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diff --git a/include/gudhi/Cech_complex.h b/include/gudhi/Cech_complex.h
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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/>.
+ */
+
+#ifndef CECH_COMPLEX_H_
+#define CECH_COMPLEX_H_
+
+#include <gudhi/distance_functions.h>        // for Gudhi::Minimal_enclosing_ball_radius
+#include <gudhi/graph_simplicial_complex.h>  // for Gudhi::Proximity_graph
+#include <gudhi/Debug_utils.h>               // for GUDHI_CHECK
+#include <gudhi/Cech_complex_blocker.h>      // for Gudhi::cech_complex::Cech_blocker
+
+#include <iostream>
+#include <stdexcept>  // for exception management
+#include <vector>
+
+namespace Gudhi {
+
+namespace cech_complex {
+
+/**
+ * \class Cech_complex
+ * \brief Cech complex data structure.
+ *
+ * \ingroup cech_complex
+ *
+ * \details
+ * The data structure is a proximity graph, containing edges when the edge length is less or equal
+ * to a given max_radius. Edge length is computed from `Gudhi::Minimal_enclosing_ball_radius` distance function.
+ *
+ * \tparam SimplicialComplexForProximityGraph furnishes `Vertex_handle` and `Filtration_value` type definition required
+ * by `Gudhi::Proximity_graph`.
+ *
+ * \tparam ForwardPointRange must be a range for which `std::begin()` and `std::end()` methods return input
+ * iterators on a point. `std::begin()` and `std::end()` methods are also required for a point.
+ */
+template <typename SimplicialComplexForProximityGraph, typename ForwardPointRange>
+class Cech_complex {
+ private:
+  // Required by compute_proximity_graph
+  using Vertex_handle = typename SimplicialComplexForProximityGraph::Vertex_handle;
+  using Filtration_value = typename SimplicialComplexForProximityGraph::Filtration_value;
+  using Proximity_graph = Gudhi::Proximity_graph<SimplicialComplexForProximityGraph>;
+
+  // Retrieve Coordinate type from ForwardPointRange
+  using Point_from_range_iterator = typename boost::range_const_iterator<ForwardPointRange>::type;
+  using Point_from_range = typename std::iterator_traits<Point_from_range_iterator>::value_type;
+  using Coordinate_iterator = typename boost::range_const_iterator<Point_from_range>::type;
+  using Coordinate = typename std::iterator_traits<Coordinate_iterator>::value_type;
+
+ public:
+  // Point and Point_cloud type definition
+  using Point = std::vector<Coordinate>;
+  using Point_cloud = std::vector<Point>;
+
+ public:
+  /** \brief Cech_complex constructor from a list of points.
+   *
+   * @param[in] points Range of points.
+   * @param[in] max_radius Maximal radius value.
+   *
+   * \tparam ForwardPointRange must be a range of Point. Point must be a range of <b>copyable</b> Cartesian coordinates.
+   *
+   */
+  Cech_complex(const ForwardPointRange& points, Filtration_value max_radius) : max_radius_(max_radius) {
+    // Point cloud deep copy
+    point_cloud_.reserve(boost::size(points));
+    for (auto&& point : points) point_cloud_.emplace_back(std::begin(point), std::end(point));
+
+    cech_skeleton_graph_ = Gudhi::compute_proximity_graph<SimplicialComplexForProximityGraph>(
+        point_cloud_, max_radius_, Gudhi::Minimal_enclosing_ball_radius());
+  }
+
+  /** \brief Initializes the simplicial complex from the proximity graph and expands it until a given maximal
+   * dimension, using the Cech blocker oracle.
+   *
+   * @param[in] complex SimplicialComplexForCech to be created.
+   * @param[in] dim_max graph expansion until this given maximal dimension.
+   * @exception std::invalid_argument In debug mode, if `complex.num_vertices()` does not return 0.
+   *
+   */
+  template <typename SimplicialComplexForCechComplex>
+  void create_complex(SimplicialComplexForCechComplex& complex, int dim_max) {
+    GUDHI_CHECK(complex.num_vertices() == 0,
+                std::invalid_argument("Cech_complex::create_complex - simplicial complex is not empty"));
+
+    // insert the proximity graph in the simplicial complex
+    complex.insert_graph(cech_skeleton_graph_);
+    // expand the graph until dimension dim_max
+    complex.expansion_with_blockers(dim_max,
+                                    Cech_blocker<SimplicialComplexForCechComplex, Cech_complex>(&complex, this));
+  }
+
+  /** @return max_radius value given at construction. */
+  Filtration_value max_radius() const { return max_radius_; }
+
+  /** @param[in] vertex Point position in the range.
+   * @return The point.
+   */
+  const Point& get_point(Vertex_handle vertex) const { return point_cloud_[vertex]; }
+
+ private:
+  Proximity_graph cech_skeleton_graph_;
+  Filtration_value max_radius_;
+  Point_cloud point_cloud_;
+};
+
+}  // namespace cech_complex
+
+}  // namespace Gudhi
+
+#endif  // CECH_COMPLEX_H_