Replace Delaunay_triangulation_off_io.h and Delaunay_triangulation_off_rw.cpp with

        Points_off_io.h and CGAL_points_off_reader.cpp
Adapt UT and examples for this
Adapt Alpha complex for it
Alpha complex is now inserting points in a faster way (after a spatial_sort).
Remove Alpha complex construction from a pointer on Delaunay triangulation (no more needed).
Adapt documentation to all these modifications
Forbid copy/move constructor/assignment operator on Alpha complex


git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@1098 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 08a673b66451b5cb03fbdf482d696d93b35d220f

14 files changed, 247 insertions, 183 deletions

diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h
index 0dea2b16..9d0dcefa 100644
--- a/src/Alpha_complex/doc/Intro_alpha_complex.h
+++ b/src/Alpha_complex/doc/Intro_alpha_complex.h
@@ -112,14 +112,14 @@ namespace alphacomplex {
  * 
  * \subsubsection dimension2 Dimension 2
  * 
- * From the example above, it means the algorithm looks into each triangle ([4,2,1], [2,4,6], [4,5,6], ...),
+ * From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...),
  * computes the filtration value of the triangle, and then propagates the filtration value as described
  * here :
- * \image html "alpha_complex_doc_421.png" "Filtration value propagation example"
+ * \image html "alpha_complex_doc_420.png" "Filtration value propagation example"
  * 
  * \subsubsection dimension1 Dimension 1
  * 
- * Then, the algorithm looks into each edge ([1,2], [4,2], [4,1], ...),
+ * Then, the algorithm looks into each edge ([0,1], [0,2], [1,2], ...),
  * computes the filtration value of the edge (in this case, propagation will have no effect).
  * 
  * \subsubsection dimension0 Dimension 0
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index 99bd05af..baf0d26a 100644
--- a/src/Alpha_complex/doc/alpha_complex_doc.ipe
+++ b/src/Alpha_complex/doc/alpha_complex_doc.ipe
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diff --git a/src/Alpha_complex/doc/alpha_complex_doc.png b/src/Alpha_complex/doc/alpha_complex_doc.png
index cfe3ede6..0b6201da 100644
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index 727816c5..5d1d29d4 100644
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+<text matrix="1 0 0 1 -264 -162" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 -264 -162" stroke="lightgray">
 280 660 m
 300 710 l
@@ -333,7 +333,7 @@ modified (NaN)
 320 580 l
 280 660 l
 </path>
-<text matrix="1 0 0 1 -166.834 -240.52" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{42}$</text>
+<text matrix="1 0 0 1 -166.834 -240.52" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{20}$</text>
 <path matrix="1 0 0 1 -264 -162" stroke="darkcyan" pen="heavier">
 290 530 m
 320 580 l
@@ -365,11 +365,11 @@ modified (NaN)
 350 520 l
 320 580 l
 </path>
-<text matrix="1 0 0 1 -199.21 -189.117" transformations="translations" pos="380 530" stroke="darkred" type="label" width="168.308" height="8.965" depth="2.99" valign="baseline" size="large">[2,1] is not Gabriel $\rightarrow$ $\alpha_{21} = \alpha_{421}$</text>
-<text matrix="1 0 0 1 -40.1546 -167.501" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
-<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
-<text matrix="1 0 0 1 -37.2997 -174.154" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
-<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 -199.21 -189.117" transformations="translations" pos="380 530" stroke="darkred" type="label" width="168.308" height="8.965" depth="2.99" valign="baseline" size="large">[0,4] is not Gabriel $\rightarrow$ $\alpha_{40} = \alpha_{420}$</text>
+<text matrix="1 0 0 1 -40.1546 -167.501" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
+<text matrix="1 0 0 1 -37.2997 -174.154" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
+<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 -38 -164" stroke="lightgray">
 280 660 m
 300 710 l
@@ -388,7 +388,7 @@ modified (NaN)
 320 580 l
 280 660 l
 </path>
-<text matrix="1 0 0 1 52.4654 -193.97" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{12}$</text>
+<text matrix="1 0 0 1 52.4654 -193.97" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{40}$</text>
 <path matrix="1 0 0 1 -38 -164" stroke="darkcyan" pen="heavier">
 290 530 m
 280 660 l
@@ -413,12 +413,12 @@ modified (NaN)
 350 520 l
 320 580 l
 </path>
-<text matrix="1 0 0 1 123.845 -165.501" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
-<text matrix="1 0 0 1 126 -162" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
-<text matrix="1 0 0 1 126 -162" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
-<text matrix="1 0 0 1 126 -162" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
-<text matrix="1 0 0 1 126.7 -172.154" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
-<text matrix="1 0 0 1 126 -162" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 123.845 -165.501" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 126 -162" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
+<text matrix="1 0 0 1 126 -162" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
+<text matrix="1 0 0 1 126 -162" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
+<text matrix="1 0 0 1 126.7 -172.154" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
+<text matrix="1 0 0 1 126 -162" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 126 -162" stroke="lightgray">
 280 660 m
 300 710 l
@@ -437,8 +437,8 @@ modified (NaN)
 320 580 l
 280 660 l
 </path>
-<text matrix="1 0 0 1 225.859 -165.729" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{41}$</text>
-<text matrix="1 0 0 1 122 -164" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
+<text matrix="1 0 0 1 225.859 -165.729" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="14.814" height="4.294" depth="1.49" valign="baseline">$\alpha_{42}$</text>
+<text matrix="1 0 0 1 122 -164" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
 <path stroke="darkcyan" pen="heavier">
 406.093 497.775 m
 446.094 418.092 l
@@ -450,7 +450,7 @@ modified (NaN)
 425.854 457.774 m
 470.795 457.774 l
 </path>
-<text matrix="1 0 0 1 -48.9756 -209.799" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="231.798" height="8.965" depth="2.99" valign="baseline" size="large">[4,1] is Gabriel $\rightarrow$ $\alpha_{41}$ is not modified (NaN)
+<text matrix="1 0 0 1 -48.9756 -209.799" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="231.798" height="8.965" depth="2.99" valign="baseline" size="large">[2,4] is Gabriel $\rightarrow$ $\alpha_{42}$ is not modified (NaN)
 </text>
 <path stroke="darkblue" arrow="normal/normal">
 205.028 596.091 m
@@ -464,9 +464,9 @@ modified (NaN)
 341.123 594.316 m
 413.904 554.079 l
 </path>
-<text matrix="1 0 0 1 39.645 -2.36686" transformations="translations" pos="199.703 569.464" stroke="darkblue" type="label" width="93.206" height="7.473" depth="2.49" valign="baseline">For all faces of [4,2,1]</text>
+<text matrix="1 0 0 1 39.645 -2.36686" transformations="translations" pos="199.703 569.464" stroke="darkblue" type="label" width="93.206" height="7.473" depth="2.49" valign="baseline">For all faces of [4,2,0]</text>
 <text matrix="1 0 0 1 -93.391 2.68003" transformations="translations" pos="104.437 300.174" stroke="black" type="label" width="208.621" height="6.926" depth="1.93" valign="baseline">N.B. : is Gabriel on a single point has no sense.</text>
-<text matrix="1 0 0 1 -36.9231 10" transformations="translations" pos="48 784" stroke="black" type="label" width="118.324" height="7.473" depth="2.49" valign="baseline">Dimension =2 - $\sigma$ = [4,2,1]</text>
+<text matrix="1 0 0 1 -36.9231 10" transformations="translations" pos="48 784" stroke="black" type="label" width="118.324" height="7.473" depth="2.49" valign="baseline">Dimension =2 - $\sigma$ = [4,2,0]</text>
 <path stroke="darkcyan">
 247.333 430.892 m
 311.764 430.892 l
@@ -484,19 +484,19 @@ modified (NaN)
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 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="370 580" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="350 520" size="normal" stroke="black" fill="white"/>
-<text matrix="1 0 0 1 -264 -162" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<text matrix="1 0 0 1 -264 -162" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="305 555" size="normal" stroke="darkcyan" fill="white"/>
 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="290 530" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="320 580" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -37.2997 -174.154" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="black" fill="white"/>
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-<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
+<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
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-<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
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-<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="310.693 578.759" stroke="darkred" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
+<text matrix="1 0 0 1 -38 -164" transformations="translations" pos="310.693 578.759" stroke="darkred" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
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 </path>
diff --git a/src/Alpha_complex/doc/alpha_complex_doc_420.png b/src/Alpha_complex/doc/alpha_complex_doc_420.png
new file mode 100644
index 00000000..ef7187f7
--- /dev/null
+++ b/src/Alpha_complex/doc/alpha_complex_doc_420.png
diff --git a/src/Alpha_complex/doc/alpha_complex_doc_421.png b/src/Alpha_complex/doc/alpha_complex_doc_421.png
deleted file mode 100644
index 1cce4402..00000000
--- a/src/Alpha_complex/doc/alpha_complex_doc_421.png
+++ /dev/null
diff --git a/src/Alpha_complex/doc/alpha_complex_representation.ipe b/src/Alpha_complex/doc/alpha_complex_representation.ipe
index fead1661..e8096b93 100644
--- a/src/Alpha_complex/doc/alpha_complex_representation.ipe
+++ b/src/Alpha_complex/doc/alpha_complex_representation.ipe
@@ -1,7 +1,7 @@
 <?xml version="1.0"?>
 <!DOCTYPE ipe SYSTEM "ipe.dtd">
 <ipe version="70107" creator="Ipe 7.1.10">
-<info created="D:20150603143945" modified="D:20151127174742"/>
+<info created="D:20150603143945" modified="D:20160404172133"/>
 <ipestyle name="basic">
 <symbol name="arrow/arc(spx)">
 <path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
@@ -251,13 +251,13 @@ h
 h
 </path>
 <text matrix="1 0 0 1 -230.178 22.1775" transformations="translations" pos="380 530" stroke="seagreen" type="label" width="76.735" height="8.307" depth="2.32" valign="baseline" size="large">Alpha complex</text>
-<text matrix="1 0 0 1 -212.333 18.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
-<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
-<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
-<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
-<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
-<text matrix="1 0 0 1 -209.478 12.0238" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
-<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 -212.333 18.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text>
+<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
+<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
+<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
+<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
+<text matrix="1 0 0 1 -209.478 12.0238" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
+<text matrix="1 0 0 1 -210.178 22.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 31.9779 -58.7483" stroke="darkgray">
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 </path>
diff --git a/src/Alpha_complex/doc/alpha_complex_representation.png b/src/Alpha_complex/doc/alpha_complex_representation.png
index 9833bff3..7b81cd69 100644
--- a/src/Alpha_complex/doc/alpha_complex_representation.png
+++ b/src/Alpha_complex/doc/alpha_complex_representation.png
diff --git a/src/Alpha_complex/example/Alpha_complex_from_off.cpp b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
index 18a1a20d..963ef5ca 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_off.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
@@ -4,17 +4,15 @@
 #include <iostream>
 #include <string>
 
-void usage(char * const progName) {
+void usage(int nbArgs, char * const progName) {
+  std::cerr << "Error: Number of arguments (" << nbArgs << ") is not correct\n";
   std::cerr << "Usage: " << progName << " filename.off alpha_square_max_value [ouput_file.txt]\n";
   std::cerr << "       i.e.: " << progName << " ../../data/points/alphacomplexdoc.off 60.0\n";
   exit(-1);  // ----- >>
 }
 
 int main(int argc, char **argv) {
-  if ((argc != 3) && (argc != 4)) {
-    std::cerr << "Error: Number of arguments (" << argc << ") is not correct\n";
-    usage(argv[0]);
-  }
+  if ((argc != 3) && (argc != 4)) usage(argc, (argv[0] - 1));
 
   std::string off_file_name(argv[1]);
   double alpha_square_max_value = atof(argv[2]);
diff --git a/src/Alpha_complex/example/Alpha_complex_from_points.cpp b/src/Alpha_complex/example/Alpha_complex_from_points.cpp
index 815e40d7..cd17af1e 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_points.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_points.cpp
@@ -4,13 +4,26 @@
 #include <iostream>
 #include <string>
 #include <vector>
+#include <limits>  // for numeric limits
 
 typedef CGAL::Epick_d< CGAL::Dimension_tag<2> > Kernel;
 typedef Kernel::Point_d Point;
 typedef std::vector<Point> Vector_of_points;
 
+void usage(int nbArgs, char * const progName) {
+  std::cerr << "Error: Number of arguments (" << nbArgs << ") is not correct\n";
+  std::cerr << "Usage: " << progName << " [alpha_square_max_value]\n";
+  std::cerr << "       i.e.: " << progName << " 60.0\n";
+  exit(-1);  // ----- >>
+}
+
 int main(int argc, char **argv) {
-  double alpha_square_max_value = 60.0;
+  if ((argc != 1) && (argc != 2)) usage(argc, (argv[0] - 1));
+
+  // Delaunay complex if alpha_square_max_value is not given by the user.
+  double alpha_square_max_value = std::numeric_limits<double>::infinity();
+  if (argc == 2)
+    alpha_square_max_value = atof(argv[1]);
 
   // ----------------------------------------------------------------------------
   // Init of a list of points
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt b/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt
index 5869fdff..13183e86 100644
--- a/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc_32.txt
@@ -7,16 +7,16 @@ Iterator on alpha complex simplices in the filtration order, with [filtration va
    ( 4 ) -> [0] 
    ( 5 ) -> [0] 
    ( 6 ) -> [0] 
-   ( 5 4 ) -> [6.25] 
-   ( 3 1 ) -> [7.25] 
-   ( 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] 
+   ( 3 2 ) -> [6.25] 
+   ( 5 4 ) -> [7.25] 
+   ( 2 0 ) -> [8.5] 
+   ( 1 0 ) -> [9.25] 
+   ( 3 1 ) -> [10] 
+   ( 2 1 ) -> [11.25] 
+   ( 3 2 1 ) -> [12.5] 
+   ( 2 1 0 ) -> [12.9959] 
+   ( 6 5 ) -> [13.25] 
+   ( 4 2 ) -> [20] 
+   ( 6 4 ) -> [22.7367] 
+   ( 6 5 4 ) -> [22.7367] 
+   ( 6 3 ) -> [30.25] 
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt b/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt
index 1d17a58a..71f29a00 100644
--- a/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc_60.txt
@@ -7,21 +7,21 @@ Iterator on alpha complex simplices in the filtration order, with [filtration va
    ( 4 ) -> [0] 
    ( 5 ) -> [0] 
    ( 6 ) -> [0] 
-   ( 5 4 ) -> [6.25] 
-   ( 3 1 ) -> [7.25] 
-   ( 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] 
-   ( 4 0 ) -> [36.5] 
-   ( 5 4 0 ) -> [36.5] 
-   ( 4 1 0 ) -> [37.2449] 
-   ( 2 1 ) -> [59.7107] 
-   ( 4 2 1 ) -> [59.7107] 
+   ( 3 2 ) -> [6.25] 
+   ( 5 4 ) -> [7.25] 
+   ( 2 0 ) -> [8.5] 
+   ( 1 0 ) -> [9.25] 
+   ( 3 1 ) -> [10] 
+   ( 2 1 ) -> [11.25] 
+   ( 3 2 1 ) -> [12.5] 
+   ( 2 1 0 ) -> [12.9959] 
+   ( 6 5 ) -> [13.25] 
+   ( 4 2 ) -> [20] 
+   ( 6 4 ) -> [22.7367] 
+   ( 6 5 4 ) -> [22.7367] 
+   ( 6 3 ) -> [30.25] 
+   ( 6 2 ) -> [36.5] 
+   ( 6 3 2 ) -> [36.5] 
+   ( 6 4 2 ) -> [37.2449] 
+   ( 4 0 ) -> [59.7107] 
+   ( 4 2 0 ) -> [59.7107] 
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index 2b27a459..21eb5f48 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -27,14 +27,16 @@
 #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>
+// to construct Alpha_complex from a OFF file of points
+#include <gudhi/Points_off_io.h>
 
 #include <stdlib.h>
 #include <math.h>  // isnan, fmax
 
+//#include <CGAL/Triangulation_data_structure.h>
 #include <CGAL/Delaunay_triangulation.h>
 #include <CGAL/Epick_d.h>
+#include <CGAL/Spatial_sort_traits_adapter_d.h>
 
 #include <iostream>
 #include <vector>
@@ -43,6 +45,7 @@
 #include <map>
 #include <utility>  // std::pair
 #include <stdexcept>
+#include <numeric>  // for std::iota
 
 namespace Gudhi {
 
@@ -57,7 +60,7 @@ namespace alphacomplex {
  * \details
  * The data structure can be constructed from a CGAL Delaunay triangulation (for more informations on CGAL Delaunay 
  * triangulation, please refer to the corresponding chapter in page http://doc.cgal.org/latest/Triangulation/) or from
- * an OFF file (cf. Delaunay_triangulation_off_reader).
+ * an OFF file (cf. Points_off_reader).
  * 
  * Please refer to \ref alpha_complex for examples.
  *
@@ -74,13 +77,19 @@ namespace alphacomplex {
 template<class Kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>>
 class Alpha_complex : public Simplex_tree<> {
  public:
+  // Add an int in TDS to save point index in the structure
+  typedef CGAL::Triangulation_data_structure<CGAL::Dynamic_dimension_tag,
+                              CGAL::Triangulation_vertex<Kernel, int>,
+                              CGAL::Triangulation_full_cell<Kernel> > TDS;
   /** \brief A Delaunay triangulation of a set of points in \f$ \mathbb{R}^D\f$.*/
-  typedef typename CGAL::Delaunay_triangulation<Kernel> Delaunay_triangulation;
+  typedef CGAL::Delaunay_triangulation<Kernel, TDS> Delaunay_triangulation;
+
   /** \brief A point in Euclidean space.*/
   typedef typename Kernel::Point_d Point_d;
   /** \brief Geometric traits class that provides the geometric types and predicates needed by Delaunay
    * triangulations.*/
   typedef Kernel Geom_traits;
+
  private:
   // From Simplex_tree
   // Type required to insert into a simplex_tree (with or without subfaces).
@@ -104,7 +113,7 @@ class Alpha_complex : public Simplex_tree<> {
 
   // Double map type to switch from CGAL vertex iterator to simplex tree vertex handle and vice versa.
   typedef typename std::map< CGAL_vertex_iterator, Vertex_handle > Map_vertex_iterator_to_handle;
-  typedef typename std::vector< CGAL_vertex_iterator > Vector_vertex_iterator;
+  typedef typename std::map< Vertex_handle, CGAL_vertex_iterator > Vector_vertex_iterator;
 
  private:
   /** \brief Map to switch from CGAL vertex iterator to simplex tree vertex handle.*/
@@ -128,28 +137,13 @@ class Alpha_complex : public Simplex_tree<> {
   Alpha_complex(const std::string& off_file_name,
                 Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity())
       : triangulation_(nullptr) {
-    Gudhi::Delaunay_triangulation_off_reader<Delaunay_triangulation> off_reader(off_file_name);
+    Gudhi::Points_off_reader<Point_d> off_reader(off_file_name);
     if (!off_reader.is_valid()) {
       std::cerr << "Alpha_complex - Unable to read file " << off_file_name << "\n";
       exit(-1);  // ----- >>
     }
-    triangulation_ = off_reader.get_complex();
-    init(max_alpha_square);
-  }
 
-  /** \brief Alpha_complex constructor from a Delaunay triangulation.
-   *
-   * @param[in] triangulation_ptr Pointer on a <a target="_blank"
-   * href="http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations">
-   * CGAL::Delaunay_triangulation<Kernel></a> \cite cgal:hdj-t-15b.
-   * Alpha_complex takes ownership of the Delaunay_triangulation object, which must have been allocated using operator
-   * new.
-   * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$.
-   */
-  Alpha_complex(Delaunay_triangulation* triangulation_ptr,
-                Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity())
-      : triangulation_(triangulation_ptr) {
-    init(max_alpha_square);
+    init_from_range(off_reader.get_point_cloud(), max_alpha_square);
   }
 
   /** \brief Alpha_complex constructor from a list of points.
@@ -164,23 +158,7 @@ class Alpha_complex : public Simplex_tree<> {
   Alpha_complex(const InputPointRange& points,
                 Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity())
       : triangulation_(nullptr) {
-    auto first = std::begin(points);
-    auto last = std::end(points);
-
-    if (first != last) {
-      // point_dimension function initialization
-      Point_Dimension point_dimension = kernel_.point_dimension_d_object();
-
-      // Delaunay triangulation is point dimension.
-      triangulation_ = new Delaunay_triangulation(point_dimension(*first));
-
-      size_type inserted = triangulation_->insert(first, last);
-      if (inserted != (last -first)) {
-        std::cerr << "Alpha_complex - insertion failed " << inserted << " != " << (last -first) << "\n";
-        exit(-1);  // ----- >>
-      }
-      init(max_alpha_square);
-    }
+    init_from_range(points, max_alpha_square);
   }
 
   /** \brief Alpha_complex destructor.
@@ -191,6 +169,12 @@ class Alpha_complex : public Simplex_tree<> {
     delete triangulation_;
   }
 
+  // Forbid copy/move constructor/assignment operator
+  Alpha_complex(const Alpha_complex& other) = delete;
+  Alpha_complex& operator= (const Alpha_complex& other) = delete;
+  Alpha_complex (Alpha_complex&& other) = delete;
+  Alpha_complex& operator= (Alpha_complex&& other) = delete;
+
   /** \brief get_point returns the point corresponding to the vertex given as parameter.
    *
    * @param[in] vertex Vertex handle of the point to retrieve.
@@ -202,6 +186,44 @@ class Alpha_complex : public Simplex_tree<> {
   }
 
  private:
+  template<typename InputPointRange >
+  void init_from_range(const InputPointRange& points, Filtration_value max_alpha_square) {
+    auto first = std::begin(points);
+    auto last = std::end(points);
+    if (first != last) {
+      // point_dimension function initialization
+      Point_Dimension point_dimension = kernel_.point_dimension_d_object();
+
+      // Delaunay triangulation is point dimension.
+      triangulation_ = new Delaunay_triangulation(point_dimension(*first));
+
+      std::vector<Point_d> points(first, last);
+    
+      // Creates a vector {0, 1, ..., N-1}
+      std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0),
+                                          boost::counting_iterator<std::ptrdiff_t>(points.size()));
+  
+      // Sort indices considering CGAL spatial sort
+      typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_d*> Search_traits_d;
+      spatial_sort(indices.begin(),indices.end(),Search_traits_d(&(points[0])));
+    
+      typename Delaunay_triangulation::Full_cell_handle hint;
+      for (auto index : indices) {
+        typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(points[index], hint);
+        // Save index value as data to retrieve it after insertion
+        pos->data() = index;
+        hint = pos->full_cell();
+      }
+
+      if (triangulation_->number_of_vertices() != (last -first)) {
+        std::cerr << "Alpha_complex - insertion failed " << triangulation_->number_of_vertices() << " != " <<
+            (last -first) << "\n";
+        exit(-1);  // ----- >>
+      }
+      init(max_alpha_square);
+    }
+  }
+
   /** \brief Initialize the Alpha_complex from the Delaunay triangulation.
    *
    * @param[in] max_alpha_square maximum for alpha square value.
@@ -233,18 +255,15 @@ class Alpha_complex : public Simplex_tree<> {
 
     // --------------------------------------------------------------------------------------------
     // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa
-    // Start to insert at handle = 0 - default integer value
-    Vertex_handle vertex_handle = Vertex_handle();
     // Loop on triangulation vertices list
     for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
       if (!triangulation_->is_infinite(*vit)) {
 #ifdef DEBUG_TRACES
-        std::cout << "Vertex insertion - " << vertex_handle << " -> " << vit->point() << std::endl;
+        std::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl;
 #endif  // DEBUG_TRACES
 
-        vertex_iterator_to_handle_.emplace(vit, vertex_handle);
-        vertex_handle_to_iterator_.push_back(vit);
-        vertex_handle++;
+        vertex_iterator_to_handle_.emplace(vit, vit->data());
+        vertex_handle_to_iterator_.emplace(vit->data(), vit);
       }
     }
     // --------------------------------------------------------------------------------------------
diff --git a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
index 315582d1..80b39924 100644
--- a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
+++ b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
@@ -32,8 +32,6 @@
 #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>
 
 // Use dynamic_dimension_tag for the user to be able to set dimension