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

8 files changed, 135 insertions, 99 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
diff --git a/src/Alpha_complex/doc/alpha_complex_doc.ipe b/src/Alpha_complex/doc/alpha_complex_doc.ipe
index 99bd05af..baf0d26a 100644
--- a/src/Alpha_complex/doc/alpha_complex_doc.ipe
+++ b/src/Alpha_complex/doc/alpha_complex_doc.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:20160315144626"/>
+<info created="D:20150603143945" modified="D:20160406112209"/>
 <ipestyle name="basic">
 <symbol name="arrow/arc(spx)">
 <path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
@@ -253,13 +253,13 @@ h
 320 580 l
 </path>
 <text matrix="1 0 0 1 -260 0" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="118.196" height="8.307" depth="2.32" valign="baseline" size="large">Delaunay triangulation</text>
-<text matrix="1 0 0 1 -242.155 -3.50128" 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 -240 0" 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 -240 0" 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 -240 0" 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 -240 0" 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 -239.3 -10.1537" 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 -240 0" 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 -242.155 -3.50128" 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 -240 0" 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 -240 0" 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 -240 0" 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 -240 0" 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 -239.3 -10.1537" 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 -240 0" 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 -240 0" stroke="darkcyan">
 280 660 m
 300 710 l
@@ -314,7 +314,7 @@ h
 <use matrix="1 0 0 1 -240 0" name="mark/fdisk(sfx)" pos="370 580" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -240 0" name="mark/fdisk(sfx)" pos="350 520" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -240 0" name="mark/fdisk(sfx)" pos="290 530" size="normal" stroke="black" fill="white"/>
-<text matrix="1 0 0 1 -8 -96" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
+<text matrix="1 0 0 1 4 -96" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
 <path matrix="1 0 0 1 4 -96" stroke="black">
 300 688 m
 300 676 l
@@ -322,15 +322,14 @@ h
 312 688 l
 h
 </path>
-<path matrix="1 0 0 1 -8 -96" stroke="black">
+<text matrix="1 0 0 1 24 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
+<path matrix="1 0 0 1 36 -76" stroke="black">
 300 688 m
 300 676 l
 312 676 l
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 -8 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
-<text matrix="1 0 0 1 12 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
 <path matrix="1 0 0 1 24 -76" stroke="black">
 300 688 m
 300 676 l
@@ -338,6 +337,8 @@ h
 312 688 l
 h
 </path>
+<text matrix="1 0 0 1 24 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
+<text matrix="1 0 0 1 12 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
 <path matrix="1 0 0 1 12 -76" stroke="black">
 300 688 m
 300 676 l
@@ -345,39 +346,15 @@ h
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 12 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
-<text matrix="1 0 0 1 0 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text>
-<path matrix="1 0 0 1 36 -76" stroke="black">
-300 688 m
-300 676 l
-312 676 l
-312 688 l
-h
-</path>
-<path matrix="1 0 0 1 0 -76" stroke="black">
-300 688 m
-300 676 l
-312 676 l
-312 688 l
-h
-</path>
-<text matrix="1 0 0 1 24 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
-<path matrix="1 0 0 1 20 -96" stroke="black">
+<path matrix="1 0 0 1 24 -96" stroke="black">
 300 688 m
 300 676 l
 312 676 l
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 8 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
+<text matrix="1 0 0 1 12 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
 <text matrix="1 0 0 1 64 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
-<path matrix="1 0 0 1 76 -76" stroke="black">
-300 688 m
-300 676 l
-312 676 l
-312 688 l
-h
-</path>
 <path matrix="1 0 0 1 64 -76" stroke="black">
 300 688 m
 300 676 l
@@ -385,7 +362,6 @@ h
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 64 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
 <text matrix="1 0 0 1 52 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text>
 <path matrix="1 0 0 1 52 -76" stroke="black">
 300 688 m
@@ -401,7 +377,7 @@ h
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 36 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
+<text matrix="1 0 0 1 36 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
 <text matrix="1 0 0 1 104 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 104 -76" stroke="black">
 300 688 m
@@ -418,14 +394,14 @@ h
 312 688 l
 h
 </path>
-<path matrix="1 0 0 1 92 -96" stroke="black">
+<path matrix="1 0 0 1 96 -96" stroke="black">
 300 688 m
 300 676 l
 312 676 l
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 80 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<text matrix="1 0 0 1 84 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <text matrix="1 0 0 1 148 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 148 -76" stroke="black">
 300 688 m
@@ -442,22 +418,22 @@ h
 312 688 l
 h
 </path>
-<path matrix="1 0 0 1 168 -76" stroke="black">
+<path matrix="1 0 0 1 120 -76" stroke="black">
 300 688 m
 300 676 l
 312 676 l
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 156 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
-<path matrix="1 0 0 1 168 -76" stroke="black">
+<text matrix="1 0 0 1 108 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 120 -76" stroke="black">
 300 688 m
 300 676 l
 312 676 l
 312 688 l
 h
 </path>
-<text matrix="1 0 0 1 156 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<text matrix="1 0 0 1 108 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
 <path matrix="1 0 0 1 48 -96" stroke="black">
 292 716 m
 292 728 l
@@ -514,11 +490,11 @@ h
 <text matrix="1 0 0 1 48 -96" transformations="translations" pos="400 720" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text>
 <text matrix="1 0 0 1 48 -96" transformations="translations" pos="424 720" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text>
 <text matrix="1 0 0 1 48 -96" transformations="translations" pos="448 720" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
-<path matrix="1 0 0 1 36 -96" stroke="black">
+<path matrix="1 0 0 1 -12 -96" stroke="black">
 436 708 m
 436 716 l
 </path>
-<path matrix="1 0 0 1 36 -96" stroke="black">
+<path matrix="1 0 0 1 28 -96" stroke="black">
 364 708 m
 364 716 l
 </path>
@@ -535,11 +511,11 @@ h
 308 716 l
 308 716 l
 </path>
-<path matrix="1 0 0 1 36 -96" stroke="black">
+<path matrix="1 0 0 1 48 -96" stroke="black">
 264 688 m
 268 696 l
 </path>
-<path matrix="1 0 0 1 36 -96" stroke="black">
+<path matrix="1 0 0 1 40 -96" stroke="black">
 292 688 m
 292 696 l
 </path>
@@ -555,5 +531,65 @@ h
 448 612 m
 448 620 l
 </path>
+<text matrix="1 0 0 1 80 -76" transformations="translations" pos="304 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text>
+<path matrix="1 0 0 1 80 -76" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<path matrix="1 0 0 1 80 -96" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<text matrix="1 0 0 1 68 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 24 -96" stroke="black">
+364 688 m
+364 696 l
+</path>
+<path matrix="1 0 0 1 136 -96" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<text matrix="1 0 0 1 124 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 136 -96" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<text matrix="1 0 0 1 124 -96" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 4 -116" stroke="black">
+436 708 m
+436 716 l
+</path>
+<path matrix="1 0 0 1 168 -76" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<text matrix="1 0 0 1 156 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 168 -76" stroke="black">
+300 688 m
+300 676 l
+312 676 l
+312 688 l
+h
+</path>
+<text matrix="1 0 0 1 156 -76" transformations="translations" pos="316 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text>
+<path matrix="1 0 0 1 36 -96" stroke="black">
+436 708 m
+436 716 l
+</path>
 </page>
 </ipe>
diff --git a/src/Alpha_complex/doc/alpha_complex_doc.png b/src/Alpha_complex/doc/alpha_complex_doc.png
index cfe3ede6..0b6201da 100644
--- a/src/Alpha_complex/doc/alpha_complex_doc.png
+++ b/src/Alpha_complex/doc/alpha_complex_doc.png
diff --git a/src/Alpha_complex/doc/alpha_complex_doc_421.ipe b/src/Alpha_complex/doc/alpha_complex_doc_420.ipe
index 727816c5..5d1d29d4 100644
--- a/src/Alpha_complex/doc/alpha_complex_doc_421.ipe
+++ b/src/Alpha_complex/doc/alpha_complex_doc_420.ipe
@@ -252,14 +252,14 @@ h
 350 520 l
 320 580 l
 </path>
-<text matrix="1 0 0 1 0 80" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="54.628" height="8.965" depth="2.99" valign="baseline" size="large">Cell [4,2,1]</text>
-<text matrix="1 0 0 1 -2.15463 76.4987" 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 0 80" 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 0 80" 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 0 80" 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 0 80" 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 0.700256 69.8463" 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 0 80" 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 0 80" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="54.628" height="8.965" depth="2.99" valign="baseline" size="large">Cell [4,2,0]</text>
+<text matrix="1 0 0 1 -2.15463 76.4987" 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 0 80" 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 0 80" 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 0 80" 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 0 80" 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 0.700256 69.8463" 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 0 80" 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 0 80" stroke="lightgray">
 280 660 m
 300 710 l
@@ -285,7 +285,7 @@ h
 243.428 591.569 m
 186.061 643.28 l
 </path>
-<text matrix="1 0 0 1 0 80" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="18.785" height="4.294" depth="1.49" valign="baseline">$\alpha_{421}$</text>
+<text matrix="1 0 0 1 0 80" transformations="translations" pos="212.724 627.389" stroke="darkcyan" type="label" width="18.785" height="4.294" depth="1.49" valign="baseline">$\alpha_{420}$</text>
 <path matrix="1 0 0 1 -264 -162" stroke="lightgray">
 320 580 m
 350 520 l
@@ -306,15 +306,15 @@ h
 350 520 l
 320 580 l
 </path>
-<text matrix="0.582962 0 0 1 -211.265 -209.555" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="231.798" height="8.965" depth="2.99" valign="baseline" size="large">[4,2] is Gabriel $\rightarrow$ $\alpha_{42}$ is not$\\$
+<text matrix="0.582962 0 0 1 -211.265 -209.555" transformations="translations" pos="380 530" stroke="darkcyan" type="label" width="231.798" height="8.965" depth="2.99" valign="baseline" size="large">[2,0] is Gabriel $\rightarrow$ $\alpha_{20}$ is not$\\$
 modified (NaN)
 </text>
-<text matrix="1 0 0 1 -266.155 -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 -264 -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 -264 -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 -264 -172" 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 -263.3 -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 -264 -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 -266.155 -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 -264 -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 -264 -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 -264 -172" 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 -263.3 -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 -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)
 <use matrix="1 0 0 1 -264 -162" name="mark/fdisk(sfx)" pos="370 690" size="normal" stroke="black" fill="white"/>
 <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"/>
 <use matrix="1 0 0 1 -38 -164" name="mark/fdisk(sfx)" pos="370 690" size="normal" stroke="black" fill="white"/>
-<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>
 <use name="mark/fdisk(sfx)" pos="247 431" size="normal" stroke="darkcyan" fill="white"/>
 <use matrix="1 0 0 1 -38 -164" name="mark/fdisk(sfx)" pos="350 520" size="normal" stroke="black" fill="white"/>
-<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>
 <use matrix="1 0 0 1 -38 -164" name="mark/fdisk(sfx)" pos="370 580" size="normal" stroke="black" fill="white"/>
 <use matrix="1 0 0 1 -38 -164" name="mark/fdisk(sfx)" pos="320 580" size="normal" stroke="darkred" fill="white"/>
-<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>
 <path matrix="1 0 0 1 -38 -164" stroke="darkred" pen="heavier">
 65.192 0 0 65.192 285 595 e
 </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">
 58.1341 0 0 58.1341 218.925 692.601 e
 </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