Add of src/common/include/gudhi/Points_3D_off_io.h to read specific 3D OFF Files for CGAL Point_3

Add an example to read 3D OFF Files for CGAL Point_3
Modify alpha_complex_3d_persistence.cpp to read OFF files
Add periodic_alpha_complex_3d_persistence.cpp in Persistent_cohomology examples
Add info about new examples in README


git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/periodic_alpha_complex_3d@1116 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 6b423b598869a0f4f9c62d93c93b69efd93c0161

1 files changed, 92 insertions, 6 deletions

diff --git a/src/Persistent_cohomology/example/README b/src/Persistent_cohomology/example/README
index 8c71ccf5..92b80c76 100644
--- a/src/Persistent_cohomology/example/README
+++ b/src/Persistent_cohomology/example/README
@@ -4,13 +4,13 @@ cd /path-to-example/
 cmake .
 make
 
-
-Example of use :
+***********************************************************************************************************************
+Example of use of RIPS:
 
 Computation of the persistent homology with Z/2Z coefficients of the Rips complex on points 
 sampling a Klein bottle:
 
-./rips_persistence ../../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -m 100
+./rips_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -m 100
 
 output:
 210  0 0 inf
@@ -29,7 +29,7 @@ where
 
 with Z/3Z coefficients:
 
-./rips_persistence ../../../data/points/Kl.txt -r 0.25 -d 3 -p 3 -m 100
+./rips_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 3 -m 100
 
 output:
 3  0 0 inf
@@ -37,7 +37,7 @@ output:
 
 and the computation with Z/2Z and Z/3Z coefficients simultaneously:
 
-./rips_multifield_persistence ../../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 3 -m 100
+./rips_multifield_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 3 -m 100
 
 output:
 6  0 0 inf
@@ -47,10 +47,96 @@ output:
 
 and finally the computation with all Z/pZ for 2 <= p <= 71 (20 first prime numbers):
 
- ./rips_multifield_persistence ../../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 71 -m 100
+ ./rips_multifield_persistence ../../data/points/Kl.txt -r 0.25 -d 3 -p 2 -q 71 -m 100
 
 output:
 557940830126698960967415390  0 0 inf
 557940830126698960967415390  1 0.0702103 inf
 2  1 0.0702103 inf
 2  2 0.159992 inf
+
+***********************************************************************************************************************
+Example of use of ALPHA:
+
+For a more verbose mode, please run cmake with option "DEBUG_TRACES=TRUE" and recompile the programs.
+
+1) 3D special case
+------------------
+Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points 
+sampling a torus 3D:
+
+./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45
+
+output:
+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 
+
+Here we retrieve expected Betti numbers on a tore 3D:
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+
+N.B.: alpha_complex_3d_persistence accepts only OFF files in 3D dimension.
+
+2) d-Dimension case
+-------------------
+Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points 
+sampling a torus 3D:
+
+./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off
+
+output:
+Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
+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 
+
+Here we retrieve expected Betti numbers on a tore 3D:
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+
+N.B.: alpha_complex_persistence accepts OFF files in d-Dimension.
+
+3) 3D periodic special case
+---------------------------
+./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off 2 0.0
+
+output:
+Periodic Delaunay computed.
+Simplex_tree dim: 3
+2  0 0.0866025 inf 
+2  1 0.0866025 inf 
+2  1 0.0866025 inf 
+2  1 0.0866025 inf 
+2  2 0.0866025 inf 
+2  2 0.0866025 inf 
+2  2 0.0866025 inf 
+
+N.B.: periodic_alpha_complex_3d_persistence accepts only OFF files in 3D dimension. In this example, the periodic cube
+is hard coded to { x = [0,1]; y = [0,1]; z = [0,1] }
+
+***********************************************************************************************************************
+Example of use of PLAIN HOMOLOGY:
+
+This example computes the plain homology of the following simplicial complex without filtration values:
+  /* Complex to build. */
+  /*    1   3          */
+  /*    o---o          */
+  /*   /X\ /           */
+  /*  o---o   o        */
+  /*  2   0   4        */
+
+./plain_homology 
+
+output:
+2  0 0 inf 
+2  0 0 inf 
+2  1 0 inf 
+
+Here we retrieve the 2 entities {0,1,2,3} and {4} (Betti numbers[0] = 2) and the hole in {0,1,3} (Betti numbers[1] = 1)
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