Add alpha shapes functionnality

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@488 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: ef821bf7026520540b5869e16c08c290d3ed9477

13 files changed, 1065 insertions, 0 deletions

diff --git a/src/Alpha_shapes/example/CMakeLists.txt b/src/Alpha_shapes/example/CMakeLists.txt
new file mode 100644
index 00000000..fb94ca05
--- /dev/null
+++ b/src/Alpha_shapes/example/CMakeLists.txt
@@ -0,0 +1,31 @@
+cmake_minimum_required(VERSION 2.6)
+project(GUDHIAlphaShapesExample)
+
+# need CGAL 4.6
+# cmake -DCGAL_DIR=~/workspace/CGAL-4.6-beta1 ../../..
+if(CGAL_FOUND)
+  if (NOT CGAL_VERSION VERSION_LESS 4.6.0)
+    message(STATUS "CGAL version: ${CGAL_VERSION}.")
+
+    include( ${CGAL_USE_FILE} )
+ 
+    find_package(Eigen3 3.1.0)
+    if (EIGEN3_FOUND)
+      message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
+      include( ${EIGEN3_USE_FILE} )
+      include_directories (BEFORE "../../include")
+
+      add_executable ( dtoffrw Delaunay_triangulation_off_rw.cpp )
+      target_link_libraries(dtoffrw  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+      add_test(dtoffrw_tore3D ${CMAKE_CURRENT_BINARY_DIR}/dtoffrw ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off 3)
+
+      #add_definitions(-DDEBUG_TRACES)
+      add_executable ( stfromdt Simplex_tree_from_delaunay_triangulation.cpp )
+      target_link_libraries(stfromdt  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+    else()
+      message(WARNING "Eigen3 not found. Version 3.1.0 is required for Alpha shapes feature.")
+    endif()
+  else()
+    message(WARNING "CGAL version: ${CGAL_VERSION} is too old to compile Alpha shapes feature. Version 4.6.0 is required.")
+  endif ()
+endif()
diff --git a/src/Alpha_shapes/example/Delaunay_triangulation_off_rw.cpp b/src/Alpha_shapes/example/Delaunay_triangulation_off_rw.cpp
new file mode 100644
index 00000000..03f6440d
--- /dev/null
+++ b/src/Alpha_shapes/example/Delaunay_triangulation_off_rw.cpp
@@ -0,0 +1,105 @@
+/*    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) 2014  INRIA Saclay (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/>.
+ */
+
+// to construct a Delaunay_triangulation from a OFF file
+#include "gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h"
+
+#include <CGAL/Delaunay_triangulation.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/point_generators_d.h>
+#include <CGAL/algorithm.h>
+#include <CGAL/assertions.h>
+
+#include <iostream>
+#include <iterator>
+#include <vector>
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string>
+
+// Use dynamic_dimension_tag for the user to be able to set dimension
+typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > K;
+typedef CGAL::Delaunay_triangulation<K> T;
+// The triangulation uses the default instanciation of the 
+// TriangulationDataStructure template parameter
+
+void usage(char * const progName) {
+  std::cerr << "Usage: " << progName << " filename.off dimension" << std::endl;
+  exit(-1); // ----- >>
+}
+
+int main(int argc, char **argv) {
+  if (argc != 3) {
+    std::cerr << "Error: Number of arguments (" << argc << ") is not correct" << std::endl;
+    usage(argv[0]);
+  }
+
+  int dimension = 0;
+  int returnedScanValue = sscanf(argv[2], "%d", &dimension);
+  if ((returnedScanValue == EOF) || (dimension <= 0)) {
+    std::cerr << "Error: " << argv[2] << " is not correct" << std::endl;
+    usage(argv[0]);
+  }
+
+  T dt(dimension);
+  std::string offFileName(argv[1]);
+  Gudhi::alphashapes::Delaunay_triangulation_off_reader<T> off_reader(offFileName, dt, true, true);
+  if (!off_reader.is_valid()) {
+    std::cerr << "Unable to read file " << offFileName << std::endl;
+    exit(-1); // ----- >>
+  }
+
+  std::cout << "number of vertices=" << dt.number_of_vertices() << std::endl;
+  std::cout << "number of full cells=" << dt.number_of_full_cells() << std::endl;
+  std::cout << "number of finite full cells=" << dt.number_of_finite_full_cells() << std::endl;
+
+  // Points list
+  /*for (T::Vertex_iterator vit = dt.vertices_begin(); vit != dt.vertices_end(); ++vit) {
+        for (auto Coord = vit->point().cartesian_begin(); Coord != vit->point().cartesian_end(); ++Coord) {
+          std::cout << *Coord << " ";
+        }
+        std::cout << std::endl;
+  }
+  std::cout << std::endl;*/
+ 
+  int i = 0, j = 0;
+  typedef T::Full_cell_iterator Full_cell_iterator;
+  typedef T::Facet Facet;
+
+  for (Full_cell_iterator cit = dt.full_cells_begin(); cit != dt.full_cells_end(); ++cit) {
+    if (!dt.is_infinite(cit)) {
+      j++;
+      continue;
+    }
+    Facet fct(cit, cit->index(dt.infinite_vertex()));
+    i++;
+  }
+  std::cout << "There are " << i << " facets on the convex hull." << std::endl;
+  std::cout << "There are " << j << " facets not on the convex hull." << std::endl;
+
+
+  std::string offOutputFile("out.off");
+  Gudhi::alphashapes::Delaunay_triangulation_off_writer<T> off_writer(offOutputFile, dt);
+
+  return 0;
+}
\ No newline at end of file
diff --git a/src/Alpha_shapes/example/Simplex_tree_from_delaunay_triangulation.cpp b/src/Alpha_shapes/example/Simplex_tree_from_delaunay_triangulation.cpp
new file mode 100644
index 00000000..3a17b519
--- /dev/null
+++ b/src/Alpha_shapes/example/Simplex_tree_from_delaunay_triangulation.cpp
@@ -0,0 +1,103 @@
+/*    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) 2014  INRIA Saclay (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/>.
+ */
+
+// to construct a Delaunay_triangulation from a OFF file
+#include "gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h"
+#include "gudhi/Alpha_shapes.h"
+
+// to construct a simplex_tree from Delaunay_triangulation
+#include "gudhi/graph_simplicial_complex.h"
+#include "gudhi/Simplex_tree.h"
+
+#include <CGAL/Delaunay_triangulation.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/point_generators_d.h>
+#include <CGAL/algorithm.h>
+#include <CGAL/assertions.h>
+
+#include <iostream>
+#include <iterator>
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string>
+
+// Use dynamic_dimension_tag for the user to be able to set dimension
+typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > K;
+typedef CGAL::Delaunay_triangulation<K> T;
+// The triangulation uses the default instanciation of the 
+// TriangulationDataStructure template parameter
+
+void usage(char * const progName) {
+  std::cerr << "Usage: " << progName << " filename.off dimension" << std::endl;
+  exit(-1); // ----- >>
+}
+
+int main(int argc, char **argv) {
+  if (argc != 3) {
+    std::cerr << "Error: Number of arguments (" << argc << ") is not correct" << std::endl;
+    usage(argv[0]);
+  }
+
+  int dimension = 0;
+  int returnedScanValue = sscanf(argv[2], "%d", &dimension);
+  if ((returnedScanValue == EOF) || (dimension <= 0)) {
+    std::cerr << "Error: " << argv[2] << " is not correct" << std::endl;
+    usage(argv[0]);
+  }
+
+  // ----------------------------------------------------------------------------
+  //
+  // Init of an alpha-shape from a Delaunay triangulation
+  //
+  // ----------------------------------------------------------------------------
+  T dt(dimension);
+  std::string off_file_name(argv[1]);
+
+  Gudhi::alphashapes::Delaunay_triangulation_off_reader<T> off_reader(off_file_name, dt, false, false);
+  if (!off_reader.is_valid()) {
+    std::cerr << "Unable to read file " << off_file_name << std::endl;
+    exit(-1); // ----- >>
+  }
+
+  std::cout << "number of vertices=" << dt.number_of_vertices() << std::endl;
+  std::cout << "number of full cells=" << dt.number_of_full_cells() << std::endl;
+  std::cout << "number of finite full cells=" << dt.number_of_finite_full_cells() << std::endl;
+
+  Gudhi::alphashapes::Alpha_shapes alpha_shapes_from_dt(dt);
+  //std::cout << alpha_shapes_from_dt << std::endl;
+
+  // ----------------------------------------------------------------------------
+  //
+  // Init of an alpha-shape from a OFF file
+  //
+  // ----------------------------------------------------------------------------
+  Gudhi::alphashapes::Alpha_shapes alpha_shapes_from_file(off_file_name, dimension);
+  //std::cout << alpha_shapes_from_file << std::endl;
+  
+  std::cout << "alpha_shapes_from_file.dimension()=" << alpha_shapes_from_file.dimension() << std::endl;
+  std::cout << "alpha_shapes_from_file.filtration()=" << alpha_shapes_from_file.filtration() << std::endl;
+  std::cout << "alpha_shapes_from_file.num_simplices()=" << alpha_shapes_from_file.num_simplices() << std::endl;
+  std::cout << "alpha_shapes_from_file.num_vertices()=" << alpha_shapes_from_file.num_vertices() << std::endl;
+
+  return 0;
+}
\ No newline at end of file
diff --git a/src/Alpha_shapes/include/gudhi/Alpha_shapes.h b/src/Alpha_shapes/include/gudhi/Alpha_shapes.h
new file mode 100644
index 00000000..b8efdb4d
--- /dev/null
+++ b/src/Alpha_shapes/include/gudhi/Alpha_shapes.h
@@ -0,0 +1,200 @@
+/*    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) 2015  INRIA Saclay (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/>.
+ */
+
+#ifndef SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
+#define SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
+
+// to construct a Delaunay_triangulation from a OFF file
+#include <gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h>
+
+// to construct a simplex_tree from Delaunay_triangulation
+#include <gudhi/graph_simplicial_complex.h>
+#include <gudhi/Simplex_tree.h>
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <CGAL/Delaunay_triangulation.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/algorithm.h>
+#include <CGAL/assertions.h>
+
+#include <iostream>
+#include <iterator>
+#include <vector>
+#include <string>
+
+namespace Gudhi {
+
+namespace alphashapes {
+
+/** \defgroup alpha_shapes Alpha shapes in dimension N
+ *
+ <DT>Implementations:</DT>
+ Alpha shapes in dimension N are a subset of Delaunay Triangulation in dimension N.
+
+
+ * \author    Vincent Rouvreau
+ * \version   1.0
+ * \date      2015
+ * \copyright GNU General Public License v3.
+ * @{
+ */
+
+/**
+ * \brief Alpha shapes data structure.
+ *
+ * \details Every simplex \f$[v_0, \cdots ,v_d]\f$ admits a canonical orientation
+ * induced by the order relation on vertices \f$ v_0 < \cdots < v_d \f$.
+ *
+ * Details may be found in \cite boissonnatmariasimplextreealgorithmica.
+ *
+ * \implements FilteredComplex
+ *
+ */
+class Alpha_shapes {
+ private:
+  // From Simplex_tree
+  /** \brief Type required to insert into a simplex_tree (with or without subfaces).*/
+  typedef std::vector<Vertex_handle> typeVectorVertex;
+
+  // From CGAL
+  /** \brief Kernel for the Delaunay_triangulation.
+   * Dimension can be set dynamically.
+   */
+  typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel;
+  /** \brief Delaunay_triangulation type required to create an alpha-shape.
+   */
+  typedef CGAL::Delaunay_triangulation<Kernel> Delaunay_triangulation;
+
+ private:
+  /** \brief Upper bound on the simplex tree of the simplicial complex.*/
+  Gudhi::Simplex_tree<> _st;
+
+ public:
+
+  Alpha_shapes(std::string off_file_name, int dimension) {
+    Delaunay_triangulation dt(dimension);
+    Gudhi::alphashapes::Delaunay_triangulation_off_reader<Delaunay_triangulation>
+        off_reader(off_file_name, dt, true, true);
+    if (!off_reader.is_valid()) {
+      std::cerr << "Unable to read file " << off_file_name << std::endl;
+      exit(-1); // ----- >>
+    }
+#ifdef DEBUG_TRACES
+    std::cout << "number of vertices=" << dt.number_of_vertices() << std::endl;
+    std::cout << "number of full cells=" << dt.number_of_full_cells() << std::endl;
+    std::cout << "number of finite full cells=" << dt.number_of_finite_full_cells() << std::endl;
+#endif  // DEBUG_TRACES
+    init<Delaunay_triangulation>(dt);
+  }
+
+  template<typename T>
+  Alpha_shapes(T triangulation) {
+    init<T>(triangulation);
+  }
+
+  ~Alpha_shapes() { }
+
+ private:
+
+  template<typename T>
+  void init(T triangulation) {
+    _st.set_dimension(triangulation.maximal_dimension());
+    _st.set_filtration(0.0);
+    // triangulation points list
+    for (auto vit = triangulation.finite_vertices_begin();
+         vit != triangulation.finite_vertices_end(); ++vit) {
+      typeVectorVertex vertexVector;
+      Vertex_handle vertexHdl = std::distance(triangulation.finite_vertices_begin(), vit);
+      vertexVector.push_back(vertexHdl);
+
+      // Insert each point in the simplex tree
+      _st.insert_simplex(vertexVector, 0.0);
+
+#ifdef DEBUG_TRACES
+      std::cout << "P" << vertexHdl << ":";
+      for (auto Coord = vit->point().cartesian_begin(); Coord != vit->point().cartesian_end(); ++Coord) {
+        std::cout << *Coord << " ";
+      }
+      std::cout << std::endl;
+#endif  // DEBUG_TRACES
+    }
+    // triangulation finite full cells list
+    for (auto cit = triangulation.finite_full_cells_begin();
+         cit != triangulation.finite_full_cells_end(); ++cit) {
+      typeVectorVertex vertexVector;
+      for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
+        // Vertex handle is distance - 1
+        Vertex_handle vertexHdl = std::distance(triangulation.vertices_begin(), *vit) - 1;
+        vertexVector.push_back(vertexHdl);
+      }
+      // Insert each point in the simplex tree
+      _st.insert_simplex_and_subfaces(vertexVector, 0.0);
+
+#ifdef DEBUG_TRACES
+      std::cout << "C" << std::distance(triangulation.finite_full_cells_begin(), cit) << ":";
+      for (auto value : vertexVector) {
+        std::cout << value << ' ';
+      }
+      std::cout << std::endl;
+#endif  // DEBUG_TRACES
+    }
+  }
+
+ public:
+
+  /** \brief Returns the number of vertices in the complex. */
+  size_t num_vertices() {
+    return _st.num_vertices();
+  }
+
+  /** \brief Returns the number of simplices in the complex.
+   *
+   * Does not count the empty simplex. */
+  const unsigned int& num_simplices() const {
+    return _st.num_simplices();
+  }
+
+  /** \brief Returns an upper bound on the dimension of the simplicial complex. */
+  int dimension() {
+    return _st.dimension();
+  }
+
+  /** \brief Returns an upper bound of the filtration values of the simplices. */
+  Filtration_value filtration() {
+    return _st.filtration();
+  }
+
+  friend std::ostream& operator<<(std::ostream& os, const Alpha_shapes& alpha_shape) {
+    // TODO: Program terminated with signal SIGABRT, Aborted - Maybe because of copy constructor
+    Gudhi::Simplex_tree<> st = alpha_shape._st;
+    os << st << std::endl;
+    return os;
+  }
+};
+
+} // namespace alphashapes
+
+} // namespace Gudhi
+
+#endif  // SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
diff --git a/src/Alpha_shapes/include/gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h b/src/Alpha_shapes/include/gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h
new file mode 100644
index 00000000..693b393e
--- /dev/null
+++ b/src/Alpha_shapes/include/gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h
@@ -0,0 +1,213 @@
+/*    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) 2015  INRIA Saclay (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/>.
+ */
+#ifndef SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_DELAUNAY_TRIANGULATION_OFF_IO_H_
+#define SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_DELAUNAY_TRIANGULATION_OFF_IO_H_
+
+#include <string>
+#include <vector>
+#include <fstream>
+
+#include "gudhi/Off_reader.h"
+
+namespace Gudhi {
+
+namespace alphashapes {
+
+/**
+ *@brief Off reader visitor with flag that can be passed to Off_reader to read a Delaunay_triangulation_complex.
+ */
+template<typename Complex>
+class Delaunay_triangulation_off_flag_visitor_reader {
+  Complex& complex_;
+  typedef typename Complex::Point Point;
+
+  const bool load_only_points_;
+
+ public:
+  explicit Delaunay_triangulation_off_flag_visitor_reader(Complex& complex, bool load_only_points = false) :
+      complex_(complex),
+      load_only_points_(load_only_points) { }
+
+  void init(int dim, int num_vertices, int num_faces, int num_edges) {
+#ifdef DEBUG_TRACES
+    std::cout << "init" << std::endl;
+#endif  // DEBUG_TRACES
+  }
+
+  void point(const std::vector<double>& point) {
+#ifdef DEBUG_TRACES
+    std::cout << "p ";
+    for (auto coordinate: point) {
+      std::cout << coordinate << " | ";
+    }
+    std::cout << std::endl;
+#endif  // DEBUG_TRACES
+    complex_.insert(Point(point.size(), point.begin(), point.end()));
+  }
+
+  void maximal_face(const std::vector<int>& face) {
+    // For alpha shapes, only points are read
+  }
+
+  void done() {
+#ifdef DEBUG_TRACES
+    std::cout << "done" << std::endl;
+#endif  // DEBUG_TRACES
+  }
+};
+
+/**
+ *@brief Off reader visitor that can be passed to Off_reader to read a Delaunay_triangulation_complex.
+ */
+template<typename Complex>
+class Delaunay_triangulation_off_visitor_reader {
+  Complex& complex_;
+  // typedef typename Complex::Vertex_handle Vertex_handle;
+  // typedef typename Complex::Simplex_handle Simplex_handle;
+  typedef typename Complex::Point Point;
+
+  const bool load_only_points_;
+  std::vector<Point> points_;
+  // std::vector<Simplex_handle> maximal_faces_;
+
+ public:
+  explicit Delaunay_triangulation_off_visitor_reader(Complex& complex, bool load_only_points = false) :
+      complex_(complex),
+      load_only_points_(load_only_points) { }
+
+  void init(int dim, int num_vertices, int num_faces, int num_edges) {
+#ifdef DEBUG_TRACES
+    std::cout << "init - " << num_vertices << std::endl;
+#endif  // DEBUG_TRACES
+    // maximal_faces_.reserve(num_faces);
+    points_.reserve(num_vertices);
+  }
+
+  void point(const std::vector<double>& point) {
+#ifdef DEBUG_TRACES
+    std::cout << "p ";
+    for (auto coordinate: point) {
+      std::cout << coordinate << " | ";
+    }
+    std::cout << std::endl;
+#endif  // DEBUG_TRACES
+    points_.emplace_back(Point(point.size(), point.begin(), point.end()));
+  }
+
+  void maximal_face(const std::vector<int>& face) {
+    // For alpha shapes, only points are read
+  }
+
+  void done() {
+    complex_.insert(points_.begin(), points_.end());
+#ifdef DEBUG_TRACES
+    std::cout << "done" << std::endl;
+#endif  // DEBUG_TRACES
+  }
+};
+
+/**
+ *@brief Class that allows to load a Delaunay_triangulation_complex from an off file.
+ */
+template<typename Complex>
+class Delaunay_triangulation_off_reader {
+ public:
+  /**
+   * name_file : file to read
+   * read_complex : complex that will receive the file content
+   * read_only_points : specify true if only the points must be read
+   */
+  Delaunay_triangulation_off_reader(const std::string & name_file, Complex& read_complex, bool read_only_points = false,
+                                    bool is_flag = false) : valid_(false) {
+    std::ifstream stream(name_file);
+    if (stream.is_open()) {
+      if (is_flag) {
+        // For alpha shapes, only points are read
+        Delaunay_triangulation_off_flag_visitor_reader<Complex> off_visitor(read_complex, true);
+        Off_reader off_reader(stream);
+        valid_ = off_reader.read(off_visitor);
+      } else {
+        // For alpha shapes, only points are read
+        Delaunay_triangulation_off_visitor_reader<Complex> off_visitor(read_complex, true);
+        Off_reader off_reader(stream);
+        valid_ = off_reader.read(off_visitor);
+      }
+    }
+  }
+
+  /**
+   * return true if reading did not meet problems.
+   */
+  bool is_valid() const {
+    return valid_;
+  }
+
+ private:
+  bool valid_;
+};
+
+template<typename Complex>
+class Delaunay_triangulation_off_writer {
+ public:
+  /**
+   * name_file : file where the off will be written
+   * save_complex : complex that be outputted in the file
+   * for now only save triangles.
+   */
+  Delaunay_triangulation_off_writer(const std::string & name_file, const Complex& save_complex) {
+    std::ofstream stream(name_file);
+    if (stream.is_open()) {
+      // OFF header
+      stream << "OFF" << std::endl;
+      // no endl on next line - don't know why...
+      stream << save_complex.number_of_vertices() << " " << save_complex.number_of_finite_full_cells() << " 0";
+
+      // Points list
+      for (auto vit = save_complex.vertices_begin(); vit != save_complex.vertices_end(); ++vit) {
+        for (auto Coord = vit->point().cartesian_begin(); Coord != vit->point().cartesian_end(); ++Coord) {
+          stream << *Coord << " ";
+        }
+        stream << std::endl;
+      }
+
+      // Finite cells list
+      for (auto cit = save_complex.finite_full_cells_begin(); cit != save_complex.finite_full_cells_end(); ++cit) {
+        stream << std::distance(cit->vertices_begin(), cit->vertices_end()) << " ";  // Dimension
+        for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
+          auto vertexHdl = *vit;
+          // auto vertexHdl = std::distance(save_complex.vertices_begin(), *vit) - 1;
+          // stream << std::distance(save_complex.vertices_begin(), *(vit)) - 1 << " ";
+        }
+        stream << std::endl;
+      }
+      stream.close();
+    } else {
+      std::cerr << "could not open file " << name_file << std::endl;
+    }
+  }
+};
+
+}  // namespace alphashapes
+
+}  // namespace Gudhi
+
+#endif  // SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_DELAUNAY_TRIANGULATION_OFF_IO_H_
diff --git a/src/Alpha_shapes/test/Alpha_shapes_unit_test.cpp b/src/Alpha_shapes/test/Alpha_shapes_unit_test.cpp
new file mode 100644
index 00000000..a90704b6
--- /dev/null
+++ b/src/Alpha_shapes/test/Alpha_shapes_unit_test.cpp
@@ -0,0 +1,126 @@
+/*    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) 2015  INRIA Saclay (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/>.
+ */
+
+#define BOOST_TEST_MODULE alpha_shapes
+#include <boost/test/included/unit_test.hpp>
+#include <boost/system/error_code.hpp>
+#include <boost/chrono/thread_clock.hpp>
+// to construct a Delaunay_triangulation from a OFF file
+#include "gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h"
+#include "gudhi/Alpha_shapes.h"
+
+// to construct a simplex_tree from Delaunay_triangulation
+#include "gudhi/graph_simplicial_complex.h"
+#include "gudhi/Simplex_tree.h"
+
+#include <CGAL/Delaunay_triangulation.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/point_generators_d.h>
+#include <CGAL/algorithm.h>
+#include <CGAL/assertions.h>
+
+#include <iostream>
+#include <iterator>
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string>
+
+// Use dynamic_dimension_tag for the user to be able to set dimension
+typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > K;
+typedef CGAL::Delaunay_triangulation<K> T;
+// The triangulation uses the default instanciation of the 
+// TriangulationDataStructure template parameter
+
+BOOST_AUTO_TEST_CASE( OFF_file ) {
+  // ----------------------------------------------------------------------------
+  //
+  // Init of an alpha-shape from a OFF file
+  //
+  // ----------------------------------------------------------------------------
+  std::string off_file_name("S4_100.off");
+  std::cout << "========== OFF FILE NAME = " << off_file_name << " ==========" << std::endl;
+  
+  Gudhi::alphashapes::Alpha_shapes alpha_shapes_from_file(off_file_name, 4);
+
+  const int DIMENSION = 4;
+  std::cout << "alpha_shapes_from_file.dimension()=" << alpha_shapes_from_file.dimension() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_file.dimension() == DIMENSION);
+  
+  const double FILTRATION = 0.0;
+  std::cout << "alpha_shapes_from_file.filtration()=" << alpha_shapes_from_file.filtration() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_file.filtration() == FILTRATION);
+  
+  const int NUMBER_OF_VERTICES = 100;
+  std::cout << "alpha_shapes_from_file.num_vertices()=" << alpha_shapes_from_file.num_vertices() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_file.num_vertices() == NUMBER_OF_VERTICES);
+  
+  const int NUMBER_OF_SIMPLICES = 6779;
+  std::cout << "alpha_shapes_from_file.num_simplices()=" << alpha_shapes_from_file.num_simplices() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+
+}
+
+BOOST_AUTO_TEST_CASE( Delaunay_triangulation ) {
+  // ----------------------------------------------------------------------------
+  //
+  // Init of an alpha-shape from a Delauny triangulation
+  //
+  // ----------------------------------------------------------------------------
+  T dt(8);
+  std::string off_file_name("S8_10.off");
+  std::cout << "========== OFF FILE NAME = " << off_file_name << " ==========" << std::endl;
+  
+  Gudhi::alphashapes::Delaunay_triangulation_off_reader<T> off_reader(off_file_name, dt, true, true);
+  std::cout << "off_reader.is_valid()=" << off_reader.is_valid() << std::endl;
+  BOOST_CHECK(off_reader.is_valid());
+
+  const int NUMBER_OF_VERTICES = 10;
+  std::cout << "dt.number_of_vertices()=" << dt.number_of_vertices() << std::endl;
+  BOOST_CHECK(dt.number_of_vertices() == NUMBER_OF_VERTICES);
+  
+  const int NUMBER_OF_FULL_CELLS = 30;
+  std::cout << "dt.number_of_full_cells()=" << dt.number_of_full_cells() << std::endl;
+  BOOST_CHECK(dt.number_of_full_cells() == NUMBER_OF_FULL_CELLS);
+  
+  const int NUMBER_OF_FINITE_FULL_CELLS = 6;
+  std::cout << "dt.number_of_finite_full_cells()=" << dt.number_of_finite_full_cells() << std::endl;
+  BOOST_CHECK(dt.number_of_finite_full_cells() == NUMBER_OF_FINITE_FULL_CELLS);
+
+  Gudhi::alphashapes::Alpha_shapes alpha_shapes_from_dt(dt);
+
+  const int DIMENSION = 8;
+  std::cout << "alpha_shapes_from_dt.dimension()=" << alpha_shapes_from_dt.dimension() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_dt.dimension() == DIMENSION);
+  
+  const double FILTRATION = 0.0;
+  std::cout << "alpha_shapes_from_dt.filtration()=" << alpha_shapes_from_dt.filtration() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_dt.filtration() == FILTRATION);
+  
+  std::cout << "alpha_shapes_from_dt.num_vertices()=" << alpha_shapes_from_dt.num_vertices() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_dt.num_vertices() == NUMBER_OF_VERTICES);
+  
+  const int NUMBER_OF_SIMPLICES = 997;
+  std::cout << "alpha_shapes_from_dt.num_simplices()=" << alpha_shapes_from_dt.num_simplices() << std::endl;
+  BOOST_CHECK(alpha_shapes_from_dt.num_simplices() == NUMBER_OF_SIMPLICES);
+}
+
diff --git a/src/Alpha_shapes/test/CMakeLists.txt b/src/Alpha_shapes/test/CMakeLists.txt
new file mode 100644
index 00000000..a48c1a8f
--- /dev/null
+++ b/src/Alpha_shapes/test/CMakeLists.txt
@@ -0,0 +1,31 @@
+cmake_minimum_required(VERSION 2.6)
+project(GUDHIAlphaShapesTest)
+
+# need CGAL 4.6
+# cmake -DCGAL_DIR=~/workspace/CGAL-4.6-beta1 ../../..
+if(CGAL_FOUND)
+  if (NOT CGAL_VERSION VERSION_LESS 4.6.0)
+    message(STATUS "CGAL version: ${CGAL_VERSION}.")
+
+    include( ${CGAL_USE_FILE} )
+ 
+    find_package(Eigen3 3.1.0)
+    if (EIGEN3_FOUND)
+      message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
+      include( ${EIGEN3_USE_FILE} )
+      include_directories (BEFORE "../../include")
+
+      add_definitions(-DDEBUG_TRACES)
+      add_executable ( AlphaShapesUnitTest Alpha_shapes_unit_test.cpp )
+      target_link_libraries(AlphaShapesUnitTest  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+      add_test(AlphaShapesUnitTest ${CMAKE_CURRENT_BINARY_DIR}/AlphaShapesUnitTest)
+
+    else()
+      message(WARNING "Eigen3 not found. Version 3.1.0 is required for Alpha shapes feature.")
+    endif()
+  else()
+    message(WARNING "CGAL version: ${CGAL_VERSION} is too old to compile Alpha shapes feature. Version 4.6.0 is required.")
+  endif ()
+endif()
+
+cpplint_add_tests("${CMAKE_SOURCE_DIR}/src/Alpha_shapes/include/gudhi")
diff --git a/src/Alpha_shapes/test/README b/src/Alpha_shapes/test/README
new file mode 100644
index 00000000..244a2b84
--- /dev/null
+++ b/src/Alpha_shapes/test/README
@@ -0,0 +1,12 @@
+To compile:
+***********
+
+cmake .
+make
+
+To launch with details:
+***********************
+
+./AlphaShapesUnitTest --report_level=detailed --log_level=all 
+
+   ==> echo $? returns 0 in case of success (non-zero otherwise)
diff --git a/src/Alpha_shapes/test/S4_100.off b/src/Alpha_shapes/test/S4_100.off
new file mode 100644
index 00000000..0a5dc58c
--- /dev/null
+++ b/src/Alpha_shapes/test/S4_100.off
@@ -0,0 +1,102 @@
+OFF
+100 0 0
+0.562921 -0.735261 -0.256472 0.277007
+-0.803733 -0.0527915 -0.315125 0.501918
+-0.24946 -0.354982 -0.410773 -0.801887
+0.916381 -0.0512295 0.371049 0.141223
+0.182222 0.940836 -0.171362 -0.228599
+-0.787145 -0.129213 0.568102 -0.202402
+0.0187866 -0.22093 -0.832882 -0.507095
+-0.4702 -0.533814 0.353776 0.607286
+-0.159798 -0.504771 0.263586 0.806346
+0.295546 0.162541 0.452931 0.825279
+0.242043 -0.107437 -0.913612 -0.308521
+0.875759 -0.113035 -0.469189 -0.0114505
+0.547877 -0.762247 -0.256972 -0.229729
+-0.172302 0.521057 0.412013 -0.727363
+-0.724729 -0.0574074 -0.0290602 0.686023
+0.700434 -0.102636 0.687285 0.162779
+-0.681386 0.0946893 0.610047 0.393178
+-0.847553 -0.357132 0.383743 0.0827718
+0.72297 -0.161631 -0.608517 0.284424
+0.757394 0.141549 0.196065 -0.606528
+0.78094 0.00901997 0.434536 0.448586
+0.14166 -0.619339 0.614589 -0.467582
+0.473105 -0.537832 -0.0103746 0.697711
+-0.208004 0.536218 0.818027 0.00605288
+0.743694 -0.628926 0.188072 0.126488
+-0.462228 -0.278147 0.35514 -0.76345
+-0.17361 0.249211 0.758567 -0.57648
+0.416958 -0.254924 -0.576373 -0.654946
+-0.590751 -0.286089 -0.424896 0.623402
+-0.639538 -0.739693 -0.203745 0.0482932
+0.0731787 0.132121 0.864022 0.480266
+-0.149644 -0.164724 -0.249746 -0.94239
+-0.348592 0.0120379 -0.928656 -0.126239
+0.395328 -0.54513 0.149976 -0.723917
+-0.974164 0.14707 0.157191 0.068302
+-0.166425 0.119943 -0.627304 -0.751269
+0.031947 -0.358518 -0.708301 -0.607251
+0.93781 -0.155368 -0.30951 0.0240237
+0.276094 -0.753155 -0.597088 -0.00387459
+-0.642876 -0.200551 -0.263517 -0.690687
+0.178711 0.604987 -0.262989 0.729993
+-0.520347 0.497922 -0.676144 0.155374
+-0.703999 0.500219 -0.484381 0.139789
+-0.131013 0.835735 0.506779 0.166004
+-0.536116 -0.566557 0.229226 0.582279
+-0.334105 0.158252 0.926091 0.0754059
+-0.0362677 0.296076 0.897108 0.325915
+-0.57486 0.798575 0.15324 -0.0912754
+0.498602 0.0186805 0.72824 0.469801
+-0.960329 0.0473356 0.261005 -0.0860505
+0.899134 -0.381392 -0.214508 0.00921711
+0.570576 0.567224 0.393019 -0.445237
+-0.761763 -0.614589 -0.0546476 -0.197513
+0.188584 0.289531 0.174031 0.922129
+-0.458506 -0.583876 0.639297 -0.2004
+0.785343 -0.21571 0.0794082 -0.574804
+0.0819036 0.65961 -0.247426 0.704973
+0.573125 0.49706 0.373026 0.534145
+-0.513286 -0.626226 0.208535 -0.548536
+0.460558 0.468686 0.507832 -0.55707
+0.716158 -0.488201 0.388209 -0.313164
+0.881074 0.152441 0.380128 -0.236589
+0.885793 0.0386389 0.161009 -0.433537
+-0.365162 0.298384 0.292846 0.831784
+0.364934 0.632269 -0.197205 -0.654346
+-0.31469 -0.429991 0.665304 -0.522923
+-0.734198 0.462914 -0.135691 -0.477756
+-0.422885 0.674444 -0.364143 -0.483419
+0.829218 -0.154622 -0.381147 0.378439
+0.887881 0.310479 -0.109528 0.321363
+-0.354398 -0.693974 0.456019 -0.429941
+-0.492045 -0.160008 0.044387 0.854587
+0.0595532 0.158421 0.412577 -0.895062
+-0.211441 0.491794 -0.153521 0.83058
+-0.33558 -0.504711 0.353831 -0.71236
+-0.735211 -0.197714 0.525626 0.379593
+0.465818 -0.424245 0.769469 -0.104627
+-0.641071 -0.286339 -0.704442 -0.103923
+-0.00446569 0.0249849 -0.194417 -0.980591
+-0.610081 -0.252448 0.176698 -0.729966
+-0.0859217 -0.154471 0.715027 0.676382
+0.091315 0.0723382 -0.855023 -0.505337
+0.165362 0.200983 -0.428242 -0.865373
+-0.587465 0.303019 -0.152442 0.734729
+0.454946 -0.319828 0.437063 -0.706902
+-0.384368 0.277509 0.879225 -0.0470385
+0.523335 -0.330233 -0.208592 0.757335
+0.895086 0.0448492 0.268089 -0.353466
+-0.0272491 -0.567336 -0.72254 -0.39411
+-0.0745014 -0.121818 -0.882466 0.448179
+0.382304 -0.240135 0.851109 -0.267941
+-0.418057 -0.852847 -0.3128 0.00606452
+-0.554046 0.304237 0.272381 -0.725453
+0.155115 -0.0894732 -0.245017 -0.952838
+0.114459 -0.130722 0.953669 0.245614
+0.0913002 -0.462466 0.244433 0.847374
+-0.198849 0.0785111 0.131441 -0.967997
+-0.303154 -0.686484 0.639333 0.167604
+0.521455 0.256835 -0.0584503 -0.811606
+-0.109787 0.870544 0.161523 0.451676
diff --git a/src/Alpha_shapes/test/S8_10.off b/src/Alpha_shapes/test/S8_10.off
new file mode 100644
index 00000000..1d67e10f
--- /dev/null
+++ b/src/Alpha_shapes/test/S8_10.off
@@ -0,0 +1,12 @@
+OFF
+10 0 0
+0.440036 -0.574754 -0.200485 0.216537 -0.501251 -0.0329236 -0.196529 0.313023
+-0.129367 -0.184089 -0.213021 -0.415848 0.783529 -0.0438025 0.317256 0.120749
+0.132429 0.683748 -0.124536 -0.166133 -0.540695 -0.0887576 0.390234 -0.139031
+0.0137399 -0.161581 -0.609142 -0.370872 -0.320669 -0.364053 0.24127 0.41416
+-0.115313 -0.36425 0.190208 0.581871 0.204605 0.112527 0.313562 0.571337
+0.168272 -0.0746917 -0.635156 -0.214488 0.629498 -0.0812499 -0.337255 -0.00823068
+0.369896 -0.514626 -0.173493 -0.1551 -0.127105 0.384377 0.303936 -0.536566
+-0.49013 -0.0388242 -0.0196532 0.463953 0.515962 -0.0756047 0.506276 0.119908
+-0.434258 0.060347 0.388793 0.250579 -0.653127 -0.275207 0.295714 0.0637842
+0.596172 -0.133284 -0.501793 0.234541 0.428452 0.0800735 0.110912 -0.343109
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index b67ab2f8..d20d6d8a 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -37,5 +37,6 @@ else()
   add_subdirectory(example/Skeleton_blocker)                   
   add_subdirectory(example/Contraction)                   
   add_subdirectory(example/Hasse_complex)
+  add_subdirectory(example/Alpha_shapes)
 
 endif()  
diff --git a/src/Hasse_complex/example/CMakeLists.txt b/src/Hasse_complex/example/CMakeLists.txt
new file mode 100644
index 00000000..564df49d
--- /dev/null
+++ b/src/Hasse_complex/example/CMakeLists.txt
@@ -0,0 +1,5 @@
+cmake_minimum_required(VERSION 2.6)
+project(GUDHIHasseComplexExample)
+
+add_executable ( hasse_complex_from_simplex_tree hasse_complex_from_simplex_tree.cpp )
+add_test(hasse_complex_from_simplex_tree ${CMAKE_CURRENT_BINARY_DIR}/hasse_complex_from_simplex_tree)
diff --git a/src/Hasse_complex/example/hasse_complex_from_simplex_tree.cpp b/src/Hasse_complex/example/hasse_complex_from_simplex_tree.cpp
new file mode 100644
index 00000000..1de43ab7
--- /dev/null
+++ b/src/Hasse_complex/example/hasse_complex_from_simplex_tree.cpp
@@ -0,0 +1,124 @@
+/*    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) 2014  INRIA Saclay (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 <ctime>
+#include "gudhi/graph_simplicial_complex.h"
+#include "gudhi/Simplex_tree.h"
+
+using namespace Gudhi;
+
+typedef std::vector< Vertex_handle > typeVectorVertex;
+typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
+typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
+typedef Simplex_tree<> typeST;
+
+int main(int argc, char * const argv[]) {
+  // TEST OF INSERTION
+  std::cout << "********************************************************************" << std::endl;
+  std::cout << "TEST OF INSERTION" << std::endl;
+  typeST st;
+
+  // ++ FIRST
+  std::cout << "   - INSERT (2,1,0)" << std::endl;
+  typeVectorVertex SimplexVector1;
+  SimplexVector1.push_back(2);
+  SimplexVector1.push_back(1);
+  SimplexVector1.push_back(0);
+  st.insert_simplex_and_subfaces(SimplexVector1, 0.3);
+
+  // ++ SECOND
+  std::cout << "   - INSERT 3" << std::endl;
+  typeVectorVertex SimplexVector2;
+  SimplexVector2.push_back(3);
+  st.insert_simplex_and_subfaces(SimplexVector2, 0.1);
+
+  // ++ THIRD
+  std::cout << "   - INSERT (0,3)" << std::endl;
+  typeVectorVertex SimplexVector3;
+  SimplexVector3.push_back(3);
+  SimplexVector3.push_back(0);
+  st.insert_simplex_and_subfaces(SimplexVector3, 0.2);
+
+  // ++ FOURTH
+  std::cout << "   - INSERT (1,0) (already inserted)" << std::endl;
+  typeVectorVertex SimplexVector4;
+  SimplexVector4.push_back(1);
+  SimplexVector4.push_back(0);
+  st.insert_simplex_and_subfaces(SimplexVector4, 0.2);
+
+  // ++ FIFTH
+  std::cout << "   - INSERT (3,4,5)" << std::endl;
+  typeVectorVertex SimplexVector5;
+  SimplexVector5.push_back(3);
+  SimplexVector5.push_back(4);
+  SimplexVector5.push_back(5);
+  st.insert_simplex_and_subfaces(SimplexVector5, 0.3);
+
+  // ++ SIXTH
+  std::cout << "   - INSERT (0,1,6,7)" << std::endl;
+  typeVectorVertex SimplexVector6;
+  SimplexVector6.push_back(0);
+  SimplexVector6.push_back(1);
+  SimplexVector6.push_back(6);
+  SimplexVector6.push_back(7);
+  st.insert_simplex_and_subfaces(SimplexVector6, 0.4);
+
+  /* Inserted simplex:         */
+  /*    1   6                  */
+  /*    o---o                  */
+  /*   /X\7/      4            */
+  /*  o---o---o---o            */
+  /*  2   0   3\X/             */
+  /*            o              */
+  /*            5              */
+
+  /* In other words:          */
+  /*   A facet [2,1,0]        */
+  /*   An edge [0,3]          */
+  /*   A facet [3,4,5]        */
+  /*   A cell  [0,1,6,7]      */
+  /*   A cell  [4,5,8,9]      */
+  /*   A facet [9,10,11]      */
+  /*   An edge [11,6]         */
+  /*   An edge [10,12,2]      */
+
+  // ++ GENERAL VARIABLE SET
+  st.set_filtration(0.4); // Max filtration value
+  st.set_dimension(3); // Max dimension = 3 -> (0,1,6,7)
+
+  std::cout << "The complex contains " << st.num_simplices() << " simplices - " << st.num_vertices() << " vertices " << std::endl;
+  std::cout << "   - dimension " << st.dimension() << "   - filtration " << st.filtration() << std::endl;
+  std::cout << std::endl << std::endl << "Iterator on Simplices in the filtration, with [filtration value]:" << std::endl;
+  std::cout << "**************************************************************" << std::endl;
+
+  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 << (int)vertex;
+    }
+  }
+
+  return 0;
+}