Merge trunk + alpha complex fixes

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@753 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: a0a1f71420736a0a702e6dbc76bc010b36bf5e13

6 files changed, 131 insertions, 382 deletions

diff --git a/src/Alpha_complex/example/Alpha_complex_from_off.cpp b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
index 3ce4c7f4..b698d6d7 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_off.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
@@ -10,7 +10,7 @@
 void usage(char * const progName) {
   std::cerr << "Usage: " << progName << " filename.off alpha_square_max_value" << std::endl;
   std::cerr << "       i.e.: " << progName << " ../../data/points/alphacomplexdoc.off 60.0" << std::endl;
-  exit(-1);  // ----- >>
+  exit(-1); // ----- >>
 }
 
 int main(int argc, char **argv) {
@@ -37,12 +37,14 @@ int main(int argc, char **argv) {
 
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
   for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    std::cout << "   ( ";
-    for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
-      std::cout << vertex << " ";
+    if (alpha_complex_from_file.filtration(f_simplex) <= alpha_complex_from_file.filtration()) {
+      std::cout << "   ( ";
+      for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
+        std::cout << vertex << " ";
+      }
+      std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
+      std::cout << std::endl;
     }
-    std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
-    std::cout << std::endl;
   }
   return 0;
 }
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc.txt b/src/Alpha_complex/example/alphaoffreader_for_doc.txt
index 1153f097..71f29a00 100644
--- a/src/Alpha_complex/example/alphaoffreader_for_doc.txt
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc.txt
@@ -1,27 +1,27 @@
 Alpha complex is of dimension 2 - 25 simplices - 7 vertices.
 Iterator on alpha complex simplices in the filtration order, with [filtration value]:
+   ( 0 ) -> [0] 
    ( 1 ) -> [0] 
    ( 2 ) -> [0] 
    ( 3 ) -> [0] 
    ( 4 ) -> [0] 
    ( 5 ) -> [0] 
    ( 6 ) -> [0] 
-   ( 7 ) -> [0] 
-   ( 4 3 ) -> [6.25] 
-   ( 6 5 ) -> [7.25] 
-   ( 3 1 ) -> [8.5] 
-   ( 2 1 ) -> [9.25] 
-   ( 4 2 ) -> [10] 
-   ( 3 2 ) -> [11.25] 
-   ( 4 3 2 ) -> [12.5] 
-   ( 3 2 1 ) -> [12.9959] 
-   ( 7 6 ) -> [13.25] 
-   ( 5 3 ) -> [20] 
-   ( 7 5 ) -> [22.7367] 
-   ( 7 6 5 ) -> [22.7367] 
-   ( 7 4 ) -> [30.25] 
-   ( 7 3 ) -> [36.5] 
-   ( 7 4 3 ) -> [36.5] 
-   ( 7 5 3 ) -> [37.2449] 
-   ( 5 1 ) -> [59.7107] 
-   ( 5 3 1 ) -> [59.7107] 
+   ( 3 2 ) -> [6.25] 
+   ( 5 4 ) -> [7.25] 
+   ( 2 0 ) -> [8.5] 
+   ( 1 0 ) -> [9.25] 
+   ( 3 1 ) -> [10] 
+   ( 2 1 ) -> [11.25] 
+   ( 3 2 1 ) -> [12.5] 
+   ( 2 1 0 ) -> [12.9959] 
+   ( 6 5 ) -> [13.25] 
+   ( 4 2 ) -> [20] 
+   ( 6 4 ) -> [22.7367] 
+   ( 6 5 4 ) -> [22.7367] 
+   ( 6 3 ) -> [30.25] 
+   ( 6 2 ) -> [36.5] 
+   ( 6 3 2 ) -> [36.5] 
+   ( 6 4 2 ) -> [37.2449] 
+   ( 4 0 ) -> [59.7107] 
+   ( 4 2 0 ) -> [59.7107] 
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index 213436e0..518d1792 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -99,8 +99,6 @@ class Alpha_complex : public Simplex_tree<> {
   Delaunay_triangulation* triangulation_;
   /** \brief Kernel for triangulation_ functions access.*/
   Kernel kernel_;
-  /** \brief Maximum value for alpha square.*/
-  Filtration_value max_alpha_square_;
 
  public:
   /** \brief Alpha_complex constructor from an OFF file name.
@@ -110,14 +108,14 @@ class Alpha_complex : public Simplex_tree<> {
    * @param[in] off_file_name OFF file [path and] name.
    */
   Alpha_complex(const std::string& off_file_name, Filtration_value max_alpha_square)
-      : triangulation_(nullptr),
-      max_alpha_square_(max_alpha_square) {
+      : triangulation_(nullptr) {
     Gudhi::Delaunay_triangulation_off_reader<Delaunay_triangulation> off_reader(off_file_name);
     if (!off_reader.is_valid()) {
       std::cerr << "Alpha_complex - Unable to read file " << off_file_name << std::endl;
       exit(-1);  // ----- >>
     }
     triangulation_ = off_reader.get_complex();
+    set_filtration(max_alpha_square);
     init();
   }
 
@@ -126,9 +124,9 @@ class Alpha_complex : public Simplex_tree<> {
    * @param[in] triangulation_ptr Pointer on a Delaunay triangulation.
    */
   Alpha_complex(Delaunay_triangulation* triangulation_ptr, Filtration_value max_alpha_square)
-      : triangulation_(triangulation_ptr),
-      max_alpha_square_(max_alpha_square) {
-    init();
+      : triangulation_(triangulation_ptr) {
+   set_filtration(max_alpha_square);
+   init();
   }
 
   /** \brief Alpha_complex constructor from a list of points.
@@ -143,14 +141,14 @@ class Alpha_complex : public Simplex_tree<> {
   template<typename ForwardIterator >
   Alpha_complex(int dimension, size_type size, ForwardIterator firstPoint, ForwardIterator lastPoint,
                 Filtration_value max_alpha_square)
-      : triangulation_(nullptr),
-      max_alpha_square_(max_alpha_square) {
+      : triangulation_(nullptr) {
     triangulation_ = new Delaunay_triangulation(dimension);
     size_type inserted = triangulation_->insert(firstPoint, lastPoint);
     if (inserted != size) {
       std::cerr << "Alpha_complex - insertion failed " << inserted << " != " << size << std::endl;
       exit(-1);  // ----- >>
     }
+    set_filtration(max_alpha_square);
     init();
   }
 
@@ -169,8 +167,9 @@ class Alpha_complex : public Simplex_tree<> {
    * @warning Exception std::out_of_range is thrown in case vertex is not in the map vertex_handle_to_iterator_.
    */
   Point_d get_point(Vertex_handle vertex) {
-    if (vertex_handle_to_iterator_[vertex] != nullptr) {
-      return vertex_handle_to_iterator_[vertex]->point();
+    auto found_it = vertex_handle_to_iterator_.find(vertex);
+    if (found_it != vertex_handle_to_iterator_.end()) {
+      return found_it->second->point();
     } else {
       throw std::out_of_range("Vertex out of vector range");
     }
@@ -210,20 +209,21 @@ class Alpha_complex : public Simplex_tree<> {
     Vertex_handle vertex_handle = Vertex_handle();
     // Loop on triangulation vertices list
     for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
+      if (!triangulation_->is_infinite(*vit)) {
 #ifdef DEBUG_TRACES
-      std::cout << "Vertex insertion - " << vertex_handle << " -> " << vit->point() << std::endl;
+        std::cout << "Vertex insertion - " << vertex_handle << " -> " << vit->point() << std::endl;
 #endif  // DEBUG_TRACES
-      vertex_iterator_to_handle_[vit] = vertex_handle;
-      vertex_handle_to_iterator_[vertex_handle] = vit;
-      vertex_handle++;
+        vertex_iterator_to_handle_.emplace(vit, vertex_handle);
+        vertex_handle_to_iterator_.emplace(vertex_handle, vit);
+        vertex_handle++;
+      }
     }
     // --------------------------------------------------------------------------------------------
 
-    Filtration_value filtration_max = 0.0;
     // --------------------------------------------------------------------------------------------
     // Simplex_tree construction from loop on triangulation finite full cells list
     for (auto cit = triangulation_->finite_full_cells_begin(); cit != triangulation_->finite_full_cells_end(); ++cit) {
-      Vector_vertex vertex_full_cell;
+      Vector_vertex vertexVector;
 #ifdef DEBUG_TRACES
       std::cout << "Simplex_tree insertion ";
 #endif  // DEBUG_TRACES
@@ -233,149 +233,98 @@ class Alpha_complex : public Simplex_tree<> {
           std::cout << " " << vertex_iterator_to_handle_[*vit];
 #endif  // DEBUG_TRACES
           // Vector of vertex construction for simplex_tree structure
-          vertex_full_cell.push_back(vertex_iterator_to_handle_[*vit]);
+          vertexVector.push_back(vertex_iterator_to_handle_[*vit]);
         }
       }
 #ifdef DEBUG_TRACES
       std::cout << std::endl;
 #endif  // DEBUG_TRACES
-
-      Simplex_tree<> full_cell;
-      full_cell.set_dimension(triangulation_->maximal_dimension());
-      // Create a simplex tree containing only one of the full cells
-      Simplex_result insert_result = full_cell.insert_simplex_and_subfaces(vertex_full_cell);
+      // Insert each simplex and its subfaces in the simplex tree - filtration is NaN
+      Simplex_result insert_result = insert_simplex_and_subfaces(vertexVector,
+                                                                 std::numeric_limits<double>::quiet_NaN());
       if (!insert_result.second) {
         std::cerr << "Alpha_complex::init insert_simplex_and_subfaces failed" << std::endl;
         exit(-1);  // ----->>
       }
-      // +++ For i : d -> 0
-      for (int fc_decr_dim = full_cell.dimension(); (fc_decr_dim >= 0); fc_decr_dim--) {
-        // +++ Foreach Sigma of dim i
-        // No need to skip this loop in case alpha²(Sigma) > max_alpha_square_ because of
-        // if (fc_decr_dim == f_simplex_dim) which means "only for a full cell"
-        for (auto fc_simplex : full_cell.skeleton_simplex_range(fc_decr_dim)) {
-          int f_simplex_dim = full_cell.dimension(fc_simplex);
-          if (fc_decr_dim == f_simplex_dim) {
-            Vector_of_CGAL_points pointVector;
-            Vector_vertex current_vertex;
-#ifdef DEBUG_TRACES
-            std::cout << "Sigma of dim " << fc_decr_dim << " is";
-#endif  // DEBUG_TRACES
-            for (auto vertex : full_cell.simplex_vertex_range(fc_simplex)) {
-              pointVector.push_back(get_point(vertex));
-              current_vertex.push_back(vertex);
-#ifdef DEBUG_TRACES
-              std::cout << " " << vertex;
-#endif  // DEBUG_TRACES
-            }
+    }
+    // --------------------------------------------------------------------------------------------
+
+    // --------------------------------------------------------------------------------------------
+    // ### For i : d -> 0
+    for (int decr_dim = dimension(); decr_dim >= 0; decr_dim--) {
+      // ### Foreach Sigma of dim i
+      for (auto f_simplex : skeleton_simplex_range(decr_dim)) {
+        int f_simplex_dim = dimension(f_simplex);
+        if (decr_dim == f_simplex_dim) {
+          Vector_of_CGAL_points pointVector;
 #ifdef DEBUG_TRACES
-            std::cout << std::endl;
+          std::cout << "Sigma of dim " << decr_dim << " is";
 #endif  // DEBUG_TRACES
-            Simplex_handle sigma_handle = find(current_vertex);
-            bool skip_propagation = false;
-            // +++ If filt(Sigma) is NaN : filt(Sigma) = alpha²(Sigma)
-            if ((sigma_handle == null_simplex()) || isnan(filtration(sigma_handle))) {
-              Filtration_value alpha_complex_filtration = compute_alpha_square(pointVector.begin(), pointVector.end(),
-                                                                               f_simplex_dim);
-              if (alpha_complex_filtration <= max_alpha_square_) {
-                // Only insert Sigma in Simplex tree if alpha²(Sigma) <= max_alpha_square_
-                if (sigma_handle == null_simplex()) {
+          for (auto vertex : simplex_vertex_range(f_simplex)) {
+            pointVector.push_back(get_point(vertex));
 #ifdef DEBUG_TRACES
-                  std::cout << "Alpha_complex::init Sigma not found" << std::endl;
+            std::cout << " " << vertex;
 #endif  // DEBUG_TRACES
-                  insert_result = insert_simplex(current_vertex, std::numeric_limits<double>::quiet_NaN());
-                  if (!insert_result.second) {
-                    std::cerr << "Alpha_complex::init insert_simplex failed" << std::endl;
-                    exit(-1);  // ----->>
-                  }
-                  // Sigma is the new inserted simplex handle
-                  sigma_handle = insert_result.first;
-                }
+          }
 #ifdef DEBUG_TRACES
-                std::cout << "Alpha_complex::init filtration = " << alpha_complex_filtration << std::endl;
+          std::cout << std::endl;
 #endif  // DEBUG_TRACES
-                assign_filtration(sigma_handle, alpha_complex_filtration);
-                filtration_max = fmax(filtration_max, alpha_complex_filtration);
-              } else {
-                // if alpha²(Sigma) > max_alpha_square_ skip propagation
-                skip_propagation = true;
+          // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
+          if (isnan(filtration(f_simplex))) {
+            Filtration_value alpha_complex_filtration = 0.0;
+            // No need to compute squared_radius on a single point - alpha is 0.0
+            if (f_simplex_dim > 0) {
+              // squared_radius function initialization
+              Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object();
+
+              alpha_complex_filtration = squared_radius(pointVector.begin(), pointVector.end());
+            }
+            assign_filtration(f_simplex, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-                std::cout << "Alpha_complex::init skip propagation on this full cell" << std::endl;
+            std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << filtration(f_simplex) << std::endl;
 #endif  // DEBUG_TRACES
-              }
-            }  // --- If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
-            if ((filtration(sigma_handle) <= max_alpha_square_) && !skip_propagation) {
-              // Propagate alpha filtration value in Simplex tree if alpha²(Sigma) <= max_alpha_square_
-              // in case Sigma is not found AND not inserted (alpha_complex_filtration > max_alpha_square_),
-              // filtration(null_simplex()) returns INFINITY => no propagation
-              propagate_alpha_filtration(full_cell, fc_simplex, fc_decr_dim, sigma_handle);
-            }
           }
-        }  // --- Foreach Sigma of dim i
-      }  // --- For i : d -> 0
+          propagate_alpha_filtration(f_simplex, decr_dim);
+        }
+      }
     }
     // --------------------------------------------------------------------------------------------
-
-#ifdef DEBUG_TRACES
-    std::cout << "filtration_max=" << filtration_max << std::endl;
-#endif  // DEBUG_TRACES
-    set_filtration(filtration_max);
-  }
-
-  template<typename ForwardIterator >
-  Filtration_value compute_alpha_square(ForwardIterator firstPoint, ForwardIterator lastPoint, int f_simplex_dim) {
-    Filtration_value alpha_square_value = 0.0;
-    // No need to compute squared_radius on a single point - alpha is 0.0
-    if (f_simplex_dim > 0) {
-      // squared_radius function initialization
-      Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object();
-
-      alpha_square_value = squared_radius(firstPoint, lastPoint);
-    }
-    return alpha_square_value;
   }
 
-  void propagate_alpha_filtration(Simplex_tree& full_cell, Simplex_handle fc_simplex, int fc_decr_dim,
-                                  Simplex_handle sigma_handle) {
+  template<typename Simplex_handle>
+  void propagate_alpha_filtration(Simplex_handle f_simplex, int decr_dim) {
     // ### Foreach Tau face of Sigma
-    for (auto f_boundary : full_cell.boundary_simplex_range(fc_simplex)) {
+    for (auto f_boundary : boundary_simplex_range(f_simplex)) {
 #ifdef DEBUG_TRACES
       std::cout << " | --------------------------------------------------" << std::endl;
       std::cout << " | Tau ";
-#endif  // DEBUG_TRACES
-      Vector_vertex tau_vertex;
-      for (auto vertex : full_cell.simplex_vertex_range(f_boundary)) {
-        tau_vertex.push_back(vertex);
-#ifdef DEBUG_TRACES
+      for (auto vertex : simplex_vertex_range(f_boundary)) {
         std::cout << vertex << " ";
-#endif  // DEBUG_TRACES
       }
-#ifdef DEBUG_TRACES
       std::cout << "is a face of Sigma" << std::endl;
+      std::cout << " | isnan(filtration(Tau)=" << isnan(filtration(f_boundary)) << std::endl;
 #endif  // DEBUG_TRACES
-      Simplex_handle tau_handle = find(tau_vertex);
       // ### If filt(Tau) is not NaN
-
-      if ((tau_handle != null_simplex()) && (!isnan(filtration(tau_handle)))) {
+      if (!isnan(filtration(f_boundary))) {
         // ### filt(Tau) = fmin(filt(Tau), filt(Sigma))
-        Filtration_value alpha_complex_filtration = fmin(filtration(tau_handle), filtration(sigma_handle));
-        assign_filtration(tau_handle, alpha_complex_filtration);
-        // No need to check for filtration_max, alpha_complex_filtration is a min of an existing filtration value
+        Filtration_value alpha_complex_filtration = fmin(filtration(f_boundary), filtration(f_simplex));
+        assign_filtration(f_boundary, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-        std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << alpha_complex_filtration << std::endl;
+        std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << filtration(f_boundary) << std::endl;
 #endif  // DEBUG_TRACES
+        // ### Else
       } else {
         // No need to compute is_gabriel for dimension <= 2
         // i.e. : Sigma = (3,1) => Tau = 1
-        if (fc_decr_dim > 1) {
+        if (decr_dim > 1) {
           // insert the Tau points in a vector for is_gabriel function
           Vector_of_CGAL_points pointVector;
           Vertex_handle vertexForGabriel = Vertex_handle();
-          for (auto vertex : full_cell.simplex_vertex_range(f_boundary)) {
+          for (auto vertex : simplex_vertex_range(f_boundary)) {
             pointVector.push_back(get_point(vertex));
           }
           // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function
-          for (auto vertex : simplex_vertex_range(sigma_handle)) {
+          for (auto vertex : simplex_vertex_range(f_simplex)) {
             if (std::find(pointVector.begin(), pointVector.end(), get_point(vertex)) == pointVector.end()) {
               // vertex is not found in Tau
               vertexForGabriel = vertex;
@@ -392,24 +341,11 @@ class Alpha_complex : public Simplex_tree<> {
 #endif  // DEBUG_TRACES
           // ### If Tau is not Gabriel of Sigma
           if (false == is_gab) {
-            if (tau_handle == null_simplex()) {
-#ifdef DEBUG_TRACES
-              std::cout << " | Tau not found" << std::endl;
-#endif  // DEBUG_TRACES
-              // in case Tau is not yet created
-              Simplex_result insert_result = insert_simplex(tau_vertex, std::numeric_limits<double>::quiet_NaN());
-              if (!insert_result.second) {
-                std::cerr << "Alpha_complex::propagate_alpha_filtration insert_simplex failed" << std::endl;
-                exit(-1);  // ----->>
-              }
-              // Sigma is the new inserted simplex handle
-              tau_handle = insert_result.first;
-            }
             // ### filt(Tau) = filt(Sigma)
-            assign_filtration(tau_handle, filtration(sigma_handle));
-            // No need to check for filtration_max, alpha_complex_filtration is an existing filtration value
+            Filtration_value alpha_complex_filtration = filtration(f_simplex);
+            assign_filtration(f_boundary, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-            std::cout << " | filt(Tau) = filt(Sigma) = " << filtration(sigma_handle) << std::endl;
+            std::cout << " | filt(Tau) = filt(Sigma) = " << filtration(f_boundary) << std::endl;
 #endif  // DEBUG_TRACES
           }
         }
diff --git a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
index c15f07e1..b2597eff 100644
--- a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
+++ b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
@@ -40,144 +40,68 @@
 typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel_d;
 // The triangulation uses the default instantiation of the TriangulationDataStructure template parameter
 
-BOOST_AUTO_TEST_CASE(S4_100_OFF_file) {
+BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file) {
   // ----------------------------------------------------------------------------
   //
   // Init of an alpha-complex from a OFF file
   //
   // ----------------------------------------------------------------------------
-  std::string off_file_name("S4_100.off");
-  double max_alpha_square_value = 1e10;
-  std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
-      max_alpha_square_value << "==========" << std::endl;
-
-  Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
-
-  const int DIMENSION = 4;
-  std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
-
-  const int NUMBER_OF_VERTICES = 100;
-  std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
-
-  const int NUMBER_OF_SIMPLICES = 6879;
-  std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
-
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
-}
-
-BOOST_AUTO_TEST_CASE(S4_100_OFF_file_filtered) {
-  // ----------------------------------------------------------------------------
-  //
-  // Init of an alpha-complex from a OFF file
-  //
-  // ----------------------------------------------------------------------------
-  std::string off_file_name("S4_100.off");
-  double max_alpha_square_value = 0.999;
+  std::string off_file_name("../../../data/points/alphacomplexdoc.off");
+  double max_alpha_square_value = 60.0;
   std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
       max_alpha_square_value << "==========" << std::endl;
 
   Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
 
-  const int DIMENSION = 4;
+  const int DIMENSION = 2;
   std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
 
-  const int NUMBER_OF_VERTICES = 100;
+  const int NUMBER_OF_VERTICES = 7;
   std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
 
-  const int NUMBER_OF_SIMPLICES = 5966;  // Versus 6879, because of filtered alpha value
+  const int NUMBER_OF_SIMPLICES = 25;
   std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
 }
 
-BOOST_AUTO_TEST_CASE(S8_10_OFF_file) {
+BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file_filtered) {
   // ----------------------------------------------------------------------------
   //
   // Init of an alpha-complex from a OFF file
   //
   // ----------------------------------------------------------------------------
-  std::string off_file_name("S8_10.off");
-  double max_alpha_square_value = 1e10;
+  std::string off_file_name("../../../data/points/alphacomplexdoc.off");
+  double max_alpha_square_value = 59.0;
   std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
       max_alpha_square_value << "==========" << std::endl;
 
   Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
 
-  const int DIMENSION = 8;
+  const int DIMENSION = 2;
   std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
 
-  const int NUMBER_OF_VERTICES = 10;
+  const int NUMBER_OF_VERTICES = 7;
   std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
 
-  const int NUMBER_OF_SIMPLICES = 1007;
+  const int NUMBER_OF_SIMPLICES = 25;
   std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
+  int num_filtered_simplices = 0;
   for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
+    if (alpha_complex_from_file.filtration(f_simplex) <= alpha_complex_from_file.filtration()) {
+      num_filtered_simplices++;
+    }
   }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
-}
-
-BOOST_AUTO_TEST_CASE(S8_10_OFF_file_filtered) {
-  // ----------------------------------------------------------------------------
-  //
-  // Init of an alpha-complex from a OFF file
-  //
-  // ----------------------------------------------------------------------------
-  std::string off_file_name("S8_10.off");
-  double max_alpha_square_value = 1.0;
-  std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
-      max_alpha_square_value << "==========" << std::endl;
-
-  Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
-
-  const int DIMENSION = 8;
-  std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
-
-  const int NUMBER_OF_VERTICES = 10;
-  std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
-
-  const int NUMBER_OF_SIMPLICES = 1004;  // Versus 1007, because of filtered alpha value
-  std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  const int NUMBER_OF_FILTERED_SIMPLICES = 23;
+  std::cout << "num_filtered_simplices=" << num_filtered_simplices << std::endl;
+  BOOST_CHECK(num_filtered_simplices == NUMBER_OF_FILTERED_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
 }
 
 bool are_almost_the_same(float a, float b) {
@@ -222,10 +146,11 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
 
   std::cout << "========== Alpha_complex_from_points ==========" << std::endl;
 
+  // Another way to check num_simplices
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
-  int num_simplices = 0;  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
+  int num_simplices = 0;
   for (auto f_simplex : alpha_complex_from_points.filtration_simplex_range()) {
-    num_simplices++;  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
+    num_simplices++;
     std::cout << "   ( ";
     for (auto vertex : alpha_complex_from_points.simplex_vertex_range(f_simplex)) {
       std::cout << vertex << " ";
@@ -233,13 +158,12 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
     std::cout << ") -> " << "[" << alpha_complex_from_points.filtration(f_simplex) << "] ";
     std::cout << std::endl;
   }
+  BOOST_CHECK(num_simplices == 15);
+  std::cout << "alpha_complex_from_points.num_simplices()=" << alpha_complex_from_points.num_simplices() << std::endl;
+  BOOST_CHECK(alpha_complex_from_points.num_simplices() == 15);
 
   std::cout << "alpha_complex_from_points.dimension()=" << alpha_complex_from_points.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_points.dimension() == 4);
-  // TODO(VR) : std::cout << "alpha_complex_from_points.num_simplices()=" << alpha_complex_from_points.num_simplices()
-  // << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_points.num_simplices() == 15);
-  BOOST_CHECK(num_simplices == 15);  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
   std::cout << "alpha_complex_from_points.num_vertices()=" << alpha_complex_from_points.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_points.num_vertices() == 4);
 
@@ -263,6 +187,11 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
     }
   }
 
+  Point p0 = alpha_complex_from_points.get_point(0);
+  std::cout << "alpha_complex_from_points.get_point(0)=" << p0 << std::endl;
+  BOOST_CHECK(4 == p0.dimension());
+  BOOST_CHECK(is_point_in_list(points, p0));
+
   Point p1 = alpha_complex_from_points.get_point(1);
   std::cout << "alpha_complex_from_points.get_point(1)=" << p1 << std::endl;
   BOOST_CHECK(4 == p1.dimension());
@@ -278,12 +207,8 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
   BOOST_CHECK(4 == p3.dimension());
   BOOST_CHECK(is_point_in_list(points, p3));
 
-  Point p4 = alpha_complex_from_points.get_point(4);
-  std::cout << "alpha_complex_from_points.get_point(4)=" << p4 << std::endl;
-  BOOST_CHECK(4 == p4.dimension());
-  BOOST_CHECK(is_point_in_list(points, p4));
-
-  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(5), std::out_of_range);
-  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(0), std::out_of_range);
+  // Test to the limit
+  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(4), std::out_of_range);
+  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(-1), std::out_of_range);
   BOOST_CHECK_THROW (alpha_complex_from_points.get_point(1234), std::out_of_range);
 }
diff --git a/src/Alpha_complex/test/S4_100.off b/src/Alpha_complex/test/S4_100.off
deleted file mode 100644
index cd017e12..00000000
--- a/src/Alpha_complex/test/S4_100.off
+++ /dev/null
@@ -1,102 +0,0 @@
-nOFF
-4 100 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_complex/test/S8_10.off b/src/Alpha_complex/test/S8_10.off
deleted file mode 100644
index 4e147c44..00000000
--- a/src/Alpha_complex/test/S8_10.off
+++ /dev/null
@@ -1,12 +0,0 @@
-nOFF
-8 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