17 files changed, 459 insertions, 548 deletions
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 197b6f95..d42f7af7 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -69,6 +69,12 @@ else()
   message(STATUS "boost include dirs:" ${Boost_INCLUDE_DIRS})
   message(STATUS "boost library dirs:" ${Boost_LIBRARY_DIRS})
 
+  if (DEBUG_TRACES)
+    # For programs to be more verbose
+    message(STATUS "DEBUG_TRACES are activated")
+    add_definitions(-DDEBUG_TRACES)
+  endif()
+
   include_directories(src/common/include/)
   include_directories(src/Alpha_complex/include/)
   include_directories(src/Bottleneck/include/)
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h
index 1fb8fdee..685a4c2f 100644
--- a/src/Alpha_complex/doc/Intro_alpha_complex.h
+++ b/src/Alpha_complex/doc/Intro_alpha_complex.h
@@ -36,48 +36,58 @@ namespace alphacomplex {
  * 
  * \section definition Definition
  * 
- * Alpha_complex is a Simplex_tree constructed from each finite cell of a Delaunay Triangulation.
+ * Alpha_complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
+ * constructed from each finite cell of a Delaunay Triangulation.
  * 
  * The filtration value of each simplex is computed from the alpha square value of the simplex if it is Gabriel or
  * from the alpha value of the simplex coface that makes the simplex not Gabriel.
  * 
- * Please refer to \cite AlphaShapesDefinition for a more complete alpha complex definition.
+ * All simplices that have a filtration value strictly greater than a given alpha square value are not inserted into
+ * the simplex.
  * 
- * Alpha complex are interesting because it looks like an \ref alpha-shape "Alpha shape" as described in
- * \cite AlphaShapesIntroduction (an alpha complex concept vulgarization).
+ * \image html "alpha_complex_representation.png" "Alpha simplicial complex representation"
  * 
- * \section example Example
+ * Alpha_complex is constructing a `Simplex_tree` using <a target="_blank"
+ * href="http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations">Delaunay Triangulation</a>
+ * \cite cgal:hdj-t-15b from <a target="_blank" href="http://www.cgal.org/">CGAL</a> (the Computational Geometry
+ * Algorithms Library \cite cgal:eb-15b).
  * 
- * This example loads points from an OFF file, builds the Delaunay triangulation from the points, and finally
- * initialize the alpha complex with it.
+ * The complex is a template class requiring a <a target="_blank"
+ * href="http://doc.cgal.org/latest/Kernel_d/index.html#Chapter_dD_Geometry_Kernel">dD Geometry Kernel</a>
+ * \cite cgal:s-gkd-15b from CGAL as template.
+ * 
+ * \section pointsexample Example from points
+ * 
+ * This example builds the Delaunay triangulation from the given points in a 2D static kernel, and initializes the
+ * alpha complex with it.
  * 
  * Then, it is asked to display information about the alpha complex.
  * 
- * \include Alpha_complex_from_off.cpp
+ * \include Alpha_complex_from_points.cpp
  * 
  * When launching:
  * 
- * \code $> ./alphaoffreader ../../data/points/alphacomplexdoc.off 60.0
+ * \code $> ./alphapoints 60.0
  * \endcode
  *
  * the program output is:
  * 
- * \include alphaoffreader_for_doc.txt
+ * \include alphaoffreader_for_doc_60.txt
  * 
  * \section algorithm Algorithm
  * 
- * <b>Data structure</b>
+ * \subsection datastructure Data structure
  * 
  * In order to build the alpha complex, first, a Simplex tree is build from the cells of a Delaunay Triangulation.
  * (The filtration value is set to NaN, which stands for unknown value):
  * \image html "alpha_complex_doc.png" "Simplex tree structure construction example"
  *
- * <b>Filtration value computation algorithm</b>
- *
+ * \subsection filtrationcomputation Filtration value computation algorithm
+ * 
  * \f{algorithm}{ 
  * \caption{Filtration value computation algorithm}\label{alpha}
  * \begin{algorithmic}
- * \For{i : dimension $\rightarrow$ 1}
+ * \For{i : dimension $\rightarrow$ 0}
  *   \ForAll{$\sigma$ of dimension i}
  *     \If {filtration($\sigma$) is NaN}
  *       \State filtration($\sigma$) = $\alpha^2(\sigma)$
@@ -93,25 +103,58 @@ namespace alphacomplex {
  *     \EndFor
  *   \EndFor
  * \EndFor
+ * \State make\_filtration\_non\_decreasing()
+ * \State prune\_above\_filtration()
  * \end{algorithmic}
  * \f}
  * 
- * From the example above, it means the algorithm will look into each triangle ([1,2,3], [2,3,4], [1,3,5], ...),
- * will compute the filtration value of the triangle, and then will propagate the filtration value as described
+ * \subsubsection dimension2 Dimension 2
+ * 
+ * From the example above, it means the algorithm looks into each triangle ([1,2,3], [2,3,4], [1,3,5], ...),
+ * computes the filtration value of the triangle, and then propagates the filtration value as described
  * here :
  * \image html "alpha_complex_doc_135.png" "Filtration value propagation example"
- * Then, the algorithm will look into each edge ([1,2], [2,3], [1,3], ...),
- * will compute the filtration value of the edge (in this case, propagation will have no effect).
  * 
- * Finally, the algorithm will look into each vertex ([1], [2], [3], [4], [5], [6] and [7]),
- * will set the filtration value (0 in case of a vertex - propagation will have no effect).
+ * \subsubsection dimension1 Dimension 1
+ * 
+ * Then, the algorithm looks into each edge ([1,2], [2,3], [1,3], ...),
+ * computes the filtration value of the edge (in this case, propagation will have no effect).
+ * 
+ * \subsubsection dimension0 Dimension 0
+ * 
+ * Finally, the algorithm looks into each vertex ([1], [2], [3], [4], [5], [6] and [7]) and
+ * sets the filtration value (0 in case of a vertex - propagation will have no effect).
+ * 
+ * \subsubsection nondecreasing Non decreasing filtration values
+ * 
+ * As Alpha square value computed from CGAL is an approximation, we have to make filtration non decreasing while
+ * increasing the dimension for our simplicial complex to be valid (cf.
+ * `Simplex_tree::make_filtration_non_decreasing()`).
+ * 
+ * \subsubsection pruneabove Prune above given filtration value
+ * 
+ * The simplex tree is pruned from the given maximum alpha square value (cf. `Simplex_tree::prune_above_filtration()`).
+ * In this example, the value is given by the user as argument of the program.
  * 
- * \section alpha-shape Alpha shape
  * 
- * In the example above, the alpha shape of \f$\alpha^2_{63} < \alpha^2 < \alpha^2_{62}\f$ is the alpha complex where the 
- * \f$\alpha^2_{63} <\f$ filtration value \f$< \alpha^2_{62}\f$ as described in \cite AlphaShapesIntroduction
+ * \section offexample Example from OFF file
+ * 
+ * This example builds the Delaunay triangulation in a dynamic kernel, and initializes the alpha complex with it.
+ * 
+ * 
+ * Then, it is asked to display information about the alpha complex.
+ * 
+ * \include Alpha_complex_from_off.cpp
+ * 
+ * When launching:
+ * 
+ * \code $> ./alphaoffreader ../../data/points/alphacomplexdoc.off 32.0
+ * \endcode
+ *
+ * the program output is:
+ * 
+ * \include alphaoffreader_for_doc_32.txt
  * 
- * \image html "alpha_complex_doc_alpha_shape.png" "Alpha shape example"
  * \copyright GNU General Public License v3.                         
  * \verbatim  Contact: gudhi-users@lists.gforge.inria.fr \endverbatim
  */
diff --git a/src/Alpha_complex/doc/alpha_complex_doc_alpha_shape.ipe b/src/Alpha_complex/doc/alpha_complex_doc_alpha_shape.ipe
deleted file mode 100644
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diff --git a/src/Alpha_complex/example/Alpha_complex_from_off.cpp b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
index cd6f5a4b..4f381892 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_off.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
@@ -1,8 +1,6 @@
 #include <iostream>
 #include <string>
 
-// to construct a Delaunay_triangulation from a OFF file
-#include <gudhi/Delaunay_triangulation_off_io.h>
 #include <gudhi/Alpha_complex.h>
 
 void usage(char * const progName) {
@@ -35,14 +33,12 @@ int main(int argc, char **argv) {
 
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
   for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    //if (alpha_complex_from_file.filtration(f_simplex) <= alpha_complex_from_file.filtration()) {
-      std::cout << "   ( ";
-      for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
-        std::cout << vertex << " ";
-      }
-      std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
-      std::cout << std::endl;
-    //}
+    std::cout << "   ( ";
+    for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
+      std::cout << vertex << " ";
+    }
+    std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
+    std::cout << std::endl;
   }
   return 0;
 }
diff --git a/src/Alpha_complex/example/Alpha_complex_from_points.cpp b/src/Alpha_complex/example/Alpha_complex_from_points.cpp
index e460f177..62f594d1 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_points.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_points.cpp
@@ -6,34 +6,50 @@
 #include <string>
 #include <vector>
 
-// to construct a Delaunay_triangulation from a OFF file
-#include "gudhi/Delaunay_triangulation_off_io.h"
-#include "gudhi/Alpha_complex.h"
+#include <gudhi/Alpha_complex.h>
 
-typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel;
+typedef CGAL::Epick_d< CGAL::Dimension_tag<2> > Kernel;
 typedef Kernel::Point_d Point;
 typedef std::vector<Point> Vector_of_points;
 
+void usage(char * const progName) {
+  std::cerr << "Usage: " << progName << " alpha_square_max_value" << std::endl;
+  std::cerr << "       i.e.: " << progName << " 32.0" << std::endl;
+  exit(-1); // ----- >>
+}
+
 int main(int argc, char **argv) {
+  if (argc != 2) {
+    std::cerr << "Error: Number of arguments (" << argc << ") is not correct" << std::endl;
+    usage(argv[0]);
+  }
+
+  double alpha_square_max_value = atof(argv[1]);
+  
   // ----------------------------------------------------------------------------
   // Init of a list of points
   // ----------------------------------------------------------------------------
   Vector_of_points points;
 
-  std::vector<double> coords = { 0.0, 0.0, 0.0, 1.0 };
+  std::vector<double> coords = { 1.0, 1.0 };
+  points.push_back(Point(coords.begin(), coords.end()));
+  coords = { 7.0, 0.0 };
+  points.push_back(Point(coords.begin(), coords.end()));
+  coords = { 4.0, 6.0 };
+  points.push_back(Point(coords.begin(), coords.end()));
+  coords = { 9.0, 6.0 };
   points.push_back(Point(coords.begin(), coords.end()));
-  coords = { 0.0, 0.0, 1.0, 0.0 };
+  coords = { 0.0, 14.0 };
   points.push_back(Point(coords.begin(), coords.end()));
-  coords = { 0.0, 1.0, 0.0, 0.0 };
+  coords = { 2.0, 19.0 };
   points.push_back(Point(coords.begin(), coords.end()));
-  coords = { 1.0, 0.0, 0.0, 0.0 };
+  coords = { 9.0, 17.0 };
   points.push_back(Point(coords.begin(), coords.end()));
 
   // ----------------------------------------------------------------------------
   // Init of an alpha complex from the list of points
   // ----------------------------------------------------------------------------
-  double max_alpha_square_value = 1e10;
-  Gudhi::alphacomplex::Alpha_complex<Kernel> alpha_complex_from_points(points, max_alpha_square_value);
+  Gudhi::alphacomplex::Alpha_complex<Kernel> alpha_complex_from_points(points, alpha_square_max_value);
 
   // ----------------------------------------------------------------------------
   // Display information about the alpha complex
diff --git a/src/Alpha_complex/example/CMakeLists.txt b/src/Alpha_complex/example/CMakeLists.txt
index 10b87f04..33ff6805 100644
--- a/src/Alpha_complex/example/CMakeLists.txt
+++ b/src/Alpha_complex/example/CMakeLists.txt
@@ -27,10 +27,6 @@ if(CGAL_FOUND)
     if (EIGEN3_FOUND)
       message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
       include( ${EIGEN3_USE_FILE} )
-      if (CMAKE_BUILD_TYPE MATCHES Debug)
-        # For programs to be more verbose
-        add_definitions(-DDEBUG_TRACES)
-      endif()
       
       add_executable ( alphaoffreader Alpha_complex_from_off.cpp )
       target_link_libraries(alphaoffreader  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt b/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt
new file mode 100644
index 00000000..553431a9
--- /dev/null
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt
@@ -0,0 +1,22 @@
+Alpha complex is of dimension 2 - 20 simplices - 7 vertices.
+Iterator on alpha complex simplices in the filtration order, with [filtration value]:
+   ( 0 ) -> [0] 
+   ( 1 ) -> [0] 
+   ( 2 ) -> [0] 
+   ( 3 ) -> [0] 
+   ( 4 ) -> [0] 
+   ( 5 ) -> [0] 
+   ( 6 ) -> [0] 
+   ( 5 4 ) -> [6.25] 
+   ( 4 1 ) -> [20] 
+   ( 4 2 ) -> [8.5] 
+   ( 6 2 ) -> [9.25] 
+   ( 6 5 ) -> [10] 
+   ( 6 4 ) -> [11.25] 
+   ( 6 5 4 ) -> [12.5] 
+   ( 6 4 2 ) -> [12.9959] 
+   ( 3 0 ) -> [13.25] 
+   ( 4 1 ) -> [20] 
+   ( 1 0 ) -> [22.7367] 
+   ( 3 1 0 ) -> [22.7367] 
+   ( 5 0 ) -> [30.25] 
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc.txt b/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt
index 71f29a00..71f29a00 100644
--- a/src/Alpha_complex/example/alphaoffreader_for_doc.txt
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index 6adfa2e6..2dae4028 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -27,6 +27,8 @@
 #include <gudhi/graph_simplicial_complex.h>
 #include <gudhi/Simplex_tree.h>
 #include <gudhi/Debug_utils.h>
+// to construct a Delaunay_triangulation from a OFF file
+#include <gudhi/Delaunay_triangulation_off_io.h>
 
 #include <stdlib.h>
 #include <math.h>  // isnan, fmax
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 9d1eac80..3a75527e 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -42,6 +42,12 @@ else()
   INCLUDE_DIRECTORIES(${Boost_INCLUDE_DIRS})
   LINK_DIRECTORIES(${Boost_LIBRARY_DIRS})
 
+  if (DEBUG_TRACES)
+    message(STATUS "DEBUG_TRACES are activated")
+    # For programs to be more verbose
+    add_definitions(-DDEBUG_TRACES)
+  endif()
+
   #---------------------------------------------------------------------------------------
   # Gudhi compilation part
   include_directories(include)
diff --git a/src/Doxyfile b/src/Doxyfile
index 81f55e29..9cd73444 100644
--- a/src/Doxyfile
+++ b/src/Doxyfile
@@ -673,6 +673,7 @@ LAYOUT_FILE            =
 # also \cite for info how to create references.
 
 CITE_BIB_FILES         = biblio/bibliography.bib \
+                        biblio/how_to_cite_cgal.bib \
                         biblio/how_to_cite_gudhi.bib
 
 #---------------------------------------------------------------------------
@@ -812,7 +813,7 @@ EXCLUDE_SYMBOLS        =
 # that contain example code fragments that are included (see the \include
 # command).
 
-EXAMPLE_PATH           = biblio/
+EXAMPLE_PATH           = biblio/ \
     example/common/ \
     example/Alpha_complex/
 
diff --git a/src/GudhUI/CMakeLists.txt b/src/GudhUI/CMakeLists.txt
index 5c2afdd0..75adba08 100644
--- a/src/GudhUI/CMakeLists.txt
+++ b/src/GudhUI/CMakeLists.txt
@@ -102,10 +102,6 @@ if ( CGAL_FOUND AND QT4_FOUND AND OPENGL_FOUND AND QGLVIEWER_FOUND )
     if (EIGEN3_FOUND)
       message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
       include( ${EIGEN3_USE_FILE} )
-      if (CMAKE_BUILD_TYPE MATCHES Debug)
-        # For programs to be more verbose
-        add_definitions(-DDEBUG_TRACES)
-      endif()
       
       add_executable (acp alpha_complex_persistence.cpp)
       target_link_libraries(acp ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY} ${QT_LIBRARIES})
diff --git a/src/Persistent_cohomology/example/CMakeLists.txt b/src/Persistent_cohomology/example/CMakeLists.txt
index 8caf7d8b..eb4ee3e3 100644
--- a/src/Persistent_cohomology/example/CMakeLists.txt
+++ b/src/Persistent_cohomology/example/CMakeLists.txt
@@ -35,10 +35,6 @@ if(GMPXX_FOUND AND GMP_FOUND)
    target_link_libraries(performance_rips_persistence ${Boost_SYSTEM_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY} ${GMPXX_LIBRARIES} ${GMP_LIBRARIES})
 
    if(CGAL_FOUND)
-     if (CMAKE_BUILD_TYPE MATCHES Debug)
-       # For programs to be more verbose
-       add_definitions(-DDEBUG_TRACES)
-     endif()
      add_executable(alpha_shapes_persistence alpha_shapes_persistence.cpp)
      target_link_libraries(alpha_shapes_persistence ${Boost_SYSTEM_LIBRARY} ${GMPXX_LIBRARIES} ${GMP_LIBRARIES} ${CGAL_LIBRARY})
      add_test(alpha_shapes_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/alpha_shapes_persistence ${CMAKE_SOURCE_DIR}/data/points/bunny_5000 2 0.5)
@@ -70,10 +66,6 @@ if(GMPXX_FOUND AND GMP_FOUND)
     if (EIGEN3_FOUND)
       message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
       include( ${EIGEN3_USE_FILE} )
-      if (CMAKE_BUILD_TYPE MATCHES Debug)
-        # For programs to be more verbose
-        add_definitions(-DDEBUG_TRACES)
-      endif()
       
       add_executable (alphacomplexpersistence alpha_complex_persistence.cpp)
       target_link_libraries(alphacomplexpersistence  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h
index 3edcbd0b..3c42f72d 100644
--- a/src/common/doc/main_page.h
+++ b/src/common/doc/main_page.h
@@ -63,7 +63,7 @@
  * CGAL is a C++ library which provides easy access to efficient and reliable geometric algorithms.
  * 
  * The following examples require the <a target="_blank" href="http://www.cgal.org/">Computational Geometry Algorithms
- * Library</a> (CGAL) and will not be built if CGAL is not installed:
+ * Library</a> (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed:
  * \li GudhUI
  * \li Persistent_cohomology/alpha_shapes_persistence
  * \li Simplex_tree/simplex_tree_from_alpha_shapes_3
diff --git a/src/common/example/CMakeLists.txt b/src/common/example/CMakeLists.txt
index 089f0c04..d29e31e7 100644
--- a/src/common/example/CMakeLists.txt
+++ b/src/common/example/CMakeLists.txt
@@ -26,10 +26,6 @@ if(CGAL_FOUND)
     if (EIGEN3_FOUND)
       message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
       include( ${EIGEN3_USE_FILE} )
-      if (CMAKE_BUILD_TYPE MATCHES Debug)
-        # For programs to be more verbose
-        add_definitions(-DDEBUG_TRACES)
-      endif()
       
       add_executable ( dtoffrw Delaunay_triangulation_off_rw.cpp )
       target_link_libraries(dtoffrw  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})