Add doc for exact alpha

CMake for exact alpha
Factorization


git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alpha_3d_fix@2170 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: b2ac281dd21313602590fc834e7ad22bbf081021

6 files changed, 84 insertions, 104 deletions

diff --git a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
index 40dd3f93..d758687c 100644
--- a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
+++ b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
@@ -172,6 +172,18 @@ Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persiste
 2  1 0.0934117 1.00003 
 2  2 0.56444 1.03938 \endcode
 
+\li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
+Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
+\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
+Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid
+for instance.
+\code $> ./exact_alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45 \endcode
+\code Simplex_tree dim: 3
+2  0 0 inf
+2  1 0.0682162 1.0001
+2  1 0.0934117 1.00003
+2  2 0.56444 1.03938 \endcode
+
 \li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html">
 Persistent_cohomology/alpha_complex_persistence.cpp</a> computes the persistent homology with
 \f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
diff --git a/src/Persistent_cohomology/example/CMakeLists.txt b/src/Persistent_cohomology/example/CMakeLists.txt
index d2a84b1e..a7905284 100644
--- a/src/Persistent_cohomology/example/CMakeLists.txt
+++ b/src/Persistent_cohomology/example/CMakeLists.txt
@@ -55,11 +55,15 @@ endif(GMP_FOUND)
 if(CGAL_FOUND)
   add_executable(alpha_complex_3d_persistence alpha_complex_3d_persistence.cpp)
   target_link_libraries(alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+  add_executable(exact_alpha_complex_3d_persistence exact_alpha_complex_3d_persistence.cpp)
+  target_link_libraries(exact_alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
 
   if (TBB_FOUND)
     target_link_libraries(alpha_complex_3d_persistence ${TBB_LIBRARIES})
+    target_link_libraries(exact_alpha_complex_3d_persistence ${TBB_LIBRARIES})
   endif(TBB_FOUND)
   add_test(alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/alpha_complex_3d_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off 2 0.45)
+  add_test(exact_alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/exact_alpha_complex_3d_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off 2 0.45)
 
 
   if (NOT CGAL_VERSION VERSION_LESS 4.7.0)
diff --git a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
index 371acede..ffb98283 100644
--- a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
@@ -42,36 +42,37 @@
 #include <vector>
 
 // Alpha_shape_3 templates type definitions
-typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
-typedef CGAL::Alpha_shape_vertex_base_3<Kernel> Vb;
-typedef CGAL::Alpha_shape_cell_base_3<Kernel> Fb;
-typedef CGAL::Triangulation_data_structure_3<Vb, Fb> Tds;
-typedef CGAL::Delaunay_triangulation_3<Kernel, Tds> Triangulation_3;
-typedef CGAL::Alpha_shape_3<Triangulation_3> Alpha_shape_3;
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Kernel>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3>;
 
 // From file type definition
-typedef Kernel::Point_3 Point_3;
+using Point_3 = Kernel::Point_3;
 
 // filtration with alpha values needed type definition
-typedef Alpha_shape_3::FT Alpha_value_type;
-typedef CGAL::Object Object;
-typedef CGAL::Dispatch_output_iterator<
-CGAL::cpp11::tuple<Object, Alpha_value_type>,
-CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
-    std::back_insert_iterator< std::vector<Alpha_value_type> > > > Dispatch;
-typedef Alpha_shape_3::Cell_handle Cell_handle;
-typedef Alpha_shape_3::Facet Facet;
-typedef Alpha_shape_3::Edge Edge_3;
-typedef std::list<Alpha_shape_3::Vertex_handle> Vertex_list;
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch = CGAL::Dispatch_output_iterator<
+          CGAL::cpp11::tuple<Object, Alpha_value_type>,
+          CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
+          std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;
 
 // gudhi type definition
-typedef Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence> ST;
-typedef ST::Filtration_value Filtration_value;
-typedef ST::Vertex_handle Simplex_tree_vertex;
-typedef std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex > Alpha_shape_simplex_tree_map;
-typedef std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex> Alpha_shape_simplex_tree_pair;
-typedef std::vector< Simplex_tree_vertex > Simplex_tree_vector_vertex;
-typedef Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp > PCOH;
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
+using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
+using PCOH = Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp >;
 
 void usage(const std::string& progName) {
   std::cerr << "Usage: " << progName <<
@@ -161,10 +162,9 @@ int main(int argc, char * const argv[]) {
         // Edge_3 is of dim 1
         dim_max = 1;
       }
-    } else if (const Alpha_shape_3::Vertex_handle * vertex =
-               CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
+    } else if (const Vertex_handle * vertex = CGAL::object_cast<Vertex_handle>(&object_iterator)) {
       count_vertices++;
-      vertex_list = from_vertex<Vertex_list, Alpha_shape_3::Vertex_handle>(*vertex);
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
     }
     // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
     Simplex_tree_vector_vertex the_simplex_tree;
diff --git a/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp
index fc6ee8dd..c016a596 100644
--- a/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp
@@ -42,37 +42,38 @@
 #include <vector>
 
 // Alpha_shape_3 templates type definitions
-typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
-typedef CGAL::Tag_true Exact_tag;
-typedef CGAL::Alpha_shape_vertex_base_3<Kernel, CGAL::Default, Exact_tag> Vb;
-typedef CGAL::Alpha_shape_cell_base_3<Kernel, CGAL::Default, Exact_tag> Fb;
-typedef CGAL::Triangulation_data_structure_3<Vb, Fb> Tds;
-typedef CGAL::Delaunay_triangulation_3<Kernel, Tds> Triangulation_3;
-typedef CGAL::Alpha_shape_3<Triangulation_3, Exact_tag> Alpha_shape_3;
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Exact_tag = CGAL::Tag_true;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel, CGAL::Default, Exact_tag>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Kernel, CGAL::Default, Exact_tag>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3, Exact_tag>;
 
 // From file type definition
-typedef Kernel::Point_3 Point_3;
+using Point_3 = Kernel::Point_3;
 
 // filtration with alpha values needed type definition
-typedef Alpha_shape_3::FT Alpha_value_type;
-typedef CGAL::Object Object;
-typedef CGAL::Dispatch_output_iterator<
-CGAL::cpp11::tuple<Object, Alpha_value_type>,
-CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
-    std::back_insert_iterator< std::vector<Alpha_value_type> > > > Dispatch;
-typedef Alpha_shape_3::Cell_handle Cell_handle;
-typedef Alpha_shape_3::Facet Facet;
-typedef Alpha_shape_3::Edge Edge_3;
-typedef Alpha_shape_3::Vertex_handle Vertex_handle;
-typedef std::list<Vertex_handle> Vertex_list;
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch = CGAL::Dispatch_output_iterator<
+          CGAL::cpp11::tuple<Object, Alpha_value_type>,
+          CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
+          std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+using Vertex_list = std::list<Vertex_handle>;
 
 // gudhi type definition
-typedef Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence> ST;
-typedef ST::Vertex_handle Simplex_tree_vertex;
-typedef std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex > Alpha_shape_simplex_tree_map;
-typedef std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex> Alpha_shape_simplex_tree_pair;
-typedef std::vector< Simplex_tree_vertex > Simplex_tree_vector_vertex;
-typedef Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp > PCOH;
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
+using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
+using PCOH = Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp >;
 
 void usage(char * const progName) {
   std::cerr << "Usage: " << progName <<
@@ -90,7 +91,7 @@ int main(int argc, char * const argv[]) {
   int coeff_field_characteristic = atoi(argv[2]);
 
   Filtration_value min_persistence = 0.0;
-  int returnedScanValue = sscanf(argv[3], "%lf", &min_persistence);
+  int returnedScanValue = sscanf(argv[3], "%f", &min_persistence);
   if ((returnedScanValue == EOF) || (min_persistence < -1.0)) {
     std::cerr << "Error: " << argv[3] << " is not correct\n";
     usage(argv[0]);
@@ -188,7 +189,8 @@ int main(int argc, char * const argv[]) {
       }
     }
     // Construction of the simplex_tree
-    Filtration_value filtr = /*std::sqrt*/CGAL::to_double(the_alpha_value_iterator->approx());
+    // you can also use the_alpha_value_iterator->exact()
+    Filtration_value filtr = /*std::sqrt*/CGAL::to_double(the_alpha_value_iterator->exact());
 #ifdef DEBUG_TRACES
     std::cout << "filtration = " << filtr << std::endl;
 #endif  // DEBUG_TRACES
diff --git a/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
index dbc42706..4f6ea40e 100644
--- a/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
@@ -31,6 +31,8 @@
 #include <CGAL/Alpha_shape_3.h>
 #include <CGAL/iterator.h>
 
+#include "alpha_complex_3d_helper.h"
+
 #include <fstream>
 #include <cmath>
 #include <string>
@@ -67,6 +69,7 @@ using Dispatch = CGAL::Dispatch_output_iterator<
 using Cell_handle = Alpha_shape_3::Cell_handle;
 using Facet = Alpha_shape_3::Facet;
 using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
 using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;
 
 // gudhi type definition
@@ -79,52 +82,6 @@ using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
 using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<
     ST, Gudhi::persistent_cohomology::Field_Zp >;
 
-Vertex_list from(const Cell_handle& ch) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-#ifdef DEBUG_TRACES
-    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-    the_list.push_back(ch->vertex(i));
-  }
-  return the_list;
-}
-
-Vertex_list from(const Facet& fct) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if (fct.second != i) {
-#ifdef DEBUG_TRACES
-      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(fct.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Edge_3& edg) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if ((edg.second == i) || (edg.third == i)) {
-#ifdef DEBUG_TRACES
-      std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(edg.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Alpha_shape_3::Vertex_handle& vh) {
-  Vertex_list the_list;
-#ifdef DEBUG_TRACES
-  std::cout << "from vertex=" << vh->point() << std::endl;
-#endif  // DEBUG_TRACES
-  the_list.push_back(vh);
-  return the_list;
-}
-
 void usage(char * const progName) {
   std::cerr << "Usage: " << progName <<
       " path_to_file_graph path_to_iso_cuboid_3_file coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
@@ -203,21 +160,21 @@ int main(int argc, char * const argv[]) {
   for (auto object_iterator : the_objects) {
     // Retrieve Alpha shape vertex list from object
     if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
-      vertex_list = from(*cell);
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
       count_cells++;
       if (dim_max < 3) {
         // Cell is of dim 3
         dim_max = 3;
       }
     } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
-      vertex_list = from(*facet);
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
       count_facets++;
       if (dim_max < 2) {
         // Facet is of dim 2
         dim_max = 2;
       }
     } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
-      vertex_list = from(*edge);
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
       count_edges++;
       if (dim_max < 1) {
         // Edge_3 is of dim 1
@@ -226,7 +183,7 @@ int main(int argc, char * const argv[]) {
     } else if (const Alpha_shape_3::Vertex_handle * vertex =
                CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
       count_vertices++;
-      vertex_list = from(*vertex);
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
     }
     // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
     Simplex_tree_vector_vertex the_simplex_tree;
diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h
index 5ca0a6bc..34ad1710 100644
--- a/src/common/doc/main_page.h
+++ b/src/common/doc/main_page.h
@@ -259,6 +259,8 @@ make \endverbatim
  * Library</a> (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed:
  * \li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html">
  * Persistent_cohomology/alpha_complex_3d_persistence.cpp</a>
+ * \li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
+ * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
  * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a>
  * 
@@ -350,6 +352,8 @@ make \endverbatim
  * Persistent_cohomology/rips_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2rips_persistence_step_by_step_8cpp-example.html">
  * Persistent_cohomology/rips_persistence_step_by_step.cpp</a>
+ * \li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
+ * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
  * Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp</a>
  * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
@@ -394,6 +398,7 @@ make \endverbatim
  * @example Persistent_cohomology/alpha_complex_3d_persistence.cpp
  * @example Persistent_cohomology/alpha_complex_persistence.cpp
  * @example Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp
+ * @example Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp
  * @example Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp
  * @example Persistent_cohomology/persistence_from_file.cpp
  * @example Persistent_cohomology/persistence_from_simple_simplex_tree.cpp