Merge alpha_complex_3d_module_vincent after second review round

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@4014 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: d2f4f38b34ef898ed3b1f267278aaa2ae4cab58f

11 files changed, 769 insertions, 644 deletions

diff --git a/src/Alpha_complex/benchmark/Alpha_complex_3d_benchmark.cpp b/src/Alpha_complex/benchmark/Alpha_complex_3d_benchmark.cpp
index 1a33f2b4..005a712a 100644
--- a/src/Alpha_complex/benchmark/Alpha_complex_3d_benchmark.cpp
+++ b/src/Alpha_complex/benchmark/Alpha_complex_3d_benchmark.cpp
@@ -25,7 +25,7 @@ void benchmark_points_on_torus_dD(const std::string& msg) {
   results_csv << "\"nb_points\";"
               << "\"nb_simplices\";"
               << "\"alpha_creation_time(sec.)\";"
-              << "\"simplex_creation_time(sec.)\";" << std::endl;
+              << "\"complex_creation_time(sec.)\";" << std::endl;
 
   using K = CGAL::Epick_d<CGAL::Dimension_tag<3>>;
   for (int nb_points = 1000; nb_points <= 125000; nb_points *= 5) {
@@ -43,17 +43,17 @@ void benchmark_points_on_torus_dD(const std::string& msg) {
     ac_create_clock.end();
     std::cout << ac_create_clock;
 
-    Gudhi::Simplex_tree<> simplex;
-    Gudhi::Clock st_create_clock("    benchmark_points_on_torus_dD - simplex tree creation");
+    Gudhi::Simplex_tree<> complex;
+    Gudhi::Clock st_create_clock("    benchmark_points_on_torus_dD - complex creation");
     st_create_clock.begin();
-    alpha_complex_from_points.create_complex(simplex);
+    alpha_complex_from_points.create_complex(complex);
     st_create_clock.end();
     std::cout << st_create_clock;
 
-    results_csv << nb_points << ";" << simplex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
+    results_csv << nb_points << ";" << complex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
                 << st_create_clock.num_seconds() << ";" << std::endl;
 
-    std::cout << "    benchmark_points_on_torus_dD - nb simplices = " << simplex.num_simplices() << std::endl;
+    std::cout << "    benchmark_points_on_torus_dD - nb simplices = " << complex.num_simplices() << std::endl;
   }
 }
 
@@ -66,7 +66,7 @@ void benchmark_points_on_torus_3D(const std::string& msg) {
   results_csv << "\"nb_points\";"
               << "\"nb_simplices\";"
               << "\"alpha_creation_time(sec.)\";"
-              << "\"simplex_creation_time(sec.)\";" << std::endl;
+              << "\"complex_creation_time(sec.)\";" << std::endl;
 
   for (int nb_points = 1000; nb_points <= 125000; nb_points *= 5) {
     std::cout << "  Alpha complex 3d on torus with " << nb_points << " points." << std::endl;
@@ -83,17 +83,17 @@ void benchmark_points_on_torus_3D(const std::string& msg) {
     ac_create_clock.end();
     std::cout << ac_create_clock;
 
-    Gudhi::Simplex_tree<> simplex;
-    Gudhi::Clock st_create_clock("    benchmark_points_on_torus_3D - simplex tree creation");
+    Gudhi::Simplex_tree<> complex;
+    Gudhi::Clock st_create_clock("    benchmark_points_on_torus_3D - complex creation");
     st_create_clock.begin();
-    alpha_complex_from_points.create_complex(simplex);
+    alpha_complex_from_points.create_complex(complex);
     st_create_clock.end();
     std::cout << st_create_clock;
 
-    results_csv << nb_points << ";" << simplex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
+    results_csv << nb_points << ";" << complex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
                 << st_create_clock.num_seconds() << ";" << std::endl;
 
-    std::cout << "    benchmark_points_on_torus_3D - nb simplices = " << simplex.num_simplices() << std::endl;
+    std::cout << "    benchmark_points_on_torus_3D - nb simplices = " << complex.num_simplices() << std::endl;
   }
 }
 
@@ -107,7 +107,7 @@ void benchmark_weighted_points_on_torus_3D(const std::string& msg) {
   results_csv << "\"nb_points\";"
               << "\"nb_simplices\";"
               << "\"alpha_creation_time(sec.)\";"
-              << "\"simplex_creation_time(sec.)\";" << std::endl;
+              << "\"complex_creation_time(sec.)\";" << std::endl;
 
   CGAL::Random random(8);
 
@@ -116,7 +116,7 @@ void benchmark_weighted_points_on_torus_3D(const std::string& msg) {
     std::vector<K::Point_d> points_on_torus = Gudhi::generate_points_on_torus_3D<K>(nb_points, 1.0, 0.5);
 
     using Point = typename Weighted_alpha_complex_3d::Point_3;
-    using Weighted_point = typename Weighted_alpha_complex_3d::Triangulation_3::Weighted_point;
+    using Weighted_point = typename Weighted_alpha_complex_3d::Weighted_point_3;
 
     std::vector<Weighted_point> points;
 
@@ -130,17 +130,17 @@ void benchmark_weighted_points_on_torus_3D(const std::string& msg) {
     ac_create_clock.end();
     std::cout << ac_create_clock;
 
-    Gudhi::Simplex_tree<> simplex;
-    Gudhi::Clock st_create_clock("    benchmark_weighted_points_on_torus_3D - simplex tree creation");
+    Gudhi::Simplex_tree<> complex;
+    Gudhi::Clock st_create_clock("    benchmark_weighted_points_on_torus_3D - complex creation");
     st_create_clock.begin();
-    alpha_complex_from_points.create_complex(simplex);
+    alpha_complex_from_points.create_complex(complex);
     st_create_clock.end();
     std::cout << st_create_clock;
 
-    results_csv << nb_points << ";" << simplex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
+    results_csv << nb_points << ";" << complex.num_simplices() << ";" << ac_create_clock.num_seconds() << ";"
                 << st_create_clock.num_seconds() << ";" << std::endl;
 
-    std::cout << "    benchmark_weighted_points_on_torus_3D - nb simplices = " << simplex.num_simplices() << std::endl;
+    std::cout << "    benchmark_weighted_points_on_torus_3D - nb simplices = " << complex.num_simplices() << std::endl;
   }
 }
 
@@ -152,7 +152,7 @@ void benchmark_periodic_points(const std::string& msg) {
   results_csv << "\"nb_points\";"
               << "\"nb_simplices\";"
               << "\"alpha_creation_time(sec.)\";"
-              << "\"simplex_creation_time(sec.)\";" << std::endl;
+              << "\"complex_creation_time(sec.)\";" << std::endl;
 
   CGAL::Random random(8);
 
@@ -176,17 +176,17 @@ void benchmark_periodic_points(const std::string& msg) {
     ac_create_clock.end();
     std::cout << ac_create_clock;
 
-    Gudhi::Simplex_tree<> simplex;
-    Gudhi::Clock st_create_clock("    benchmark_periodic_points - simplex tree creation");
+    Gudhi::Simplex_tree<> complex;
+    Gudhi::Clock st_create_clock("    benchmark_periodic_points - complex creation");
     st_create_clock.begin();
-    alpha_complex_from_points.create_complex(simplex);
+    alpha_complex_from_points.create_complex(complex);
     st_create_clock.end();
     std::cout << st_create_clock;
 
-    results_csv << nb_points * nb_points * nb_points << ";" << simplex.num_simplices() << ";"
+    results_csv << nb_points * nb_points * nb_points << ";" << complex.num_simplices() << ";"
                 << ac_create_clock.num_seconds() << ";" << st_create_clock.num_seconds() << ";" << std::endl;
 
-    std::cout << "    benchmark_periodic_points - nb simplices = " << simplex.num_simplices() << std::endl;
+    std::cout << "    benchmark_periodic_points - nb simplices = " << complex.num_simplices() << std::endl;
   }
 }
 
@@ -198,7 +198,7 @@ void benchmark_weighted_periodic_points(const std::string& msg) {
   results_csv << "\"nb_points\";"
               << "\"nb_simplices\";"
               << "\"alpha_creation_time(sec.)\";"
-              << "\"simplex_creation_time(sec.)\";" << std::endl;
+              << "\"complex_creation_time(sec.)\";" << std::endl;
 
   CGAL::Random random(8);
 
@@ -207,7 +207,7 @@ void benchmark_weighted_periodic_points(const std::string& msg) {
               << std::endl;
 
     using Point = typename Weighted_periodic_alpha_complex_3d::Point_3;
-    using Weighted_point = typename Weighted_periodic_alpha_complex_3d::Triangulation_3::Weighted_point;
+    using Weighted_point = typename Weighted_periodic_alpha_complex_3d::Weighted_point_3;
     std::vector<Weighted_point> points;
 
     for (double i = 0; i < nb_points; i++) {
@@ -226,17 +226,17 @@ void benchmark_weighted_periodic_points(const std::string& msg) {
     ac_create_clock.end();
     std::cout << ac_create_clock;
 
-    Gudhi::Simplex_tree<> simplex;
-    Gudhi::Clock st_create_clock("    benchmark_weighted_periodic_points - simplex tree creation");
+    Gudhi::Simplex_tree<> complex;
+    Gudhi::Clock st_create_clock("    benchmark_weighted_periodic_points - complex creation");
     st_create_clock.begin();
-    alpha_complex_from_points.create_complex(simplex);
+    alpha_complex_from_points.create_complex(complex);
     st_create_clock.end();
     std::cout << st_create_clock;
 
-    results_csv << nb_points * nb_points * nb_points << ";" << simplex.num_simplices() << ";"
+    results_csv << nb_points * nb_points * nb_points << ";" << complex.num_simplices() << ";"
                 << ac_create_clock.num_seconds() << ";" << st_create_clock.num_seconds() << ";" << std::endl;
 
-    std::cout << "    benchmark_weighted_periodic_points - nb simplices = " << simplex.num_simplices() << std::endl;
+    std::cout << "    benchmark_weighted_periodic_points - nb simplices = " << complex.num_simplices() << std::endl;
   }
 }
 
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h
index 2fe9f4ca..ab7c4794 100644
--- a/src/Alpha_complex/doc/Intro_alpha_complex.h
+++ b/src/Alpha_complex/doc/Intro_alpha_complex.h
@@ -168,8 +168,10 @@ namespace alpha_complex {
  *
  * \section weighted3dexample 3d specific example
  *
- * A specific module for Alpha complex is available in 3d (cf. Alpha_complex_3d) and allows to construct default, exact,
- * weighted, periodic or weighted and periodic versions of alpha complexes
+ * A specific module for Alpha complex is available in 3d (cf. Alpha_complex_3d) and allows to construct standard,
+ * weighted, periodic or weighted and periodic versions of alpha complexes. Alpha values computation can be
+ * Gudhi::alpha_complex::complexity::FAST, Gudhi::alpha_complex::complexity::SAFE (default value) or
+ * Gudhi::alpha_complex::complexity::EXACT.
  *
  * This example builds the CGAL 3d weighted alpha shapes from a small molecule, and initializes the alpha complex with
  * it. This example is taken from <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title13">CGAL 3d
diff --git a/src/Alpha_complex/example/Alpha_complex_3d_from_points.cpp b/src/Alpha_complex/example/Alpha_complex_3d_from_points.cpp
index 3acebd2e..0e359a27 100644
--- a/src/Alpha_complex/example/Alpha_complex_3d_from_points.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_3d_from_points.cpp
@@ -7,7 +7,7 @@
 #include <vector>
 #include <limits>  // for numeric limits
 
-using Alpha_complex_3d = Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, false>;
+using Alpha_complex_3d = Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, false>;
 using Point = Alpha_complex_3d::Point_3;
 using Vector_of_points = std::vector<Point>;
 
diff --git a/src/Alpha_complex/example/Weighted_alpha_complex_3d_from_points.cpp b/src/Alpha_complex/example/Weighted_alpha_complex_3d_from_points.cpp
index 68f72f0a..ac11b68c 100644
--- a/src/Alpha_complex/example/Weighted_alpha_complex_3d_from_points.cpp
+++ b/src/Alpha_complex/example/Weighted_alpha_complex_3d_from_points.cpp
@@ -7,24 +7,17 @@
 #include <vector>
 #include <limits>  // for numeric limits
 
+// Complexity = FAST, weighted = true, periodic = false
 using Weighted_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, false>;
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
 using Point = Weighted_alpha_complex_3d::Point_3;
-using Weighted_point = Weighted_alpha_complex_3d::Triangulation_3::Weighted_point;
-using Vector_of_weighted_points = std::vector<Weighted_point>;
-using Vector_of_weights = std::vector<Weighted_alpha_complex_3d::Alpha_shape_3::FT>;
+using Weighted_point = Weighted_alpha_complex_3d::Weighted_point_3;
 
 int main(int argc, char **argv) {
-  if (argc != 1) {
-    std::cerr << "Error: Number of arguments (" << argc << ") is not correct\n";
-    std::cerr << "Usage: " << (argv[0] - 1) << " \n";
-    exit(-1);  // ----- >>
-  }
-
   // ----------------------------------------------------------------------------
   // Init of a list of points and weights from a small molecule
   // ----------------------------------------------------------------------------
-  Vector_of_weighted_points weighted_points;
+  std::vector<Weighted_point> weighted_points;
   weighted_points.push_back(Weighted_point(Point(1, -1, -1), 4.));
   weighted_points.push_back(Weighted_point(Point(-1, 1, -1), 4.));
   weighted_points.push_back(Weighted_point(Point(-1, -1, 1), 4.));
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
index 00a47d5c..19445637 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
@@ -26,10 +26,6 @@
 #include <boost/version.hpp>
 #include <boost/variant.hpp>
 
-#if BOOST_VERSION >= 105400
-#include <boost/container/static_vector.hpp>
-#endif
-
 #include <gudhi/Debug_utils.h>
 #include <gudhi/Alpha_complex_options.h>
 
@@ -50,6 +46,8 @@
 #include <CGAL/iterator.h>
 #include <CGAL/version.h>
 
+#include <boost/container/static_vector.hpp>
+
 #include <iostream>
 #include <vector>
 #include <unordered_map>
@@ -60,7 +58,7 @@
 
 #if CGAL_VERSION_NR < 1041101000
 // Make compilation fail - required for external projects - https://gitlab.inria.fr/GUDHI/gudhi-devel/issues/10
-static_assert(false, "Alpha_complex_3d is only available for CGAL >= 4.11");
+# error Alpha_complex_3d is only available for CGAL >= 4.11
 #endif
 
 namespace Gudhi {
@@ -74,62 +72,22 @@ thread_local
 
 // Value_from_iterator returns the filtration value from an iterator on alpha shapes values
 //
-//                        FAST                         SAFE                         EXACT
-// not weighted and       *iterator                    Specific case due to CGAL    CGAL::to_double(iterator->exact())
-// not periodic                                        issue # 3153
-//
-// otherwise              *iterator                    CGAL::to_double(*iterator)   CGAL::to_double(iterator->exact())
+// FAST                         SAFE                         EXACT
+// CGAL::to_double(*iterator)   CGAL::to_double(*iterator)   CGAL::to_double(iterator->exact())
 
-template <complexity Complexity, bool Weighted_or_periodic>
+template <complexity Complexity>
 struct Value_from_iterator {
   template <typename Iterator>
   static double perform(Iterator it) {
-    // Default behaviour is to return the value pointed by the given iterator
-    return *it;
-  }
-};
-
-template <>
-struct Value_from_iterator<complexity::SAFE, true> {
-  template <typename Iterator>
-  static double perform(Iterator it) {
-    // In SAFE mode, we are with Epick with EXACT value set to CGAL::Tag_true.
+    // Default behaviour
     return CGAL::to_double(*it);
   }
 };
 
 template <>
-struct Value_from_iterator<complexity::SAFE, false> {
+struct Value_from_iterator<complexity::EXACT> {
   template <typename Iterator>
   static double perform(Iterator it) {
-    // In SAFE mode, we are with Epeck with EXACT value set to CGAL::Tag_true.
-    // Specific case due to CGAL issue https://github.com/CGAL/cgal/issues/3153
-    auto approx = it->approx();
-    double r;
-    if (CGAL::fit_in_double(approx, r)) return r;
-
-    // If it's precise enough, then OK.
-    if (CGAL::has_smaller_relative_precision(approx, RELATIVE_PRECISION_OF_TO_DOUBLE)) return CGAL::to_double(approx);
-
-    it->exact();
-    return CGAL::to_double(it->approx());
-  }
-};
-
-template <>
-struct Value_from_iterator<complexity::EXACT, true> {
-  template <typename Iterator>
-  static double perform(Iterator it) {
-    // In EXACT mode, we are with Epeck or Epick with EXACT value set to CGAL::Tag_true.
-    return CGAL::to_double(it->exact());
-  }
-};
-
-template <>
-struct Value_from_iterator<complexity::EXACT, false> {
-  template <typename Iterator>
-  static double perform(Iterator it) {
-    // In EXACT mode, we are with Epeck or Epick with EXACT value set to CGAL::Tag_true.
     return CGAL::to_double(it->exact());
   }
 };
@@ -145,8 +103,8 @@ struct Value_from_iterator<complexity::EXACT, false> {
  * Shapes</a> from a range of points (can be read from an OFF file, cf. Points_off_reader).
  * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous.
  *
- * \tparam Complexity shall be `Gudhi::alpha_complex::complexity`. Default value is
- * `Gudhi::alpha_complex::complexity::FAST`.
+ * \tparam Complexity shall be `Gudhi::alpha_complex::complexity` type. Default value is
+ * `Gudhi::alpha_complex::complexity::SAFE`.
  *
  * \tparam Weighted Boolean used to set/unset the weighted version of Alpha_complex_3d. Default value is false.
  *
@@ -169,22 +127,22 @@ struct Value_from_iterator<complexity::EXACT, false> {
  * 3d Delaunay complex.
  *
  */
-template <complexity Complexity = complexity::FAST, bool Weighted = false, bool Periodic = false>
+template <complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>
 class Alpha_complex_3d {
   // Epick = Exact_predicates_inexact_constructions_kernel
   // Epeck = Exact_predicates_exact_constructions_kernel
-  // ExactAlphaComparisonTag = exact version of CGAL Alpha_shape_3 and of its objects (Alpha_shape_vertex_base_3 and
+  // Exact_alpha_comparison_tag = exact version of CGAL Alpha_shape_3 and of its objects (Alpha_shape_vertex_base_3 and
   //                           Alpha_shape_cell_base_3). Not available if weighted or periodic.
-  //                           Can be CGAL::Tag_false or CGAL::Tag_true
+  //                           Can be CGAL::Tag_false or CGAL::Tag_true. Default is False.
   //                           cf. https://doc.cgal.org/latest/Alpha_shapes_3/classCGAL_1_1Alpha__shape__3.html
   //
+  // We could use Epick + CGAL::Tag_true for not weighted nor periodic, but during benchmark, we found a bug
+  // https://github.com/CGAL/cgal/issues/3460
+  // This is the reason we only use Epick + CGAL::Tag_false, or Epeck
   //
-  //                        FAST                         SAFE                         EXACT
-  // not weighted and       Epick + CGAL::Tag_false      Epick + CGAL::Tag_true       Epick + CGAL::Tag_true
-  // not periodic
-  //
-  // otherwise              Epick + CGAL::Tag_false      Epeck                        Epeck
-  using Predicates = typename std::conditional<((!Weighted && !Periodic) || (Complexity == complexity::FAST)),
+  // FAST                         SAFE                         EXACT
+  // Epick + CGAL::Tag_false      Epeck                        Epeck
+  using Predicates = typename std::conditional<(Complexity == complexity::FAST),
                                                CGAL::Exact_predicates_inexact_constructions_kernel,
                                                CGAL::Exact_predicates_exact_constructions_kernel>::type;
 
@@ -192,14 +150,11 @@ class Alpha_complex_3d {
   template <typename Predicates, bool Weighted_version, bool Periodic_version>
   struct Kernel_3 {};
 
-  template <typename Predicates>
-  struct Kernel_3<Predicates, false, false> {
-    using Kernel = Predicates;
-  };
-  template <typename Predicates>
-  struct Kernel_3<Predicates, true, false> {
+  template <typename Predicates, bool Is_periodic>
+  struct Kernel_3<Predicates, Is_periodic, false> {
     using Kernel = Predicates;
   };
+
   template <typename Predicates>
   struct Kernel_3<Predicates, false, true> {
     using Kernel = CGAL::Periodic_3_Delaunay_triangulation_traits_3<Predicates>;
@@ -211,15 +166,13 @@ class Alpha_complex_3d {
 
   using Kernel = typename Kernel_3<Predicates, Weighted, Periodic>::Kernel;
 
-  using Exact_tag = typename std::conditional<(Complexity == complexity::FAST), CGAL::Tag_false, CGAL::Tag_true>::type;
-
   using TdsVb = typename std::conditional<Periodic, CGAL::Periodic_3_triangulation_ds_vertex_base_3<>,
                                           CGAL::Triangulation_ds_vertex_base_3<>>::type;
 
   using Tvb = typename std::conditional<Weighted, CGAL::Regular_triangulation_vertex_base_3<Kernel, TdsVb>,
                                         CGAL::Triangulation_vertex_base_3<Kernel, TdsVb>>::type;
 
-  using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel, Tvb, Exact_tag>;
+  using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel, Tvb>;
 
   using TdsCb = typename std::conditional<Periodic, CGAL::Periodic_3_triangulation_ds_cell_base_3<>,
                                           CGAL::Triangulation_ds_cell_base_3<>>::type;
@@ -227,64 +180,101 @@ class Alpha_complex_3d {
   using Tcb = typename std::conditional<Weighted, CGAL::Regular_triangulation_cell_base_3<Kernel, TdsCb>,
                                         CGAL::Triangulation_cell_base_3<Kernel, TdsCb>>::type;
 
-  using Cb = CGAL::Alpha_shape_cell_base_3<Kernel, Tcb, Exact_tag>;
+  using Cb = CGAL::Alpha_shape_cell_base_3<Kernel, Tcb>;
   using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb>;
 
   // The other way to do a conditional type. Here there 4 possibilities, cannot use std::conditional
   template <typename Kernel, typename Tds, bool Weighted_version, bool Periodic_version>
-  struct Triangulation {};
+  struct Triangulation_3 {};
 
   template <typename Kernel, typename Tds>
-  struct Triangulation<Kernel, Tds, false, false> {
-    using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+  struct Triangulation_3<Kernel, Tds, false, false> {
+    using Dt = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+    using Weighted_point_3 = void;
   };
   template <typename Kernel, typename Tds>
-  struct Triangulation<Kernel, Tds, true, false> {
-    using Triangulation_3 = CGAL::Regular_triangulation_3<Kernel, Tds>;
+  struct Triangulation_3<Kernel, Tds, true, false> {
+    using Dt = CGAL::Regular_triangulation_3<Kernel, Tds>;
+    using Weighted_point_3 = typename Dt::Weighted_point;
   };
   template <typename Kernel, typename Tds>
-  struct Triangulation<Kernel, Tds, false, true> {
-    using Triangulation_3 = CGAL::Periodic_3_Delaunay_triangulation_3<Kernel, Tds>;
+  struct Triangulation_3<Kernel, Tds, false, true> {
+    using Dt = CGAL::Periodic_3_Delaunay_triangulation_3<Kernel, Tds>;
+    using Weighted_point_3 = void;
   };
   template <typename Kernel, typename Tds>
-  struct Triangulation<Kernel, Tds, true, true> {
-    using Triangulation_3 = CGAL::Periodic_3_regular_triangulation_3<Kernel, Tds>;
+  struct Triangulation_3<Kernel, Tds, true, true> {
+    using Dt = CGAL::Periodic_3_regular_triangulation_3<Kernel, Tds>;
+    using Weighted_point_3 = typename Dt::Weighted_point;
   };
 
- public:
-  using Triangulation_3 = typename Triangulation<Kernel, Tds, Weighted, Periodic>::Triangulation_3;
-
-  using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3, Exact_tag>;
+  /** \brief Is either Delaunay_triangulation_3 (Weighted = false and Periodic = false),
+   * Regular_triangulation_3 (Weighted = true and Periodic = false),
+   * Periodic_3_Delaunay_triangulation_3 (Weighted = false and Periodic = true)
+   * or Periodic_3_regular_triangulation_3 (Weighted = true and Periodic = true).
+   *
+   * This type is required by `Gudhi::alpha_complex::Alpha_complex_3d::Alpha_shape_3`.
+   * */
+  using Dt = typename Triangulation_3<Kernel, Tds, Weighted, Periodic>::Dt;
 
+public:
+  /** \brief The <a href="https://doc.cgal.org/latest/Alpha_shapes_3/classCGAL_1_1Alpha__shape__3.html">CGAL 3D Alpha
+   * Shapes</a> type.
+   *
+   *  The `Gudhi::alpha_complex::Alpha_complex_3d` is a wrapper on top of this class to ease the standard, weighted
+   *  and/or periodic build of the Alpha complex 3d.*/
+  using Alpha_shape_3 = CGAL::Alpha_shape_3<Dt>;
+
+  /** \brief The alpha values type.
+   * Must be compatible with double. */
+  using FT = typename Alpha_shape_3::FT;
+
+  /** \brief Gives public access to the Point_3 type. Here is a Point_3 constructor example:
+\code{.cpp}
+using Alpha_complex_3d = Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, false>;
+
+// x0 = 1., y0 = -1.1, z0 = -1..
+Alpha_complex_3d::Point_3 p0(1., -1.1, -1.);
+\endcode
+   * */
   using Point_3 = typename Kernel::Point_3;
 
- private:
-  using Alpha_value_type = typename Alpha_shape_3::FT;
+  /** \brief Gives public access to the Weighted_point_3 type. A Weighted point can be constructed as follows:
+\code{.cpp}
+using Weighted_alpha_complex_3d =
+  Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
+
+// x0 = 1., y0 = -1.1, z0 = -1., weight = 4.
+Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Point_3(1., -1.1, -1.), 4.);
+\endcode
+ *
+ * Note: This type is defined to void if Alpha complex is not weighted.
+ *
+ * */
+  using Weighted_point_3 = typename Triangulation_3<Kernel, Tds, Weighted, Periodic>::Weighted_point_3;
+
+private:
   using Dispatch =
-      CGAL::Dispatch_output_iterator<CGAL::cpp11::tuple<CGAL::Object, Alpha_value_type>,
+      CGAL::Dispatch_output_iterator<CGAL::cpp11::tuple<CGAL::Object, FT>,
                                      CGAL::cpp11::tuple<std::back_insert_iterator<std::vector<CGAL::Object>>,
-                                                        std::back_insert_iterator<std::vector<Alpha_value_type>>>>;
+                                                        std::back_insert_iterator<std::vector<FT>>>>;
 
   using Cell_handle = typename Alpha_shape_3::Cell_handle;
   using Facet = typename Alpha_shape_3::Facet;
   using Edge = typename Alpha_shape_3::Edge;
   using Alpha_vertex_handle = typename Alpha_shape_3::Vertex_handle;
-#if BOOST_VERSION >= 105400
   using Vertex_list = boost::container::static_vector<Alpha_vertex_handle, 4>;
-#else
-  using Vertex_list = std::vector<Alpha_vertex_handle>;
-#endif
 
  public:
   /** \brief Alpha_complex constructor from a list of points.
    *
    * @param[in] points Range of points to triangulate. Points must be in `Alpha_complex_3d::Point_3` or
-   * `Alpha_complex_3d::Triangulation_3::Weighted_point`.
+   * `Alpha_complex_3d::Weighted_point_3`.
    *
    * @pre Available if Alpha_complex_3d is not Periodic.
    *
    * The type InputPointRange must be a range for which std::begin and std::end return input iterators on a
-   * `Alpha_complex_3d::Point_3` or a `Alpha_complex_3d::Triangulation_3::Weighted_point`.
+   * `Alpha_complex_3d::Point_3` or a `Alpha_complex_3d::Weighted_point_3`.
    */
   template <typename InputPointRange>
   Alpha_complex_3d(const InputPointRange& points) {
@@ -298,15 +288,15 @@ class Alpha_complex_3d {
    *
    * @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 `Alpha_complex_3d::Point_3`
-   * @param[in] weights Range of weights on points. Weights shall be in `Alpha_complex_3d::Alpha_shape_3::FT`
+   * @param[in] points Range of points to triangulate. Points must be in `Alpha_complex_3d::Point_3`.
+   * @param[in] weights Range of weights on points. Weights shall be in double.
    *
    * @pre Available if Alpha_complex_3d is Weighted and not Periodic.
    *
    * The type InputPointRange must be a range for which std::begin and
    * std::end return input iterators on a `Alpha_complex_3d::Point_3`.
    * The type WeightRange must be a range for which std::begin and
-   * std::end return an input iterator on a `Alpha_complex_3d::Alpha_shape_3::FT`.
+   * std::end return an input iterator on a double.
    */
   template <typename InputPointRange, typename WeightRange>
   Alpha_complex_3d(const InputPointRange& points, WeightRange weights) {
@@ -315,7 +305,6 @@ class Alpha_complex_3d {
     GUDHI_CHECK((weights.size() == points.size()),
                 std::invalid_argument("Points number in range different from weights range number"));
 
-    using Weighted_point_3 = typename Triangulation_3::Weighted_point;
     std::vector<Weighted_point_3> weighted_points_3;
 
     std::size_t index = 0;
@@ -334,7 +323,7 @@ class Alpha_complex_3d {
    * @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 `Alpha_complex_3d::Point_3` or
-   * `Alpha_complex_3d::Triangulation_3::Weighted_point`.
+   * `Alpha_complex_3d::Weighted_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.
@@ -345,14 +334,14 @@ class Alpha_complex_3d {
    * @pre Available if Alpha_complex_3d is Periodic.
    *
    * The type InputPointRange must be a range for which std::begin and std::end return input iterators on a
-   * `Alpha_complex_3d::Point_3` or a `Alpha_complex_3d::Triangulation_3::Weighted_point`.
+   * `Alpha_complex_3d::Point_3` or a `Alpha_complex_3d::Weighted_point_3`.
    *
    * @note In weighted version, please check weights are greater than zero, and lower than 1/64*cuboid length
    * squared.
    */
   template <typename InputPointRange>
-  Alpha_complex_3d(const InputPointRange& points, Alpha_value_type x_min, Alpha_value_type y_min,
-                   Alpha_value_type z_min, Alpha_value_type x_max, Alpha_value_type y_max, Alpha_value_type z_max) {
+  Alpha_complex_3d(const InputPointRange& points, FT x_min, FT y_min,
+                   FT z_min, FT x_max, FT y_max, FT z_max) {
     static_assert(Periodic, "This constructor is not available for non-periodic versions of Alpha_complex_3d");
     // Checking if the cuboid is the same in x,y and z direction. If not, CGAL will not process it.
     GUDHI_CHECK(
@@ -360,7 +349,7 @@ class Alpha_complex_3d {
         std::invalid_argument("The size of the cuboid in every directions is not the same."));
 
     // Define the periodic cube
-    Triangulation_3 pdt(typename Kernel::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
+    Dt pdt(typename Kernel::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
     // Heuristic for inserting large point sets (if pts is reasonably large)
     pdt.insert(std::begin(points), std::end(points), true);
     // As pdt won't be modified anymore switch to 1-sheeted cover if possible
@@ -381,8 +370,8 @@ class Alpha_complex_3d {
    * @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 `Alpha_complex_3d::Point_3`
-   * @param[in] weights Range of weights on points. Weights shall be in `Alpha_complex_3d::Alpha_shape_3::FT`
+   * @param[in] points Range of points to triangulate. Points must be in `Alpha_complex_3d::Point_3`.
+   * @param[in] weights Range of weights on points. Weights shall be in double.
    * @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.
@@ -395,12 +384,12 @@ class Alpha_complex_3d {
    * The type InputPointRange must be a range for which std::begin and
    * std::end return input iterators on a `Alpha_complex_3d::Point_3`.
    * The type WeightRange must be a range for which std::begin and
-   * std::end return an input iterator on a `Alpha_complex_3d::Alpha_shape_3::FT`.
-   * The type of x_min, y_min, z_min, x_max, y_max and z_max is `Alpha_complex_3d::Alpha_shape_3::FT`.
+   * std::end return an input iterator on a double.
+   * The type of x_min, y_min, z_min, x_max, y_max and z_max must be a double.
    */
   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, Alpha_value_type x_max, Alpha_value_type y_max, Alpha_value_type z_max) {
+  Alpha_complex_3d(const InputPointRange& points, WeightRange weights, FT x_min, FT y_min,
+                   FT z_min, FT x_max, FT y_max, FT z_max) {
     static_assert(Weighted, "This constructor is not available for non-weighted versions of Alpha_complex_3d");
     static_assert(Periodic, "This constructor is not available for non-periodic versions of Alpha_complex_3d");
     GUDHI_CHECK((weights.size() == points.size()),
@@ -410,7 +399,6 @@ class Alpha_complex_3d {
         (x_max - x_min == y_max - y_min) && (x_max - x_min == z_max - z_min) && (z_max - z_min == y_max - y_min),
         std::invalid_argument("The size of the cuboid in every directions is not the same."));
 
-    using Weighted_point_3 = typename Triangulation_3::Weighted_point;
     std::vector<Weighted_point_3> weighted_points_3;
 
     std::size_t index = 0;
@@ -418,7 +406,7 @@ class Alpha_complex_3d {
 
 #ifdef GUDHI_DEBUG
     // Defined in GUDHI_DEBUG to avoid unused variable warning for GUDHI_CHECK
-    Alpha_value_type maximal_possible_weight = 0.015625 * (x_max - x_min) * (x_max - x_min);
+    FT maximal_possible_weight = 0.015625 * (x_max - x_min) * (x_max - x_min);
 #endif
 
     while ((index < weights.size()) && (index < points.size())) {
@@ -431,7 +419,7 @@ class Alpha_complex_3d {
     }
 
     // Define the periodic cube
-    Triangulation_3 pdt(typename Kernel::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
+    Dt pdt(typename Kernel::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
     // Heuristic for inserting large point sets (if pts is reasonably large)
     pdt.insert(std::begin(weighted_points_3), std::end(weighted_points_3), true);
     // As pdt won't be modified anymore switch to 1-sheeted cover if possible
@@ -451,13 +439,12 @@ class Alpha_complex_3d {
    * \tparam SimplicialComplexForAlpha3d must meet `SimplicialComplexForAlpha3d` concept.
    *
    * @param[in] complex SimplicialComplexForAlpha3d to be created.
-   * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$.
+   * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$, and there is very
+   * little point using anything else since it does not save time.
    *
    * @return true if creation succeeds, false otherwise.
    *
-   * @pre The simplicial complex must be empty (no vertices)
-   *
-   * Initialization can be launched once.
+   * @pre The simplicial complex must be empty (no vertices).
    *
    */
   template <typename SimplicialComplexForAlpha3d,
@@ -481,9 +468,9 @@ class Alpha_complex_3d {
     std::size_t count_cells = 0;
 #endif  // DEBUG_TRACES
     std::vector<CGAL::Object> objects;
-    std::vector<Alpha_value_type> alpha_values;
+    std::vector<FT> alpha_values;
 
-    Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, Alpha_value_type>(std::back_inserter(objects),
+    Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, FT>(std::back_inserter(objects),
                                                                                 std::back_inserter(alpha_values));
 
     alpha_shape_3_ptr_->filtration_with_alpha_values(dispatcher);
@@ -492,7 +479,7 @@ class Alpha_complex_3d {
 #endif  // DEBUG_TRACES
 
     Alpha_shape_simplex_tree_map map_cgal_simplex_tree;
-    using Alpha_value_iterator = typename std::vector<Alpha_value_type>::const_iterator;
+    using Alpha_value_iterator = typename std::vector<FT>::const_iterator;
     Alpha_value_iterator alpha_value_iterator = alpha_values.begin();
     for (auto object_iterator : objects) {
       Vertex_list vertex_list;
@@ -559,7 +546,7 @@ class Alpha_complex_3d {
         }
       }
       // Construction of the simplex_tree
-      Filtration_value filtr = Value_from_iterator<Complexity, (Weighted || Periodic)>::perform(alpha_value_iterator);
+      Filtration_value filtr = Value_from_iterator<Complexity>::perform(alpha_value_iterator);
 
 #ifdef DEBUG_TRACES
       std::cout << "filtration = " << filtr << std::endl;
diff --git a/src/Alpha_complex/test/Alpha_complex_3d_unit_test.cpp b/src/Alpha_complex/test/Alpha_complex_3d_unit_test.cpp
index 9e071195..ec905d5b 100644
--- a/src/Alpha_complex/test/Alpha_complex_3d_unit_test.cpp
+++ b/src/Alpha_complex/test/Alpha_complex_3d_unit_test.cpp
@@ -23,7 +23,6 @@
 #define BOOST_TEST_DYN_LINK
 #define BOOST_TEST_MODULE "alpha_complex_3d"
 #include <boost/test/unit_test.hpp>
-#include <boost/mpl/list.hpp>
 
 #include <cmath>  // float comparison
 #include <limits>
@@ -49,41 +48,27 @@ using Safe_alpha_complex_3d =
 using Exact_alpha_complex_3d =
     Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, false>;
 
-using Fast_weighted_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, false>;
-using Safe_weighted_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
-using Exact_weighted_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, false>;
-
-using Fast_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, false, true>;
-using Safe_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, true>;
-using Exact_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, true>;
+template <typename Point>
+std::vector<Point> get_points() {
+  std::vector<Point> points;
+  points.push_back(Point(0.0, 0.0, 0.0));
+  points.push_back(Point(0.0, 0.0, 0.2));
+  points.push_back(Point(0.2, 0.0, 0.2));
+  points.push_back(Point(0.6, 0.6, 0.0));
+  points.push_back(Point(0.8, 0.8, 0.2));
+  points.push_back(Point(0.2, 0.8, 0.6));
+
+  return points;
+}
 
-using Fast_weighted_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, true>;
-using Safe_weighted_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, true>;
-using Exact_weighted_periodic_alpha_complex_3d =
-    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, true>;
 
 BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   // -----------------
   // Fast version
   // -----------------
   std::cout << "Fast alpha complex 3d" << std::endl;
-  std::vector<Fast_alpha_complex_3d::Point_3> points;
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.0, 0.0, 0.0));
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.0, 0.0, 0.2));
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.2, 0.0, 0.2));
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.6, 0.6, 0.0));
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.8, 0.8, 0.2));
-  points.push_back(Fast_alpha_complex_3d::Point_3(0.2, 0.8, 0.6));
 
-  Fast_alpha_complex_3d alpha_complex(points);
+  Fast_alpha_complex_3d alpha_complex(get_points<Fast_alpha_complex_3d::Point_3>());
 
   Gudhi::Simplex_tree<> stree;
   alpha_complex.create_complex(stree);
@@ -93,7 +78,7 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   // -----------------
   std::cout << "Exact alpha complex 3d" << std::endl;
 
-  Exact_alpha_complex_3d exact_alpha_complex(points);
+  Exact_alpha_complex_3d exact_alpha_complex(get_points<Exact_alpha_complex_3d::Point_3>());
 
   Gudhi::Simplex_tree<> exact_stree;
   exact_alpha_complex.create_complex(exact_stree);
@@ -101,13 +86,13 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   // ---------------------
   // Compare both versions
   // ---------------------
-  std::cout << "Exact Alpha complex 3d is of dimension " << exact_stree.dimension() << " - Non exact is "
+  std::cout << "Exact Alpha complex 3d is of dimension " << exact_stree.dimension() << " - Fast is "
             << stree.dimension() << std::endl;
   BOOST_CHECK(exact_stree.dimension() == stree.dimension());
-  std::cout << "Exact Alpha complex 3d num_simplices " << exact_stree.num_simplices() << " - Non exact is "
+  std::cout << "Exact Alpha complex 3d num_simplices " << exact_stree.num_simplices() << " - Fast is "
             << stree.num_simplices() << std::endl;
   BOOST_CHECK(exact_stree.num_simplices() == stree.num_simplices());
-  std::cout << "Exact Alpha complex 3d num_vertices " << exact_stree.num_vertices() << " - Non exact is "
+  std::cout << "Exact Alpha complex 3d num_vertices " << exact_stree.num_vertices() << " - Fast is "
             << stree.num_vertices() << std::endl;
   BOOST_CHECK(exact_stree.num_vertices() == stree.num_vertices());
 
@@ -115,19 +100,18 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   while (sh != stree.filtration_simplex_range().end()) {
     std::vector<int> simplex;
     std::vector<int> exact_simplex;
-    std::cout << "Non-exact ( ";
+    std::cout << "Fast ( ";
     for (auto vertex : stree.simplex_vertex_range(*sh)) {
       simplex.push_back(vertex);
       std::cout << vertex << " ";
     }
-    std::cout << ") -> "
-              << "[" << stree.filtration(*sh) << "] ";
-    std::cout << std::endl;
+    std::cout << ") -> [" << stree.filtration(*sh) << "] ";
 
     // Find it in the exact structure
     auto sh_exact = exact_stree.find(simplex);
     BOOST_CHECK(sh_exact != exact_stree.null_simplex());
 
+    std::cout << " versus [" << exact_stree.filtration(sh_exact) << "] " << std::endl;
     // Exact and non-exact version is not exactly the same due to float comparison
     GUDHI_TEST_FLOAT_EQUALITY_CHECK(exact_stree.filtration(sh_exact), stree.filtration(*sh));
 
@@ -138,7 +122,7 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   // -----------------
   std::cout << "Safe alpha complex 3d" << std::endl;
 
-  Safe_alpha_complex_3d safe_alpha_complex(points);
+  Safe_alpha_complex_3d safe_alpha_complex(get_points<Safe_alpha_complex_3d::Point_3>());
 
   Gudhi::Simplex_tree<> safe_stree;
   safe_alpha_complex.create_complex(safe_stree);
@@ -146,13 +130,13 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   // ---------------------
   // Compare both versions
   // ---------------------
-  std::cout << "Exact Alpha complex 3d is of dimension " << safe_stree.dimension() << " - Non exact is "
+  std::cout << "Safe Alpha complex 3d is of dimension " << safe_stree.dimension() << " - Fast is "
             << stree.dimension() << std::endl;
   BOOST_CHECK(safe_stree.dimension() == stree.dimension());
-  std::cout << "Exact Alpha complex 3d num_simplices " << safe_stree.num_simplices() << " - Non exact is "
+  std::cout << "Safe Alpha complex 3d num_simplices " << safe_stree.num_simplices() << " - Fast is "
             << stree.num_simplices() << std::endl;
   BOOST_CHECK(safe_stree.num_simplices() == stree.num_simplices());
-  std::cout << "Exact Alpha complex 3d num_vertices " << safe_stree.num_vertices() << " - Non exact is "
+  std::cout << "Safe Alpha complex 3d num_vertices " << safe_stree.num_vertices() << " - Fast is "
             << stree.num_vertices() << std::endl;
   BOOST_CHECK(safe_stree.num_vertices() == stree.num_vertices());
 
@@ -160,453 +144,21 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_3d_from_points) {
   while (safe_sh != stree.filtration_simplex_range().end()) {
     std::vector<int> simplex;
     std::vector<int> exact_simplex;
-#ifdef DEBUG_TRACES
-    std::cout << "Non-exact ( ";
-#endif
+    std::cout << "Fast ( ";
     for (auto vertex : stree.simplex_vertex_range(*safe_sh)) {
       simplex.push_back(vertex);
-#ifdef DEBUG_TRACES
       std::cout << vertex << " ";
-#endif
     }
-#ifdef DEBUG_TRACES
-    std::cout << ") -> "
-              << "[" << stree.filtration(*safe_sh) << "] ";
-    std::cout << std::endl;
-#endif
+    std::cout << ") -> [" << stree.filtration(*safe_sh) << "] ";
 
     // Find it in the exact structure
     auto sh_exact = safe_stree.find(simplex);
     BOOST_CHECK(sh_exact != safe_stree.null_simplex());
 
+    std::cout << " versus [" << safe_stree.filtration(sh_exact) << "] " << std::endl;
     // Exact and non-exact version is not exactly the same due to float comparison
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(safe_stree.filtration(sh_exact), stree.filtration(*safe_sh));
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(safe_stree.filtration(sh_exact), stree.filtration(*safe_sh), 1e-15);
 
     ++safe_sh;
   }
 }
-
-typedef boost::mpl::list<Fast_weighted_alpha_complex_3d, Safe_weighted_alpha_complex_3d,
-                         Exact_weighted_alpha_complex_3d>
-    weighted_variants_type_list;
-
-#ifdef GUDHI_DEBUG
-BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted_throw, Weighted_alpha_complex_3d, weighted_variants_type_list) {
-  using Point_3 = typename Weighted_alpha_complex_3d::Point_3;
-  std::vector<Point_3> w_points;
-  w_points.push_back(Point_3(0.0, 0.0, 0.0));
-  w_points.push_back(Point_3(0.0, 0.0, 0.2));
-  w_points.push_back(Point_3(0.2, 0.0, 0.2));
-  // w_points.push_back(Point_3(0.6, 0.6, 0.0));
-  // w_points.push_back(Point_3(0.8, 0.8, 0.2));
-  // w_points.push_back(Point_3(0.2, 0.8, 0.6));
-
-  // weights size is different from w_points size to make weighted Alpha_complex_3d throw in debug mode
-  std::vector<double> weights = {0.01, 0.005, 0.006, 0.01, 0.009, 0.001};
-
-  std::cout << "Check exception throw in debug mode" << std::endl;
-  BOOST_CHECK_THROW(Weighted_alpha_complex_3d wac(w_points, weights), std::invalid_argument);
-}
-#endif
-
-BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted, Weighted_alpha_complex_3d, weighted_variants_type_list) {
-  std::cout << "Weighted alpha complex 3d from points and weights" << std::endl;
-  using Point_3 = typename Weighted_alpha_complex_3d::Point_3;
-  std::vector<Point_3> w_points;
-  w_points.push_back(Point_3(0.0, 0.0, 0.0));
-  w_points.push_back(Point_3(0.0, 0.0, 0.2));
-  w_points.push_back(Point_3(0.2, 0.0, 0.2));
-  w_points.push_back(Point_3(0.6, 0.6, 0.0));
-  w_points.push_back(Point_3(0.8, 0.8, 0.2));
-  w_points.push_back(Point_3(0.2, 0.8, 0.6));
-
-  // weights size is different from w_points size to make weighted Alpha_complex_3d throw in debug mode
-  std::vector<double> weights = {0.01, 0.005, 0.006, 0.01, 0.009, 0.001};
-
-  Weighted_alpha_complex_3d alpha_complex_p_a_w(w_points, weights);
-  Gudhi::Simplex_tree<> stree;
-  alpha_complex_p_a_w.create_complex(stree);
-
-  std::cout << "Weighted alpha complex 3d from weighted points" << std::endl;
-  using Weighted_point_3 = typename Weighted_alpha_complex_3d::Triangulation_3::Weighted_point;
-
-  std::vector<Weighted_point_3> weighted_points;
-
-  for (std::size_t i = 0; i < w_points.size(); i++) {
-    weighted_points.push_back(Weighted_point_3(w_points[i], weights[i]));
-  }
-  Weighted_alpha_complex_3d alpha_complex_w_p(weighted_points);
-
-  Gudhi::Simplex_tree<> stree_bis;
-  alpha_complex_w_p.create_complex(stree_bis);
-
-  // ---------------------
-  // Compare both versions
-  // ---------------------
-  std::cout << "Weighted alpha complex 3d is of dimension " << stree_bis.dimension() << " - versus "
-            << stree.dimension() << std::endl;
-  BOOST_CHECK(stree_bis.dimension() == stree.dimension());
-  std::cout << "Weighted alpha complex 3d num_simplices " << stree_bis.num_simplices() << " - versus "
-            << stree.num_simplices() << std::endl;
-  BOOST_CHECK(stree_bis.num_simplices() == stree.num_simplices());
-  std::cout << "Weighted alpha complex 3d num_vertices " << stree_bis.num_vertices() << " - versus "
-            << stree.num_vertices() << std::endl;
-  BOOST_CHECK(stree_bis.num_vertices() == stree.num_vertices());
-
-  auto sh = stree.filtration_simplex_range().begin();
-  while (sh != stree.filtration_simplex_range().end()) {
-    std::vector<int> simplex;
-    std::vector<int> exact_simplex;
-#ifdef DEBUG_TRACES
-    std::cout << " ( ";
-#endif
-    for (auto vertex : stree.simplex_vertex_range(*sh)) {
-      simplex.push_back(vertex);
-#ifdef DEBUG_TRACES
-      std::cout << vertex << " ";
-#endif
-    }
-#ifdef DEBUG_TRACES
-    std::cout << ") -> "
-              << "[" << stree.filtration(*sh) << "] ";
-    std::cout << std::endl;
-#endif
-
-    // Find it in the exact structure
-    auto sh_exact = stree_bis.find(simplex);
-    BOOST_CHECK(sh_exact != stree_bis.null_simplex());
-
-    // Exact and non-exact version is not exactly the same due to float comparison
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree_bis.filtration(sh_exact), stree.filtration(*sh));
-
-    ++sh;
-  }
-}
-
-#ifdef GUDHI_DEBUG
-typedef boost::mpl::list<Fast_periodic_alpha_complex_3d, Safe_periodic_alpha_complex_3d,
-                         Exact_periodic_alpha_complex_3d>
-    periodic_variants_type_list;
-
-BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_periodic_throw, Periodic_alpha_complex_3d, periodic_variants_type_list) {
-  std::cout << "Periodic alpha complex 3d exception throw" << std::endl;
-  using Point_3 = typename Periodic_alpha_complex_3d::Point_3;
-  std::vector<Point_3> p_points;
-
-  // Not important, this is not what we want to check
-  p_points.push_back(Point_3(0.0, 0.0, 0.0));
-
-  std::cout << "Check exception throw in debug mode" << std::endl;
-  // Check it throws an exception when the cuboid is not iso
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 0.9, 1., 1.),
-                    std::invalid_argument);
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 0.9, 1.),
-                    std::invalid_argument);
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1., 0.9),
-                    std::invalid_argument);
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1.1, 1., 1.),
-                    std::invalid_argument);
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1.1, 1.),
-                    std::invalid_argument);
-  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1., 1.1),
-                    std::invalid_argument);
-}
-#endif
-
-BOOST_AUTO_TEST_CASE(Alpha_complex_periodic) {
-  // ---------------------
-  // Fast periodic version
-  // ---------------------
-  std::cout << "Fast periodic alpha complex 3d" << std::endl;
-
-  using Creator = CGAL::Creator_uniform_3<double, Fast_periodic_alpha_complex_3d::Point_3>;
-  CGAL::Random random(7);
-  CGAL::Random_points_in_cube_3<Fast_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
-  std::vector<Fast_periodic_alpha_complex_3d::Point_3> p_points;
-
-  for (int i = 0; i < 50; i++) {
-    Fast_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
-    p_points.push_back(p);
-  }
-
-  Fast_periodic_alpha_complex_3d periodic_alpha_complex(p_points, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> stree;
-  periodic_alpha_complex.create_complex(stree);
-
-  // ----------------------
-  // Exact periodic version
-  // ----------------------
-  std::cout << "Exact periodic alpha complex 3d" << std::endl;
-
-  std::vector<Exact_periodic_alpha_complex_3d::Point_3> e_p_points;
-
-  for (auto p : p_points) {
-    e_p_points.push_back(Exact_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
-  }
-
-  Exact_periodic_alpha_complex_3d exact_alpha_complex(e_p_points, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> exact_stree;
-  exact_alpha_complex.create_complex(exact_stree);
-
-  // ---------------------
-  // Compare both versions
-  // ---------------------
-  std::cout << "Exact periodic alpha complex 3d is of dimension " << exact_stree.dimension() << " - Non exact is "
-            << stree.dimension() << std::endl;
-  BOOST_CHECK(exact_stree.dimension() == stree.dimension());
-  std::cout << "Exact periodic alpha complex 3d num_simplices " << exact_stree.num_simplices() << " - Non exact is "
-            << stree.num_simplices() << std::endl;
-  BOOST_CHECK(exact_stree.num_simplices() == stree.num_simplices());
-  std::cout << "Exact periodic alpha complex 3d num_vertices " << exact_stree.num_vertices() << " - Non exact is "
-            << stree.num_vertices() << std::endl;
-  BOOST_CHECK(exact_stree.num_vertices() == stree.num_vertices());
-
-  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
-  // cf. https://github.com/CGAL/cgal/issues/3346
-  auto sh = stree.filtration_simplex_range().begin();
-  auto sh_exact = exact_stree.filtration_simplex_range().begin();
-
-  while (sh != stree.filtration_simplex_range().end() || sh_exact != exact_stree.filtration_simplex_range().end()) {
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), exact_stree.filtration(*sh_exact), 1e-14);
-
-    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
-    std::vector<int> exact_vh(exact_stree.simplex_vertex_range(*sh_exact).begin(),
-                              exact_stree.simplex_vertex_range(*sh_exact).end());
-
-    BOOST_CHECK(vh.size() == exact_vh.size());
-    ++sh;
-    ++sh_exact;
-  }
-
-  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
-  BOOST_CHECK(sh_exact == exact_stree.filtration_simplex_range().end());
-
-  // ----------------------
-  // Safe periodic version
-  // ----------------------
-  std::cout << "Safe periodic alpha complex 3d" << std::endl;
-
-  std::vector<Safe_periodic_alpha_complex_3d::Point_3> s_p_points;
-
-  for (auto p : p_points) {
-    s_p_points.push_back(Safe_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
-  }
-
-  Safe_periodic_alpha_complex_3d safe_alpha_complex(s_p_points, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> safe_stree;
-  safe_alpha_complex.create_complex(safe_stree);
-
-  // ---------------------
-  // Compare both versions
-  // ---------------------
-  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
-  // cf. https://github.com/CGAL/cgal/issues/3346
-  sh = stree.filtration_simplex_range().begin();
-  auto sh_safe = safe_stree.filtration_simplex_range().begin();
-
-  while (sh != stree.filtration_simplex_range().end() || sh_safe != safe_stree.filtration_simplex_range().end()) {
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), safe_stree.filtration(*sh_safe), 1e-14);
-
-    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
-    std::vector<int> safe_vh(safe_stree.simplex_vertex_range(*sh_safe).begin(),
-                             safe_stree.simplex_vertex_range(*sh_safe).end());
-
-    BOOST_CHECK(vh.size() == safe_vh.size());
-    ++sh;
-    ++sh_safe;
-  }
-
-  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
-  BOOST_CHECK(sh_safe == safe_stree.filtration_simplex_range().end());
-}
-
-typedef boost::mpl::list<Fast_weighted_periodic_alpha_complex_3d, Exact_weighted_periodic_alpha_complex_3d,
-                         Safe_weighted_periodic_alpha_complex_3d>
-    wp_variants_type_list;
-
-#ifdef GUDHI_DEBUG
-BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted_periodic_throw, Weighted_periodic_alpha_complex_3d,
-                              wp_variants_type_list) {
-  std::cout << "Weighted periodic alpha complex 3d exception throw" << std::endl;
-
-  using Creator = CGAL::Creator_uniform_3<double, Weighted_periodic_alpha_complex_3d::Point_3>;
-  CGAL::Random random(7);
-  CGAL::Random_points_in_cube_3<Weighted_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
-  std::vector<Weighted_periodic_alpha_complex_3d::Point_3> wp_points;
-
-  for (int i = 0; i < 50; i++) {
-    Weighted_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
-    wp_points.push_back(p);
-  }
-  std::vector<double> p_weights;
-  // Weights must be in range ]0, 1/64 = 0.015625[
-  for (std::size_t i = 0; i < wp_points.size(); ++i) {
-    p_weights.push_back(random.get_double(0., 0.01));
-  }
-
-  std::cout << "Cuboid is not iso exception" << std::endl;
-  // Check it throws an exception when the cuboid is not iso
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 0.9, 1., 1.),
-      std::invalid_argument);
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 0.9, 1.),
-      std::invalid_argument);
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1., 0.9),
-      std::invalid_argument);
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1.1, 1., 1.),
-      std::invalid_argument);
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1.1, 1.),
-      std::invalid_argument);
-  BOOST_CHECK_THROW(
-      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1., 1.1),
-      std::invalid_argument);
-
-  std::cout << "0 <= point.weight() < 1/64 * domain_size * domain_size exception" << std::endl;
-  // Weights must be in range ]0, 1/64 = 0.015625[
-  double temp = p_weights[25];
-  p_weights[25] = 1.0;
-  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
-                    std::invalid_argument);
-  // Weights must be in range ]0, 1/64 = 0.015625[
-  p_weights[25] = temp;
-  temp = p_weights[14];
-  p_weights[14] = -1e-10;
-  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
-                    std::invalid_argument);
-  p_weights[14] = temp;
-
-  std::cout << "wp_points and p_weights size exception" << std::endl;
-  // Weights and points must have the same size
-  // + 1
-  p_weights.push_back(1e-10);
-  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
-                    std::invalid_argument);
-  // - 1
-  p_weights.pop_back();
-  p_weights.pop_back();
-  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
-                    std::invalid_argument);
-}
-#endif
-
-BOOST_AUTO_TEST_CASE(Alpha_complex_weighted_periodic) {
-  // ---------------------
-  // Fast weighted periodic version
-  // ---------------------
-  std::cout << "Fast weighted periodic alpha complex 3d" << std::endl;
-
-  using Creator = CGAL::Creator_uniform_3<double, Fast_weighted_periodic_alpha_complex_3d::Point_3>;
-  CGAL::Random random(7);
-  CGAL::Random_points_in_cube_3<Fast_weighted_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
-  std::vector<Fast_weighted_periodic_alpha_complex_3d::Point_3> p_points;
-
-  for (int i = 0; i < 50; i++) {
-    Fast_weighted_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
-    p_points.push_back(p);
-  }
-  std::vector<double> p_weights;
-  // Weights must be in range ]0, 1/64 = 0.015625[
-  for (std::size_t i = 0; i < p_points.size(); ++i) {
-    p_weights.push_back(random.get_double(0., 0.01));
-  }
-
-  Fast_weighted_periodic_alpha_complex_3d periodic_alpha_complex(p_points, p_weights, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> stree;
-  periodic_alpha_complex.create_complex(stree);
-
-  // ----------------------
-  // Exact weighted periodic version
-  // ----------------------
-  std::cout << "Exact weighted periodic alpha complex 3d" << std::endl;
-
-  std::vector<Exact_weighted_periodic_alpha_complex_3d::Point_3> e_p_points;
-
-  for (auto p : p_points) {
-    e_p_points.push_back(Exact_weighted_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
-  }
-
-  Exact_weighted_periodic_alpha_complex_3d exact_alpha_complex(e_p_points, p_weights, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> exact_stree;
-  exact_alpha_complex.create_complex(exact_stree);
-
-  // ---------------------
-  // Compare both versions
-  // ---------------------
-  std::cout << "Exact weighted periodic alpha complex 3d is of dimension " << exact_stree.dimension()
-            << " - Non exact is " << stree.dimension() << std::endl;
-  BOOST_CHECK(exact_stree.dimension() == stree.dimension());
-  std::cout << "Exact weighted periodic alpha complex 3d num_simplices " << exact_stree.num_simplices()
-            << " - Non exact is " << stree.num_simplices() << std::endl;
-  BOOST_CHECK(exact_stree.num_simplices() == stree.num_simplices());
-  std::cout << "Exact weighted periodic alpha complex 3d num_vertices " << exact_stree.num_vertices()
-            << " - Non exact is " << stree.num_vertices() << std::endl;
-  BOOST_CHECK(exact_stree.num_vertices() == stree.num_vertices());
-
-  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
-  // cf. https://github.com/CGAL/cgal/issues/3346
-  auto sh = stree.filtration_simplex_range().begin();
-  auto sh_exact = exact_stree.filtration_simplex_range().begin();
-
-  while (sh != stree.filtration_simplex_range().end() || sh_exact != exact_stree.filtration_simplex_range().end()) {
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), exact_stree.filtration(*sh_exact), 1e-14);
-
-    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
-    std::vector<int> exact_vh(exact_stree.simplex_vertex_range(*sh_exact).begin(),
-                              exact_stree.simplex_vertex_range(*sh_exact).end());
-
-    BOOST_CHECK(vh.size() == exact_vh.size());
-    ++sh;
-    ++sh_exact;
-  }
-
-  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
-  BOOST_CHECK(sh_exact == exact_stree.filtration_simplex_range().end());
-
-  // ----------------------
-  // Safe weighted periodic version
-  // ----------------------
-  std::cout << "Safe weighted periodic alpha complex 3d" << std::endl;
-
-  std::vector<Safe_weighted_periodic_alpha_complex_3d::Point_3> s_p_points;
-
-  for (auto p : p_points) {
-    s_p_points.push_back(Safe_weighted_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
-  }
-
-  Safe_weighted_periodic_alpha_complex_3d safe_alpha_complex(s_p_points, p_weights, -1., -1., -1., 1., 1., 1.);
-
-  Gudhi::Simplex_tree<> safe_stree;
-  safe_alpha_complex.create_complex(safe_stree);
-
-  // ---------------------
-  // Compare both versions
-  // ---------------------
-  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
-  // cf. https://github.com/CGAL/cgal/issues/3346
-  sh = stree.filtration_simplex_range().begin();
-  auto sh_safe = safe_stree.filtration_simplex_range().begin();
-
-  while (sh != stree.filtration_simplex_range().end() || sh_safe != safe_stree.filtration_simplex_range().end()) {
-    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), safe_stree.filtration(*sh_safe), 1e-14);
-
-    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
-    std::vector<int> safe_vh(safe_stree.simplex_vertex_range(*sh_safe).begin(),
-                             safe_stree.simplex_vertex_range(*sh_safe).end());
-
-    BOOST_CHECK(vh.size() == safe_vh.size());
-    ++sh;
-    ++sh_safe;
-  }
-
-  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
-  BOOST_CHECK(sh_safe == safe_stree.filtration_simplex_range().end());
-}
diff --git a/src/Alpha_complex/test/CMakeLists.txt b/src/Alpha_complex/test/CMakeLists.txt
index 380380f4..7c6bf9aa 100644
--- a/src/Alpha_complex/test/CMakeLists.txt
+++ b/src/Alpha_complex/test/CMakeLists.txt
@@ -19,10 +19,22 @@ endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.7.0)
 if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
   add_executable ( Alpha_complex_3d_test_unit Alpha_complex_3d_unit_test.cpp )
   target_link_libraries(Alpha_complex_3d_test_unit ${CGAL_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+  add_executable ( Weighted_alpha_complex_3d_test_unit Weighted_alpha_complex_3d_unit_test.cpp )
+  target_link_libraries(Weighted_alpha_complex_3d_test_unit ${CGAL_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+  add_executable ( Periodic_alpha_complex_3d_test_unit Periodic_alpha_complex_3d_unit_test.cpp )
+  target_link_libraries(Periodic_alpha_complex_3d_test_unit ${CGAL_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+  add_executable ( Weighted_periodic_alpha_complex_3d_test_unit Weighted_periodic_alpha_complex_3d_unit_test.cpp )
+  target_link_libraries(Weighted_periodic_alpha_complex_3d_test_unit ${CGAL_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
   if (TBB_FOUND)
     target_link_libraries(Alpha_complex_3d_test_unit ${TBB_LIBRARIES})
+    target_link_libraries(Weighted_alpha_complex_3d_test_unit ${TBB_LIBRARIES})
+    target_link_libraries(Periodic_alpha_complex_3d_test_unit ${TBB_LIBRARIES})
+    target_link_libraries(Weighted_periodic_alpha_complex_3d_test_unit ${TBB_LIBRARIES})
   endif()
 
   gudhi_add_coverage_test(Alpha_complex_3d_test_unit)
+  gudhi_add_coverage_test(Weighted_alpha_complex_3d_test_unit)
+  gudhi_add_coverage_test(Periodic_alpha_complex_3d_test_unit)
+  gudhi_add_coverage_test(Weighted_periodic_alpha_complex_3d_test_unit)
 
 endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
diff --git a/src/Alpha_complex/test/Periodic_alpha_complex_3d_unit_test.cpp b/src/Alpha_complex/test/Periodic_alpha_complex_3d_unit_test.cpp
new file mode 100644
index 00000000..ed4cbff0
--- /dev/null
+++ b/src/Alpha_complex/test/Periodic_alpha_complex_3d_unit_test.cpp
@@ -0,0 +1,190 @@
+/*    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
+ *
+ *    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_DYN_LINK
+#define BOOST_TEST_MODULE "alpha_complex_3d"
+#include <boost/test/unit_test.hpp>
+#include <boost/mpl/list.hpp>
+
+#include <cmath>  // float comparison
+#include <limits>
+#include <string>
+#include <vector>
+#include <random>
+#include <cstddef>  // for std::size_t
+
+#include <gudhi/Alpha_complex_3d.h>
+#include <gudhi/graph_simplicial_complex.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Unitary_tests_utils.h>
+// to construct Alpha_complex from a OFF file of points
+#include <gudhi/Points_3D_off_io.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/point_generators_3.h>
+
+using Fast_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, false, true>;
+using Safe_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, true>;
+using Exact_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, true>;
+
+#ifdef GUDHI_DEBUG
+typedef boost::mpl::list<Fast_periodic_alpha_complex_3d, Safe_periodic_alpha_complex_3d,
+                         Exact_periodic_alpha_complex_3d>
+    periodic_variants_type_list;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_periodic_throw, Periodic_alpha_complex_3d, periodic_variants_type_list) {
+  std::cout << "Periodic alpha complex 3d exception throw" << std::endl;
+  using Point_3 = typename Periodic_alpha_complex_3d::Point_3;
+  std::vector<Point_3> p_points;
+
+  // Not important, this is not what we want to check
+  p_points.push_back(Point_3(0.0, 0.0, 0.0));
+
+  std::cout << "Check exception throw in debug mode" << std::endl;
+  // Check it throws an exception when the cuboid is not iso
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 0.9, 1., 1.),
+                    std::invalid_argument);
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 0.9, 1.),
+                    std::invalid_argument);
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1., 0.9),
+                    std::invalid_argument);
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1.1, 1., 1.),
+                    std::invalid_argument);
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1.1, 1.),
+                    std::invalid_argument);
+  BOOST_CHECK_THROW(Periodic_alpha_complex_3d periodic_alpha_complex(p_points, 0., 0., 0., 1., 1., 1.1),
+                    std::invalid_argument);
+}
+#endif
+
+BOOST_AUTO_TEST_CASE(Alpha_complex_periodic) {
+  // ---------------------
+  // Fast periodic version
+  // ---------------------
+  std::cout << "Fast periodic alpha complex 3d" << std::endl;
+
+  using Creator = CGAL::Creator_uniform_3<double, Fast_periodic_alpha_complex_3d::Point_3>;
+  CGAL::Random random(7);
+  CGAL::Random_points_in_cube_3<Fast_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
+  std::vector<Fast_periodic_alpha_complex_3d::Point_3> p_points;
+
+  for (int i = 0; i < 50; i++) {
+    Fast_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
+    p_points.push_back(p);
+  }
+
+  Fast_periodic_alpha_complex_3d periodic_alpha_complex(p_points, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> stree;
+  periodic_alpha_complex.create_complex(stree);
+
+  // ----------------------
+  // Exact periodic version
+  // ----------------------
+  std::cout << "Exact periodic alpha complex 3d" << std::endl;
+
+  std::vector<Exact_periodic_alpha_complex_3d::Point_3> e_p_points;
+
+  for (auto p : p_points) {
+    e_p_points.push_back(Exact_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
+  }
+
+  Exact_periodic_alpha_complex_3d exact_alpha_complex(e_p_points, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> exact_stree;
+  exact_alpha_complex.create_complex(exact_stree);
+
+  // ---------------------
+  // Compare both versions
+  // ---------------------
+  std::cout << "Exact periodic alpha complex 3d is of dimension " << exact_stree.dimension() << " - Non exact is "
+            << stree.dimension() << std::endl;
+  BOOST_CHECK(exact_stree.dimension() == stree.dimension());
+  std::cout << "Exact periodic alpha complex 3d num_simplices " << exact_stree.num_simplices() << " - Non exact is "
+            << stree.num_simplices() << std::endl;
+  BOOST_CHECK(exact_stree.num_simplices() == stree.num_simplices());
+  std::cout << "Exact periodic alpha complex 3d num_vertices " << exact_stree.num_vertices() << " - Non exact is "
+            << stree.num_vertices() << std::endl;
+  BOOST_CHECK(exact_stree.num_vertices() == stree.num_vertices());
+
+  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
+  // cf. https://github.com/CGAL/cgal/issues/3346
+  auto sh = stree.filtration_simplex_range().begin();
+  auto sh_exact = exact_stree.filtration_simplex_range().begin();
+
+  while (sh != stree.filtration_simplex_range().end() || sh_exact != exact_stree.filtration_simplex_range().end()) {
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), exact_stree.filtration(*sh_exact), 1e-14);
+
+    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
+    std::vector<int> exact_vh(exact_stree.simplex_vertex_range(*sh_exact).begin(),
+                              exact_stree.simplex_vertex_range(*sh_exact).end());
+
+    BOOST_CHECK(vh.size() == exact_vh.size());
+    ++sh;
+    ++sh_exact;
+  }
+
+  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
+  BOOST_CHECK(sh_exact == exact_stree.filtration_simplex_range().end());
+
+  // ----------------------
+  // Safe periodic version
+  // ----------------------
+  std::cout << "Safe periodic alpha complex 3d" << std::endl;
+
+  std::vector<Safe_periodic_alpha_complex_3d::Point_3> s_p_points;
+
+  for (auto p : p_points) {
+    s_p_points.push_back(Safe_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
+  }
+
+  Safe_periodic_alpha_complex_3d safe_alpha_complex(s_p_points, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> safe_stree;
+  safe_alpha_complex.create_complex(safe_stree);
+
+  // ---------------------
+  // Compare both versions
+  // ---------------------
+  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
+  // cf. https://github.com/CGAL/cgal/issues/3346
+  sh = stree.filtration_simplex_range().begin();
+  auto sh_safe = safe_stree.filtration_simplex_range().begin();
+
+  while (sh != stree.filtration_simplex_range().end() || sh_safe != safe_stree.filtration_simplex_range().end()) {
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), safe_stree.filtration(*sh_safe), 1e-14);
+
+    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
+    std::vector<int> safe_vh(safe_stree.simplex_vertex_range(*sh_safe).begin(),
+                             safe_stree.simplex_vertex_range(*sh_safe).end());
+
+    BOOST_CHECK(vh.size() == safe_vh.size());
+    ++sh;
+    ++sh_safe;
+  }
+
+  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
+  BOOST_CHECK(sh_safe == safe_stree.filtration_simplex_range().end());
+}
diff --git a/src/Alpha_complex/test/Weighted_alpha_complex_3d_unit_test.cpp b/src/Alpha_complex/test/Weighted_alpha_complex_3d_unit_test.cpp
new file mode 100644
index 00000000..c16b3718
--- /dev/null
+++ b/src/Alpha_complex/test/Weighted_alpha_complex_3d_unit_test.cpp
@@ -0,0 +1,147 @@
+/*    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
+ *
+ *    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_DYN_LINK
+#define BOOST_TEST_MODULE "alpha_complex_3d"
+#include <boost/test/unit_test.hpp>
+#include <boost/mpl/list.hpp>
+
+#include <cmath>  // float comparison
+#include <limits>
+#include <string>
+#include <vector>
+#include <random>
+#include <cstddef>  // for std::size_t
+
+#include <gudhi/Alpha_complex_3d.h>
+#include <gudhi/graph_simplicial_complex.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Unitary_tests_utils.h>
+// to construct Alpha_complex from a OFF file of points
+#include <gudhi/Points_3D_off_io.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/point_generators_3.h>
+
+using Fast_weighted_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, false>;
+using Safe_weighted_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
+using Exact_weighted_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, false>;
+
+typedef boost::mpl::list<Fast_weighted_alpha_complex_3d, Safe_weighted_alpha_complex_3d,
+                         Exact_weighted_alpha_complex_3d>
+    weighted_variants_type_list;
+
+#ifdef GUDHI_DEBUG
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted_throw, Weighted_alpha_complex_3d, weighted_variants_type_list) {
+  using Point_3 = typename Weighted_alpha_complex_3d::Point_3;
+  std::vector<Point_3> w_points;
+  w_points.push_back(Point_3(0.0, 0.0, 0.0));
+  w_points.push_back(Point_3(0.0, 0.0, 0.2));
+  w_points.push_back(Point_3(0.2, 0.0, 0.2));
+  // w_points.push_back(Point_3(0.6, 0.6, 0.0));
+  // w_points.push_back(Point_3(0.8, 0.8, 0.2));
+  // w_points.push_back(Point_3(0.2, 0.8, 0.6));
+
+  // weights size is different from w_points size to make weighted Alpha_complex_3d throw in debug mode
+  std::vector<double> weights = {0.01, 0.005, 0.006, 0.01, 0.009, 0.001};
+
+  std::cout << "Check exception throw in debug mode" << std::endl;
+  BOOST_CHECK_THROW(Weighted_alpha_complex_3d wac(w_points, weights), std::invalid_argument);
+}
+#endif
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted, Weighted_alpha_complex_3d, weighted_variants_type_list) {
+  std::cout << "Weighted alpha complex 3d from points and weights" << std::endl;
+  using Point_3 = typename Weighted_alpha_complex_3d::Point_3;
+  std::vector<Point_3> w_points;
+  w_points.push_back(Point_3(0.0, 0.0, 0.0));
+  w_points.push_back(Point_3(0.0, 0.0, 0.2));
+  w_points.push_back(Point_3(0.2, 0.0, 0.2));
+  w_points.push_back(Point_3(0.6, 0.6, 0.0));
+  w_points.push_back(Point_3(0.8, 0.8, 0.2));
+  w_points.push_back(Point_3(0.2, 0.8, 0.6));
+
+  // weights size is different from w_points size to make weighted Alpha_complex_3d throw in debug mode
+  std::vector<double> weights = {0.01, 0.005, 0.006, 0.01, 0.009, 0.001};
+
+  Weighted_alpha_complex_3d alpha_complex_p_a_w(w_points, weights);
+  Gudhi::Simplex_tree<> stree;
+  alpha_complex_p_a_w.create_complex(stree);
+
+  std::cout << "Weighted alpha complex 3d from weighted points" << std::endl;
+  using Weighted_point_3 = typename Weighted_alpha_complex_3d::Weighted_point_3;
+
+  std::vector<Weighted_point_3> weighted_points;
+
+  for (std::size_t i = 0; i < w_points.size(); i++) {
+    weighted_points.push_back(Weighted_point_3(w_points[i], weights[i]));
+  }
+  Weighted_alpha_complex_3d alpha_complex_w_p(weighted_points);
+
+  Gudhi::Simplex_tree<> stree_bis;
+  alpha_complex_w_p.create_complex(stree_bis);
+
+  // ---------------------
+  // Compare both versions
+  // ---------------------
+  std::cout << "Weighted alpha complex 3d is of dimension " << stree_bis.dimension() << " - versus "
+            << stree.dimension() << std::endl;
+  BOOST_CHECK(stree_bis.dimension() == stree.dimension());
+  std::cout << "Weighted alpha complex 3d num_simplices " << stree_bis.num_simplices() << " - versus "
+            << stree.num_simplices() << std::endl;
+  BOOST_CHECK(stree_bis.num_simplices() == stree.num_simplices());
+  std::cout << "Weighted alpha complex 3d num_vertices " << stree_bis.num_vertices() << " - versus "
+            << stree.num_vertices() << std::endl;
+  BOOST_CHECK(stree_bis.num_vertices() == stree.num_vertices());
+
+  auto sh = stree.filtration_simplex_range().begin();
+  while (sh != stree.filtration_simplex_range().end()) {
+    std::vector<int> simplex;
+    std::vector<int> exact_simplex;
+#ifdef DEBUG_TRACES
+    std::cout << " ( ";
+#endif
+    for (auto vertex : stree.simplex_vertex_range(*sh)) {
+      simplex.push_back(vertex);
+#ifdef DEBUG_TRACES
+      std::cout << vertex << " ";
+#endif
+    }
+#ifdef DEBUG_TRACES
+    std::cout << ") -> "
+              << "[" << stree.filtration(*sh) << "] ";
+    std::cout << std::endl;
+#endif
+
+    // Find it in the exact structure
+    auto sh_exact = stree_bis.find(simplex);
+    BOOST_CHECK(sh_exact != stree_bis.null_simplex());
+
+    // Exact and non-exact version is not exactly the same due to float comparison
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree_bis.filtration(sh_exact), stree.filtration(*sh));
+
+    ++sh;
+  }
+}
diff --git a/src/Alpha_complex/test/Weighted_periodic_alpha_complex_3d_unit_test.cpp b/src/Alpha_complex/test/Weighted_periodic_alpha_complex_3d_unit_test.cpp
new file mode 100644
index 00000000..e8ac83e5
--- /dev/null
+++ b/src/Alpha_complex/test/Weighted_periodic_alpha_complex_3d_unit_test.cpp
@@ -0,0 +1,239 @@
+/*    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
+ *
+ *    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_DYN_LINK
+#define BOOST_TEST_MODULE "alpha_complex_3d"
+#include <boost/test/unit_test.hpp>
+#include <boost/mpl/list.hpp>
+
+#include <cmath>  // float comparison
+#include <limits>
+#include <string>
+#include <vector>
+#include <random>
+#include <cstddef>  // for std::size_t
+
+#include <gudhi/Alpha_complex_3d.h>
+#include <gudhi/graph_simplicial_complex.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Unitary_tests_utils.h>
+// to construct Alpha_complex from a OFF file of points
+#include <gudhi/Points_3D_off_io.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/point_generators_3.h>
+
+using Fast_weighted_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, true>;
+using Safe_weighted_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, true>;
+using Exact_weighted_periodic_alpha_complex_3d =
+    Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, true>;
+
+
+typedef boost::mpl::list<Fast_weighted_periodic_alpha_complex_3d, Exact_weighted_periodic_alpha_complex_3d,
+                         Safe_weighted_periodic_alpha_complex_3d>
+    wp_variants_type_list;
+
+#ifdef GUDHI_DEBUG
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_weighted_periodic_throw, Weighted_periodic_alpha_complex_3d,
+                              wp_variants_type_list) {
+  std::cout << "Weighted periodic alpha complex 3d exception throw" << std::endl;
+
+  using Creator = CGAL::Creator_uniform_3<double, typename Weighted_periodic_alpha_complex_3d::Point_3>;
+  CGAL::Random random(7);
+  CGAL::Random_points_in_cube_3<typename Weighted_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
+  std::vector<typename Weighted_periodic_alpha_complex_3d::Point_3> wp_points;
+
+  for (int i = 0; i < 50; i++) {
+    typename Weighted_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
+    wp_points.push_back(p);
+  }
+  std::vector<double> p_weights;
+  // Weights must be in range ]0, 1/64 = 0.015625[
+  for (std::size_t i = 0; i < wp_points.size(); ++i) {
+    p_weights.push_back(random.get_double(0., 0.01));
+  }
+
+  std::cout << "Cuboid is not iso exception" << std::endl;
+  // Check it throws an exception when the cuboid is not iso
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 0.9, 1., 1.),
+      std::invalid_argument);
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 0.9, 1.),
+      std::invalid_argument);
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1., 0.9),
+      std::invalid_argument);
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1.1, 1., 1.),
+      std::invalid_argument);
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1.1, 1.),
+      std::invalid_argument);
+  BOOST_CHECK_THROW(
+      Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, -1., -1., -1., 1., 1., 1.1),
+      std::invalid_argument);
+
+  std::cout << "0 <= point.weight() < 1/64 * domain_size * domain_size exception" << std::endl;
+  // Weights must be in range ]0, 1/64 = 0.015625[
+  double temp = p_weights[25];
+  p_weights[25] = 1.0;
+  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
+                    std::invalid_argument);
+  // Weights must be in range ]0, 1/64 = 0.015625[
+  p_weights[25] = temp;
+  temp = p_weights[14];
+  p_weights[14] = -1e-10;
+  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
+                    std::invalid_argument);
+  p_weights[14] = temp;
+
+  std::cout << "wp_points and p_weights size exception" << std::endl;
+  // Weights and points must have the same size
+  // + 1
+  p_weights.push_back(1e-10);
+  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
+                    std::invalid_argument);
+  // - 1
+  p_weights.pop_back();
+  p_weights.pop_back();
+  BOOST_CHECK_THROW(Weighted_periodic_alpha_complex_3d wp_alpha_complex(wp_points, p_weights, 0., 0., 0., 1., 1., 1.),
+                    std::invalid_argument);
+}
+#endif
+
+BOOST_AUTO_TEST_CASE(Alpha_complex_weighted_periodic) {
+  // ---------------------
+  // Fast weighted periodic version
+  // ---------------------
+  std::cout << "Fast weighted periodic alpha complex 3d" << std::endl;
+
+  using Creator = CGAL::Creator_uniform_3<double, Fast_weighted_periodic_alpha_complex_3d::Point_3>;
+  CGAL::Random random(7);
+  CGAL::Random_points_in_cube_3<Fast_weighted_periodic_alpha_complex_3d::Point_3, Creator> in_cube(1, random);
+  std::vector<Fast_weighted_periodic_alpha_complex_3d::Point_3> p_points;
+
+  for (int i = 0; i < 50; i++) {
+    Fast_weighted_periodic_alpha_complex_3d::Point_3 p = *in_cube++;
+    p_points.push_back(p);
+  }
+  std::vector<double> p_weights;
+  // Weights must be in range ]0, 1/64 = 0.015625[
+  for (std::size_t i = 0; i < p_points.size(); ++i) {
+    p_weights.push_back(random.get_double(0., 0.01));
+  }
+
+  Fast_weighted_periodic_alpha_complex_3d periodic_alpha_complex(p_points, p_weights, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> stree;
+  periodic_alpha_complex.create_complex(stree);
+
+  // ----------------------
+  // Exact weighted periodic version
+  // ----------------------
+  std::cout << "Exact weighted periodic alpha complex 3d" << std::endl;
+
+  std::vector<Exact_weighted_periodic_alpha_complex_3d::Point_3> e_p_points;
+
+  for (auto p : p_points) {
+    e_p_points.push_back(Exact_weighted_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
+  }
+
+  Exact_weighted_periodic_alpha_complex_3d exact_alpha_complex(e_p_points, p_weights, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> exact_stree;
+  exact_alpha_complex.create_complex(exact_stree);
+
+  // ---------------------
+  // Compare both versions
+  // ---------------------
+  std::cout << "Exact weighted periodic alpha complex 3d is of dimension " << exact_stree.dimension()
+            << " - Non exact is " << stree.dimension() << std::endl;
+  BOOST_CHECK(exact_stree.dimension() == stree.dimension());
+  std::cout << "Exact weighted periodic alpha complex 3d num_simplices " << exact_stree.num_simplices()
+            << " - Non exact is " << stree.num_simplices() << std::endl;
+  BOOST_CHECK(exact_stree.num_simplices() == stree.num_simplices());
+  std::cout << "Exact weighted periodic alpha complex 3d num_vertices " << exact_stree.num_vertices()
+            << " - Non exact is " << stree.num_vertices() << std::endl;
+  BOOST_CHECK(exact_stree.num_vertices() == stree.num_vertices());
+
+  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
+  // cf. https://github.com/CGAL/cgal/issues/3346
+  auto sh = stree.filtration_simplex_range().begin();
+  auto sh_exact = exact_stree.filtration_simplex_range().begin();
+
+  while (sh != stree.filtration_simplex_range().end() || sh_exact != exact_stree.filtration_simplex_range().end()) {
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), exact_stree.filtration(*sh_exact), 1e-14);
+
+    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
+    std::vector<int> exact_vh(exact_stree.simplex_vertex_range(*sh_exact).begin(),
+                              exact_stree.simplex_vertex_range(*sh_exact).end());
+
+    BOOST_CHECK(vh.size() == exact_vh.size());
+    ++sh;
+    ++sh_exact;
+  }
+
+  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
+  BOOST_CHECK(sh_exact == exact_stree.filtration_simplex_range().end());
+
+  // ----------------------
+  // Safe weighted periodic version
+  // ----------------------
+  std::cout << "Safe weighted periodic alpha complex 3d" << std::endl;
+
+  std::vector<Safe_weighted_periodic_alpha_complex_3d::Point_3> s_p_points;
+
+  for (auto p : p_points) {
+    s_p_points.push_back(Safe_weighted_periodic_alpha_complex_3d::Point_3(p[0], p[1], p[2]));
+  }
+
+  Safe_weighted_periodic_alpha_complex_3d safe_alpha_complex(s_p_points, p_weights, -1., -1., -1., 1., 1., 1.);
+
+  Gudhi::Simplex_tree<> safe_stree;
+  safe_alpha_complex.create_complex(safe_stree);
+
+  // ---------------------
+  // Compare both versions
+  // ---------------------
+  // We cannot compare as objects from dispatcher on the alpha shape is not deterministic.
+  // cf. https://github.com/CGAL/cgal/issues/3346
+  sh = stree.filtration_simplex_range().begin();
+  auto sh_safe = safe_stree.filtration_simplex_range().begin();
+
+  while (sh != stree.filtration_simplex_range().end() || sh_safe != safe_stree.filtration_simplex_range().end()) {
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(stree.filtration(*sh), safe_stree.filtration(*sh_safe), 1e-14);
+
+    std::vector<int> vh(stree.simplex_vertex_range(*sh).begin(), stree.simplex_vertex_range(*sh).end());
+    std::vector<int> safe_vh(safe_stree.simplex_vertex_range(*sh_safe).begin(),
+                             safe_stree.simplex_vertex_range(*sh_safe).end());
+
+    BOOST_CHECK(vh.size() == safe_vh.size());
+    ++sh;
+    ++sh_safe;
+  }
+
+  BOOST_CHECK(sh == stree.filtration_simplex_range().end());
+  BOOST_CHECK(sh_safe == safe_stree.filtration_simplex_range().end());
+}
diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h
index 35b84d2e..b33a95a1 100644
--- a/src/common/doc/main_page.h
+++ b/src/common/doc/main_page.h
@@ -29,7 +29,9 @@
       <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; 4.11.0 and \ref eigen3
+      <b>Requires:</b> \ref eigen3 and<br>
+      \ref cgal &ge; 4.7.0 for Alpha_complex<br>
+      \ref cgal &ge; 4.11.0 for Alpha_complex_3d
     </td>
     <td width="75%">
     Alpha_complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.<br>
@@ -38,7 +40,8 @@
     values of the codimension 1 cofaces that make it not Gabriel otherwise.
     All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into
     the complex.<br>
-    <b>User manual:</b> \ref alpha_complex - <b>Reference manual:</b> Gudhi::alpha_complex::Alpha_complex
+    <b>User manual:</b> \ref alpha_complex - <b>Reference manual:</b> Gudhi::alpha_complex::Alpha_complex and
+    Gudhi::alpha_complex::Alpha_complex_3d
     </td>
  </tr>
 </table>