Documentation for Alpha complex 3d

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alpha_complex_3d_module_vincent@3664 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: c6d824cdab7ac5ea79ce458dac666d35a9a21ab7

8 files changed, 454 insertions, 114 deletions

diff --git a/src/Alpha_complex/example/CMakeLists.txt b/src/Alpha_complex/example/CMakeLists.txt
index 5a66067c..af4bfd74 100644
--- a/src/Alpha_complex/example/CMakeLists.txt
+++ b/src/Alpha_complex/example/CMakeLists.txt
@@ -1,16 +1,6 @@
 project(Alpha_complex_examples)
 
 if(CGAL_FOUND)
-  add_executable(alpha_complex_3d_step_by_step alpha_complex_3d_step_by_step.cpp)
-  target_link_libraries(alpha_complex_3d_step_by_step ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
-
-  if (TBB_FOUND)
-    target_link_libraries(alpha_complex_3d_step_by_step ${TBB_LIBRARIES})
-  endif(TBB_FOUND)
-
-  add_test(NAME Alpha_complex_example_alpha_complex_3d_step_by_step COMMAND $<TARGET_FILE:alpha_complex_3d_step_by_step>
-          "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off")
-
   # need CGAL 4.7
   # cmake -DCGAL_DIR=~/workspace/CGAL-4.7 ..
   if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.7.0)
diff --git a/src/Alpha_complex/example/alpha_complex_3d_step_by_step.cpp b/src/Alpha_complex/example/alpha_complex_3d_step_by_step.cpp
new file mode 100644
index 00000000..d76402e5
--- /dev/null
+++ b/src/Alpha_complex/example/alpha_complex_3d_step_by_step.cpp
@@ -0,0 +1,309 @@
+/*    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
+ *
+ *    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 <boost/version.hpp>
+#include <boost/program_options.hpp>
+#include <boost/variant.hpp>
+
+#if BOOST_VERSION >= 105400
+#include <boost/container/static_vector.hpp>
+#endif
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Points_3D_off_io.h>
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/Alpha_shape_3.h>
+#include <CGAL/Alpha_shape_cell_base_3.h>
+#include <CGAL/Alpha_shape_vertex_base_3.h>
+#include <CGAL/iterator.h>
+
+#include <fstream>
+#include <cmath>
+#include <string>
+#include <tuple>
+#include <map>
+#include <utility>
+#include <vector>
+#include <cstdlib>
+
+template <class Vertex_list, class Cell_handle>
+Vertex_list from_cell(const Cell_handle& ch) {
+  Vertex_list the_list;
+  for (auto i = 0; i < 4; i++) {
+#ifdef DEBUG_TRACES
+    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+    the_list.push_back(ch->vertex(i));
+  }
+  return the_list;
+}
+
+template <class Vertex_list, class Facet>
+Vertex_list from_facet(const Facet& fct) {
+  Vertex_list the_list;
+  for (auto i = 0; i < 4; i++) {
+    if (fct.second != i) {
+#ifdef DEBUG_TRACES
+      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+      the_list.push_back(fct.first->vertex(i));
+    }
+  }
+  return the_list;
+}
+
+template <class Vertex_list, class Edge_3>
+Vertex_list from_edge(const Edge_3& edg) {
+  Vertex_list the_list;
+  for (auto i : {edg.second, edg.third}) {
+#ifdef DEBUG_TRACES
+    std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+    the_list.push_back(edg.first->vertex(i));
+  }
+  return the_list;
+}
+
+template <class Vertex_list, class Vertex_handle>
+Vertex_list from_vertex(const Vertex_handle& vh) {
+  Vertex_list the_list;
+#ifdef DEBUG_TRACES
+  std::cout << "from vertex=" << vh->point() << std::endl;
+#endif  // DEBUG_TRACES
+  the_list.push_back(vh);
+  return the_list;
+}
+
+// Alpha_shape_3 templates type definitions
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Kernel>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3>;
+
+// From file type definition
+using Point_3 = Kernel::Point_3;
+
+// filtration with alpha values needed type definition
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch =
+    CGAL::Dispatch_output_iterator<CGAL::cpp11::tuple<Object, Alpha_value_type>,
+                                   CGAL::cpp11::tuple<std::back_insert_iterator<std::vector<Object> >,
+                                                      std::back_insert_iterator<std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+
+#if BOOST_VERSION >= 105400
+using Vertex_list = boost::container::static_vector<Alpha_shape_3::Vertex_handle, 4>;
+#else
+using Vertex_list = std::vector<Alpha_shape_3::Vertex_handle>;
+#endif
+
+// gudhi type definition
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector<Simplex_tree_vertex>;
+
+void program_options(int argc, char *argv[], std::string &off_file_points, std::string &output_file_diag);
+
+int main(int argc, char **argv) {
+  std::string off_file_points;
+  std::string output_file_diag;
+
+  program_options(argc, argv, off_file_points, output_file_diag);
+
+  // Read the OFF file (input file name given as parameter) and triangulate points
+  Gudhi::Points_3D_off_reader<Point_3> off_reader(off_file_points);
+  // Check the read operation was correct
+  if (!off_reader.is_valid()) {
+    std::cerr << "Unable to read file " << off_file_points << std::endl;
+    exit(-1);
+  }
+
+  // Retrieve the points
+  std::vector<Point_3> lp = off_reader.get_point_cloud();
+
+  // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode.
+  Alpha_shape_3 as(lp.begin(), lp.end(), 0, Alpha_shape_3::GENERAL);
+#ifdef DEBUG_TRACES
+  std::cout << "Alpha shape computed in GENERAL mode" << std::endl;
+#endif  // DEBUG_TRACES
+
+  // filtration with alpha values from alpha shape
+  std::vector<Object> the_objects;
+  std::vector<Alpha_value_type> the_alpha_values;
+
+  Dispatch disp = CGAL::dispatch_output<Object, Alpha_value_type>(std::back_inserter(the_objects),
+                                                                  std::back_inserter(the_alpha_values));
+
+  as.filtration_with_alpha_values(disp);
+#ifdef DEBUG_TRACES
+  std::cout << "filtration_with_alpha_values returns : " << the_objects.size() << " objects" << std::endl;
+#endif  // DEBUG_TRACES
+
+  Alpha_shape_3::size_type count_vertices = 0;
+  Alpha_shape_3::size_type count_edges = 0;
+  Alpha_shape_3::size_type count_facets = 0;
+  Alpha_shape_3::size_type count_cells = 0;
+
+  // Loop on objects vector
+  Vertex_list vertex_list;
+  ST simplex_tree;
+  Alpha_shape_simplex_tree_map map_cgal_simplex_tree;
+  std::vector<Alpha_value_type>::iterator the_alpha_value_iterator = the_alpha_values.begin();
+  for (auto object_iterator : the_objects) {
+    // Retrieve Alpha shape vertex list from object
+    if (const Cell_handle *cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
+      count_cells++;
+    } else if (const Facet *facet = CGAL::object_cast<Facet>(&object_iterator)) {
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
+      count_facets++;
+    } else if (const Edge_3 *edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
+      count_edges++;
+    } else if (const Vertex_handle *vertex = CGAL::object_cast<Vertex_handle>(&object_iterator)) {
+      count_vertices++;
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
+    }
+    // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
+    Simplex_tree_vector_vertex the_simplex;
+    for (auto the_alpha_shape_vertex : vertex_list) {
+      Alpha_shape_simplex_tree_map::iterator the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex);
+      if (the_map_iterator == map_cgal_simplex_tree.end()) {
+        // alpha shape not found
+        Simplex_tree_vertex vertex = map_cgal_simplex_tree.size();
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex.push_back(vertex);
+        map_cgal_simplex_tree.emplace(the_alpha_shape_vertex, vertex);
+      } else {
+        // alpha shape found
+        Simplex_tree_vertex vertex = the_map_iterator->second;
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex.push_back(vertex);
+      }
+    }
+    // Construction of the simplex_tree
+    Filtration_value filtr = /*std::sqrt*/ (*the_alpha_value_iterator);
+#ifdef DEBUG_TRACES
+    std::cout << "filtration = " << filtr << std::endl;
+#endif  // DEBUG_TRACES
+    simplex_tree.insert_simplex(the_simplex, filtr);
+    GUDHI_CHECK(the_alpha_value_iterator != the_alpha_values.end(), "CGAL provided more simplices than values");
+    ++the_alpha_value_iterator;
+  }
+
+#ifdef DEBUG_TRACES
+  std::cout << "vertices \t\t" << count_vertices << std::endl;
+  std::cout << "edges \t\t" << count_edges << std::endl;
+  std::cout << "facets \t\t" << count_facets << std::endl;
+  std::cout << "cells \t\t" << count_cells << std::endl;
+
+  std::cout << "Information of the Simplex Tree: " << std::endl;
+  std::cout << "  Number of vertices = " << simplex_tree.num_vertices() << " ";
+  std::cout << "  Number of simplices = " << simplex_tree.num_simplices() << std::endl << std::endl;
+  std::cout << "  Dimension = " << simplex_tree.dimension() << " ";
+#endif  // DEBUG_TRACES
+
+#ifdef DEBUG_TRACES
+  std::cout << "Iterator on vertices: " << std::endl;
+  for (auto vertex : simplex_tree.complex_vertex_range()) {
+    std::cout << vertex << " ";
+  }
+#endif  // DEBUG_TRACES
+
+  // Sort the simplices in the order of the filtration
+  simplex_tree.initialize_filtration();
+
+  std::streambuf* streambufffer;
+  std::ofstream ouput_file_stream;
+  if (output_file_diag != std::string()) {
+    ouput_file_stream.open(output_file_diag);
+    streambufffer = ouput_file_stream.rdbuf();
+  } else {
+    streambufffer = std::cout.rdbuf();
+  }
+
+  std::ostream output_stream(streambufffer);
+
+  // ----------------------------------------------------------------------------
+  // Display information about the alpha complex
+  // ----------------------------------------------------------------------------
+  output_stream << "Alpha complex is of dimension " << simplex_tree.dimension() <<
+                " - " << simplex_tree.num_simplices() << " simplices - " <<
+                                                                         simplex_tree.num_vertices() << " vertices." << std::endl;
+
+  output_stream << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" <<
+                std::endl;
+  for (auto f_simplex : simplex_tree.filtration_simplex_range()) {
+    output_stream << "   ( ";
+    for (auto vertex : simplex_tree.simplex_vertex_range(f_simplex)) {
+      output_stream << vertex << " ";
+    }
+    output_stream << ") -> " << "[" << simplex_tree.filtration(f_simplex) << "] ";
+    output_stream << std::endl;
+  }
+
+  return 0;
+}
+
+void program_options(int argc, char *argv[], std::string &off_file_points, std::string &output_file_diag) {
+  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 file containing a point set. Format is one point per line:   X1 ... Xd ");
+
+  po::options_description visible("Allowed options", 100);
+  visible.add_options()("help,h", "produce help message")(
+      "output-file,o", po::value<std::string>(&output_file_diag)->default_value(std::string()),
+      "Name of file in which the persistence diagram is written. Default print in std::cout");
+
+  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 << "Compute and displays the 3D Alpha 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;
+    exit(-1);
+  }
+}
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
index 50e344e8..1d171f7d 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
@@ -55,6 +55,22 @@ namespace Gudhi {
 
 namespace alpha_complex {
 
+/**
+ * \class Alpha_complex_3d Alpha_complex_3d.h gudhi/Alpha_complex_3d.h
+ * \brief Alpha complex data structure for 3d specific case.
+ *
+ * \ingroup alpha_complex
+ *
+ * \details
+ * The data structure is constructing a CGAL Delaunay triangulation (for more informations on CGAL Delaunay
+ * triangulation, please refer to the corresponding chapter in page http://doc.cgal.org/latest/Triangulation/) from a
+ * range of points or from an OFF file (cf. Points_off_reader).
+ *
+ * Please refer to \ref alpha_complex for examples.
+ *
+ * \remark When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex.
+ *
+ */
 template<typename AlphaComplex3dOptions>
 class Alpha_complex_3d {
   using Alpha_shape_3 = typename AlphaComplex3dOptions::Alpha_shape_3;
@@ -106,15 +122,24 @@ public:
 
   }
 
-  /** \brief Alpha_complex constructor from a list of points.
-*
-* Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
-*
-* @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d
-*
-* The type InputPointRange must be a range for which std::begin and
-* std::end return input iterators on a Kernel::Point_d.
-*/
+  /** \brief Alpha_complex constructor from a list of points and associated weights.
+  *
+  * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
+  * Weights values are explained on CGAL <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0">Alpha
+  * shape</a> and
+  * <a href="https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation">Regular
+  * triangulation</a> documentation.
+  *
+  * @exception std::invalid_argument In debug mode, if points and weights do not have the same size.
+  *
+  * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3
+  * @param[in] weights Range of weights on points. Points must be in AlphaComplex3dOptions::Point_3
+  *
+  * The type InputPointRange must be a range for which std::begin and
+  * std::end return input iterators on a AlphaComplex3dOptions::Point_3.
+  * The type WeightRange must be a range for which std::begin and
+  * std::end return an input iterator on a AlphaComplex3dOptions::Alpha_shape_3::FT.
+  */
   template<typename InputPointRange , typename WeightRange>
   Alpha_complex_3d(const InputPointRange& points, WeightRange weights) {
     static_assert(AlphaComplex3dOptions::weighted,
@@ -148,17 +173,29 @@ public:
 #endif  // DEBUG_TRACES
   }
 
-  /** \brief Alpha_complex constructor from a list of points.
-*
-* Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
-*
-* @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d
-*
-* The type InputPointRange must be a range for which std::begin and
-* std::end return input iterators on a Kernel::Point_d.
-*
-* @exception std::invalid_argument In case the number of simplices is more than Simplex_key type numeric limit.
-*/
+  /** \brief Alpha_complex constructor from a list of points and an iso-cuboid coordinates.
+  *
+  * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
+  *
+  * Refer to the <a href="https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html">CGAL’s 3D Periodic
+  * Triangulations User Manual </a> for more details.
+  * The periodicity is defined by an iso-oriented cuboid with diagonal opposite vertices (x_min, y_min, z_min) and
+  * (x_max, y_max, z_max).
+  *
+  * @exception std::invalid_argument In debug mode, if the size of the cuboid in every directions is not the same.
+  *
+  * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3
+  * @param[in] x_min Iso-oriented cuboid x_min.
+  * @param[in] y_min Iso-oriented cuboid y_min.
+  * @param[in] z_min Iso-oriented cuboid z_min.
+  * @param[in] x_max Iso-oriented cuboid x_max.
+  * @param[in] y_max Iso-oriented cuboid y_max.
+  * @param[in] z_max Iso-oriented cuboid z_max.
+  *
+  * The type InputPointRange must be a range for which std::begin and
+  * std::end return input iterators on a AlphaComplex3dOptions::Point_3.
+  * The type of x_min, y_min, z_min, x_max, y_max and z_max is AlphaComplex3dOptions::Alpha_shape_3::FT.
+  */
   template<typename InputPointRange>
   Alpha_complex_3d(const InputPointRange& points,
                    Alpha_value_type x_min, Alpha_value_type y_min, Alpha_value_type z_min,
@@ -200,15 +237,40 @@ public:
 
   }
 
-  /** \brief Alpha_complex constructor from a list of points.
-*
-* Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
-*
-* @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d
-*
-* The type InputPointRange must be a range for which std::begin and
-* std::end return input iterators on a Kernel::Point_d.
-*/
+  /** \brief Alpha_complex constructor from a list of points, associated weights and an iso-cuboid coordinates.
+  *
+  * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
+  *
+  * Weights values are explained on CGAL <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0">Alpha
+  * shape</a> and
+  * <a href="https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation">Regular
+  * triangulation</a> documentation.
+  *
+  * Refer to the <a href="https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html">CGAL’s 3D Periodic
+  * Triangulations User Manual</a> for more details.
+  * The periodicity is defined by an iso-oriented cuboid with diagonal opposite vertices (x_min, y_min, z_min) and
+  * (x_max, y_max, z_max).
+  *
+  * @exception std::invalid_argument In debug mode, if points and weights do not have the same size.
+  * @exception std::invalid_argument In debug mode, if the size of the cuboid in every directions is not the same.
+  * @exception std::invalid_argument In debug mode, if a weight is negative, zero, or greater than 1/64*cuboid length
+  * squared.
+  *
+  * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3
+  * @param[in] weights Range of weights on points. Points must be in AlphaComplex3dOptions::Point_3
+  * @param[in] x_min Iso-oriented cuboid x_min.
+  * @param[in] y_min Iso-oriented cuboid y_min.
+  * @param[in] z_min Iso-oriented cuboid z_min.
+  * @param[in] x_max Iso-oriented cuboid x_max.
+  * @param[in] y_max Iso-oriented cuboid y_max.
+  * @param[in] z_max Iso-oriented cuboid z_max.
+  *
+  * The type InputPointRange must be a range for which std::begin and
+  * std::end return input iterators on a AlphaComplex3dOptions::Point_3.
+  * The type WeightRange must be a range for which std::begin and
+  * std::end return an input iterator on a AlphaComplex3dOptions::Alpha_shape_3::FT.
+  * The type of x_min, y_min, z_min, x_max, y_max and z_max is AlphaComplex3dOptions::Alpha_shape_3::FT.
+  */
   template<typename InputPointRange , typename WeightRange>
   Alpha_complex_3d(const InputPointRange& points, WeightRange weights,
                    Alpha_value_type x_min, Alpha_value_type y_min, Alpha_value_type z_min,
diff --git a/src/Alpha_complex/utilities/CMakeLists.txt b/src/Alpha_complex/utilities/CMakeLists.txt
index b43fb6e2..86e761ef 100644
--- a/src/Alpha_complex/utilities/CMakeLists.txt
+++ b/src/Alpha_complex/utilities/CMakeLists.txt
@@ -15,7 +15,7 @@ if(CGAL_FOUND)
 
   endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.7.0)
 
-  if (NOT CGAL_VERSION VERSION_LESS 4.11.0)
+  if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
     add_executable(alpha_complex_3d_persistence alpha_complex_3d_persistence.cpp)
     target_link_libraries(alpha_complex_3d_persistence ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
     if (TBB_FOUND)
diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md
index 0fe98837..7ae5f913 100644
--- a/src/Alpha_complex/utilities/alphacomplex.md
+++ b/src/Alpha_complex/utilities/alphacomplex.md
@@ -12,15 +12,18 @@ Leave the lines above as it is required by the web site generator 'Jekyll'
 

 ## alpha_complex_persistence ##

 

-This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud.

+This program computes the persistent homology with coefficient field Z/pZ of

+the dD alpha complex built from a dD point cloud.

 The output diagram contains one bar per line, written with the convention:

 

 ```

    p dim birth death

 ```

 

-where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature,

-and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).

+where `dim` is the dimension of the homological feature, `birth` and `death`

+are respectively the birth and death of the feature, and `p` is the

+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be

+a prime number).

 

 **Usage**

 

@@ -29,15 +32,20 @@ and `p` is the characteristic of the field *Z/pZ* used for homology coefficients
 ```

 

 where

-`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

+`<input OFF file>` is the path to the input point cloud in

+[nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

 

 **Allowed options**

 

 * `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.

-* `-p [ --field-charac ]` (default = 11)     Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

+* `-o [ --output-file ]` Name of file in which the persistence diagram is

+written. Default print in standard output.

+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value

+for the Alpha complex construction.

+* `-p [ --field-charac ]` (default = 11)     Characteristic p of the

+coefficient field Z/pZ for computing homology.

+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature

+to be recorded. Enter a negative value to see zero length intervals.

 

 **Example**

 

@@ -51,13 +59,26 @@ N.B.:
 

 

 ## alpha_complex_3d_persistence ##

-This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:

+This program computes the persistent homology with coefficient field Z/pZ of

+the 3D alpha complex built from a 3D point cloud.

+One can use exact computation. It is slower, but it is necessary when points

+are on a grid for instance.

+Alpha complex 3d can be weighted and/or periodic (refer to the

+[CGAL's 3D Periodic Triangulations User Manual](

+https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html)

+for more details).

+

+The output diagram contains

+one bar per line, written with the convention:

 

 ```

 p dim birth death

 ```

 

-where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).

+where `dim` is the dimension of the homological feature, `birth` and `death`

+are respectively the birth and death of the feature, and `p` is the

+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be

+a prime number).

 

 **Usage**

 

@@ -65,14 +86,25 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are
    alpha_complex_3d_persistence [options] <input OFF file>

 ```

 

-where `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

+where `<input OFF file>` is the path to the input point cloud in

+[nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

 

 **Allowed options**

 

 * `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

+* `-o [ --output-file ]` Name of file in which the persistence diagram is

+written. Default print in standard output.

+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient

+field Z/pZ for computing homology.

+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature

+to be recorded. Enter a negative value to see zero length intervals.

+* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain.

+It must be in the format described

+[here](/doc/latest/fileformats.html#FileFormatsIsoCuboid).

+* `-w [ --weight-file ]` is the path to the file containing the weights of the

+points (one value per line).

+* `-e [ --exact ]` for the exact computation version (not compatible with

+weight and periodic version).

 

 **Example**

 

@@ -84,49 +116,16 @@ N.B.:
 

 * `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.

 * Filtration values are alpha square values.

-

-

-## exact_alpha_complex_3d_persistence ##

-

-Same as `alpha_complex_3d_persistence`, but using exact computation.

-It is slower, but it is necessary when points are on a grid for instance.

+* Weights values are explained on CGAL

+[Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)

+and

+[Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.

 

 

 

-## weighted_alpha_complex_3d_persistence ##

 

-Same as `alpha_complex_3d_persistence`, but using weighted points.

 

-**Usage**

-

-```

-   weighted_alpha_complex_3d_persistence [options] <input OFF file> <weights input file>

-```

-

-where

-

-* `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

-* `<input weights file>` is the path to the file containing the weights of the points (one value per line).

 

-**Allowed options**

-

-* `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

-

-**Example**

-

-```

-   weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45

-```

-

-

-N.B.:

-

-* Weights values are explained on CGAL [Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)

-and [Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.

-* Filtration values are alpha square values.

 

 

 ## periodic_alpha_complex_3d_persistence ##

diff --git a/src/common/doc/examples.h b/src/common/doc/examples.h
index 40f202c7..7c2a8f69 100644
--- a/src/common/doc/examples.h
+++ b/src/common/doc/examples.h
@@ -53,10 +53,6 @@
  * @example Spatial_searching/example_spatial_searching.cpp
  * @example Alpha_complex/alpha_complex_3d_persistence.cpp
  * @example Alpha_complex/alpha_complex_persistence.cpp
- * @example Alpha_complex/weighted_periodic_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/weighted_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/periodic_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/exact_alpha_complex_3d_persistence.cpp
  * @example Bottleneck_distance/bottleneck_distance.cpp
  * @example Witness_complex/weak_witness_persistence.cpp
  * @example Witness_complex/strong_witness_persistence.cpp
diff --git a/src/common/doc/installation.h b/src/common/doc/installation.h
index 12407c18..8f91e9c1 100644
--- a/src/common/doc/installation.h
+++ b/src/common/doc/installation.h
@@ -58,10 +58,6 @@ make doxygen
  * Library</a> (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed:
  * \li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html">
  * Alpha_complex/alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
  * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a>
  * 
@@ -84,8 +80,6 @@ make doxygen
  * Alpha_complex/Alpha_complex_from_points.cpp</a>
  * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
  * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
  * Persistent_cohomology/custom_persistence_sort.cpp</a>
  * 
@@ -132,8 +126,8 @@ make doxygen
  * Alpha_complex/Alpha_complex_from_points.cpp</a>
  * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
  * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
+ * \li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html">
+ * Alpha_complex/alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_bottleneck_distance_2alpha_rips_persistence_bottleneck_distance_8cpp-example.html">
  * Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp.cpp</a>
  * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
@@ -179,12 +173,6 @@ make doxygen
  * Alpha_complex/alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
  * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_bitmap_cubical_complex_2_bitmap_cubical_complex_8cpp-example.html">
  * Bitmap_cubical_complex/cubical_complex_persistence.cpp</a>
  * \li <a href="_bitmap_cubical_complex_2_bitmap_cubical_complex_periodic_boundary_conditions_8cpp-example.html">
@@ -223,10 +211,6 @@ make doxygen
  * Persistent_cohomology/rips_multifield_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2rips_persistence_step_by_step_8cpp-example.html">
  * Persistent_cohomology/rips_persistence_step_by_step.cpp</a>
- * \li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
  * Persistent_cohomology/custom_persistence_sort.cpp</a>
  * \li <a href="_rips_complex_2example_one_skeleton_rips_from_points_8cpp-example.html">
diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h
index db1e80ce..35b84d2e 100644
--- a/src/common/doc/main_page.h
+++ b/src/common/doc/main_page.h
@@ -29,7 +29,7 @@
       <b>Author:</b> Vincent Rouvreau<br>
       <b>Introduced in:</b> GUDHI 1.3.0<br>
       <b>Copyright:</b> GPL v3<br>
-      <b>Requires:</b> \ref cgal &ge; 4.7.0 and \ref eigen3
+      <b>Requires:</b> \ref cgal &ge; 4.11.0 and \ref eigen3
     </td>
     <td width="75%">
     Alpha_complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.<br>