            lambda = dist;
-        }
-    }
-  //std::cout << "\n";
-  end = clock();
-  std::cout << "Landmark choice for " << nbL << " landmarks took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  std::string out_file = "wl_result";
-  write_wl(out_file,WL);
-  
-  //******************** Constructng a witness complex
-  std::cout << "Entered witness complex construction\n";
-  Witness_complex<> witnessComplex;
-  witnessComplex.setNbL(nbL);
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  //witnessComplex.witness_complex(WL);
-  /*
-  if (witnessComplex.is_witness_complex(WL))
-    std::cout << "!!YES. IT IS A WITNESS COMPLEX!!\n";
-  else
-    std::cout << "??NO. IT IS NOT A WITNESS COMPLEX??\n";   
-  */ 
-  //******************** Making a set of bad link landmarks
-  std::cout << "Entered bad links\n";
-  std::set< int > perturbL;
-  int count_badlinks = 0;
-  //std::cout << "Bad links around ";
-  std::vector< int > count_bad(D);
-  std::vector< int > count_good(D);
-  for (auto u: witnessComplex.complex_vertex_range())
-    if (!witnessComplex.has_good_link(u, count_bad, count_good))
-      {
-        //std::cout << "Landmark " << u << " start!" << std::endl;
-        //perturbL.insert(u);
-        count_badlinks++;
-        //std::cout << u << " ";
-        Point_d& l = landmarks[u];
-        Fuzzy_sphere fs(l, sqrt(lambda), 0, traits);
-        std::vector<int> curr_perturb;
-        L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs);
-        for (int i: curr_perturb)
-          perturbL.insert(i%nbL);
-        //L.search(std::inserter(perturbL,perturbL.begin()),fs);
-        //L.search(std::ostream_iterator<int>(std::cout,"\n"),fs);
-        //std::cout << "PerturbL size is " << perturbL.size() << std::endl;
-      }
-  for (unsigned int i = 0; i != count_good.size(); i++)
-    if (count_good[i] != 0)
-      std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl;
-  for (unsigned int i = 0; i != count_bad.size(); i++)
-    if (count_bad[i] != 0)
-      std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl;
-  std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl;
-  //std::cout << "landmark[0][0] before" << landmarks[0][0] << std::endl;
-  //*********************** Perturb bad link landmarks
-  
-  for (auto u: perturbL)
-    {
-      Random_point_iterator rp(D,sqrt(lambda)/8*nbL/count_badlinks);
-      //std::cout << landmarks[u] << std::endl;
-      
-      std::vector<FT> point;
-      for (int i = 0; i < D; i++)
-        {
-          while (K().squared_distance_d_object()(*rp,origin) < lambda/256)
-            rp++;
-          FT coord = W[landmarks_ind[u]][i] + (*rp)[i];
-          //FT coord = landmarks[u][i] + (*rp)[i];
-          if (coord > 1)
-            point.push_back(coord-1);
-          else if (coord < -1)
-            point.push_back(coord+1);
-          else
-            point.push_back(coord);
-        }
-      landmarks[u] = Point_d(point);
-      //std::cout << landmarks[u] << std::endl;
-    }
-  
-  //std::cout << "landmark[0][0] after" << landmarks[0][0] << std::endl;
-  std::cout << "lambda=" << lambda << std::endl;
-
-  //std::cout << "WL size" << WL.size() << std::endl;
-  /*
-  std::cout << "L:" << std::endl;
-  for (int i = 0; i < landmarks.size(); i++)
-      std::cout << landmarks[i] << std::endl;
-  */
-  
-  char buffer[100];
-  int i = sprintf(buffer,"stree_result.txt");
-  
-  if (i >= 0)
-    {
-      std::string out_file = (std::string)buffer;
-      std::ofstream ofs (out_file, std::ofstream::out);
-      witnessComplex.st_to_file(ofs);
-      ofs.close();
-    }
-  write_edges("landmarks/edges", witnessComplex, landmarks);
-  std::cout << Distance().transformed_distance(Point_d(std::vector<double>({0.1,0.1})), Point_d(std::vector<double>({1.9,1.9}))) << std::endl;
-  return count_badlinks;
-}
-
-
-int main (int argc, char * const argv[])
-{
-  
-  if (argc != 4)
-    {
-      std::cerr << "Usage: " << argv[0]
-                << " nbP nbL dim\n";
-      return 0;
-    }
-  /*
-  boost::filesystem::path p;
-  for (; argc > 2; --argc, ++argv)
-    p /= argv[1];
-  */
-  
-  int nbP       = atoi(argv[1]);
-  int nbL       = atoi(argv[2]);
-  int dim       = atoi(argv[3]);
-  //clock_t start, end;
-  //Construct the Simplex Tree
-  //Witness_complex<> witnessComplex;
- 
-  std::cout << "Let the carnage begin!\n";
-  Point_Vector point_vector;
-  //read_points_cust(file_name, point_vector);
-  generate_points_sphere(point_vector, nbP, dim);
-  /*
-  for (auto &p: point_vector)
-    {
-      assert(std::count(point_vector.begin(),point_vector.end(),p) == 1);
-    }
-  */
-  //std::cout << "Successfully read the points\n";
-  //witnessComplex.setNbL(nbL);
-  //  witnessComplex.witness_complex_from_points(point_vector);
-  //int nbP = point_vector.size();
-  //std::vector<std::vector< int > > WL(nbP);
-  //std::set<int> L;
-  Point_Vector L;
-  std::vector<int> chosen_landmarks;
-  //Point_etiquette_map L_i;
-  //start = clock();
-  //witnessComplex.landmark_choice_by_furthest_points(point_vector, point_vector.size(), WL);
-  bool ok=false;
-  while (!ok)
-    {
-      ok = true;
-      L = {};
-      chosen_landmarks = {};
-      landmark_choice(point_vector, nbP, nbL, L, chosen_landmarks);
-      //landmark_choice_600cell(point_vector, nbP, nbL, L, chosen_landmarks);
-      /*
-      for (auto i: chosen_landmarks)
-        {
-          ok = ok && (std::count(chosen_landmarks.begin(),chosen_landmarks.end(),i) == 1);
-          if (!ok) break;
-        }
-      */
-    }
-  int bl = nbL, curr_min = bl;
-  //write_points("landmarks/initial_pointset",point_vector);
-  //write_points("landmarks/initial_landmarks",L);
-  
-  for (int i = 0; bl > 0; i++)
-    //for (int i = 0; i < 1; i++)
-    {
-      std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n";
-      bl=landmark_perturbation(point_vector, L, chosen_landmarks);
-      if (bl < curr_min)
-        curr_min=bl;
-      //write_points("landmarks/landmarks0",L);
-    }
-  //end = clock();
-  
-  /*
-  std::cout << "Landmark choice took "
-            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  start = clock();
-  witnessComplex.witness_complex(WL);
-  //
-  end = clock();
-  std::cout << "Howdy world! The process took "
-       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
-  */
-  
-  /*
-  out_file = "output/"+file_name+"_"+argv[2]+".stree";
-  std::ofstream ofs (out_file, std::ofstream::out);
-  witnessComplex.st_to_file(ofs);
-  ofs.close();
-
-  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
-  std::ofstream ofs2(out_file, std::ofstream::out);
-  witnessComplex.write_bad_links(ofs2);
-  ofs2.close();
-  */
-}