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diff --git a/example/Cech_complex/cech_complex_step_by_step.cpp b/example/Cech_complex/cech_complex_step_by_step.cpp
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+++ b/example/Cech_complex/cech_complex_step_by_step.cpp
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+/*    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):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2018 Inria
+ *
+ *    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 <gudhi/graph_simplicial_complex.h>
+#include <gudhi/distance_functions.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Points_off_io.h>
+
+#include <gudhi/Miniball.hpp>
+
+#include <boost/program_options.hpp>
+
+#include <string>
+#include <vector>
+#include <limits>   // infinity
+#include <utility>  // for pair
+#include <map>
+
+// ----------------------------------------------------------------------------
+// rips_persistence_step_by_step is an example of each step that is required to
+// build a Rips over a Simplex_tree. Please refer to rips_persistence to see
+// how to do the same thing with the Rips_complex wrapper for less detailed
+// steps.
+// ----------------------------------------------------------------------------
+
+// Types definition
+using Simplex_tree = Gudhi::Simplex_tree<>;
+using Simplex_handle = Simplex_tree::Simplex_handle;
+using Filtration_value = Simplex_tree::Filtration_value;
+using Point = std::vector<double>;
+using Points_off_reader = Gudhi::Points_off_reader<Point>;
+using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>;
+
+class Cech_blocker {
+ private:
+  using Point_cloud = std::vector<Point>;
+  using Point_iterator = Point_cloud::const_iterator;
+  using Coordinate_iterator = Point::const_iterator;
+  using Min_sphere = Gudhi::Miniball::Miniball<Gudhi::Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
+
+ public:
+  bool operator()(Simplex_handle sh) {
+    std::vector<Point> points;
+    for (auto vertex : simplex_tree_.simplex_vertex_range(sh)) {
+      points.push_back(point_cloud_[vertex]);
+#ifdef DEBUG_TRACES
+      std::cout << "#(" << vertex << ")#";
+#endif  // DEBUG_TRACES
+    }
+    Filtration_value radius = Gudhi::Minimal_enclosing_ball_radius()(points);
+#ifdef DEBUG_TRACES
+    std::cout << "radius = " << radius << " - " << (radius > max_radius_) << std::endl;
+#endif  // DEBUG_TRACES
+    simplex_tree_.assign_filtration(sh, radius);
+    return (radius > max_radius_);
+  }
+  Cech_blocker(Simplex_tree& simplex_tree, Filtration_value max_radius, const std::vector<Point>& point_cloud)
+      : simplex_tree_(simplex_tree), max_radius_(max_radius), point_cloud_(point_cloud) {
+    dimension_ = point_cloud_[0].size();
+  }
+
+ private:
+  Simplex_tree simplex_tree_;
+  Filtration_value max_radius_;
+  std::vector<Point> point_cloud_;
+  int dimension_;
+};
+
+void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& max_radius, int& dim_max);
+
+int main(int argc, char* argv[]) {
+  std::string off_file_points;
+  Filtration_value max_radius;
+  int dim_max;
+
+  program_options(argc, argv, off_file_points, max_radius, dim_max);
+
+  // Extract the points from the file filepoints
+  Points_off_reader off_reader(off_file_points);
+
+  // Compute the proximity graph of the points
+  Proximity_graph prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(off_reader.get_point_cloud(), max_radius,
+                                                                            Gudhi::Minimal_enclosing_ball_radius());
+
+  // Construct the Rips complex in a Simplex Tree
+  Simplex_tree st;
+  // insert the proximity graph in the simplex tree
+  st.insert_graph(prox_graph);
+  // expand the graph until dimension dim_max
+  st.expansion_with_blockers(dim_max, Cech_blocker(st, max_radius, off_reader.get_point_cloud()));
+
+  std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
+  std::cout << "   and has dimension " << st.dimension() << " \n";
+
+  // Sort the simplices in the order of the filtration
+  st.initialize_filtration();
+
+#if DEBUG_TRACES
+  std::cout << "********************************************************************\n";
+  std::cout << "* The complex contains " << st.num_simplices() << " simplices - dimension=" << st.dimension() << "\n";
+  std::cout << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
+  for (auto f_simplex : st.filtration_simplex_range()) {
+    std::cout << "   "
+              << "[" << st.filtration(f_simplex) << "] ";
+    for (auto vertex : st.simplex_vertex_range(f_simplex)) {
+      std::cout << static_cast<int>(vertex) << " ";
+    }
+    std::cout << std::endl;
+  }
+#endif  // DEBUG_TRACES
+
+  return 0;
+}
+
+void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& max_radius, int& dim_max) {
+  namespace po = boost::program_options;
+  po::options_description hidden("Hidden options");
+  hidden.add_options()("input-file", po::value<std::string>(&off_file_points),
+                       "Name of an OFF file containing a point set.\n");
+
+  po::options_description visible("Allowed options", 100);
+  visible.add_options()("help,h", "produce help message")(
+      "max-radius,r",
+      po::value<Filtration_value>(&max_radius)->default_value(std::numeric_limits<Filtration_value>::infinity()),
+      "Maximal length of an edge for the Rips complex construction.")(
+      "cpx-dimension,d", po::value<int>(&dim_max)->default_value(1),
+      "Maximal dimension of the Rips complex we want to compute.");
+
+  po::positional_options_description pos;
+  pos.add("input-file", 1);
+
+  po::options_description all;
+  all.add(visible).add(hidden);
+
+  po::variables_map vm;
+  po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm);
+  po::notify(vm);
+
+  if (vm.count("help") || !vm.count("input-file")) {
+    std::cout << std::endl;
+    std::cout << "Construct a Cech complex defined on a set of input points.\n \n";
+
+    std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
+    std::cout << visible << std::endl;
+    std::abort();
+  }
+}