Fix doc issue for utilities part on the web site

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@3176 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 3bafd9e13a5646ca93023144705d3ac7ed7c9b3a

1 files changed, 70 insertions, 78 deletions

diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README
index 1cd2ca95..56bce602 100644
--- a/src/Alpha_complex/utilities/README
+++ b/src/Alpha_complex/utilities/README
@@ -1,16 +1,35 @@
-# Alpha_complex #

-

-## `alpha_complex_3d_persistence` ##

+---

+layout: page

+title: "Alpha complex"

+meta_title: "alphacomplex"

+subheadline: ""

+teaser: ""

+permalink: "/alphacomplex/"

+---

+{::comment}

+These flags above are here for web site generation, please let them.

+cf. https://gitlab.inria.fr/GUDHI/website

+Must be in conformity with _data/navigation.yml

+{:/comment}

+

+

+

+## alpha_complex_3d_persistence ##

 This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:

 

-`p dim birth death`

+```

+p dim birth death

+```

 

 where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).

 

 **Usage**

-`alpha_complex_3d_persistence [options] <input OFF file>`

-where

-`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

+

+```

+   alpha_complex_3d_persistence [options] <input OFF file>

+```

+

+where `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

 

 **Allowed options**

 

@@ -20,43 +39,38 @@ where
 * `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

 

 **Example**

-`alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45`

 

-outputs:

 ```

-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

+alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45

 ```

 

-Here we retrieve expected Betti numbers on a tore 3D:

-```

-Betti numbers[0] = 1

-Betti numbers[1] = 2

-Betti numbers[2] = 1

-```

+N.B.:

 

-N.B.: 

 * `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.

 * Filtration values are alpha square values.

 

 

+## exact_alpha_complex_3d_persistence ##

+

+Same as `alpha_complex_3d_persistence`, but using exact computation.

+It is slower, but it is necessary when points are on a grid for instance.

 

-## `exact_alpha_complex_3d_persistence` ##

-Same as `alpha_complex_3d_persistence`, but using exact computation. It is slower, but it is necessary when points are on a grid for instance.

 

 

+## weighted_alpha_complex_3d_persistence ##

 

-## `weighted_alpha_complex_3d_persistence` ##

 Same as `alpha_complex_3d_persistence`, but using weighted points.

 

 **Usage**

-`weighted_alpha_complex_3d_persistence [options] <input OFF file> <weights input file>`

+

+```

+   weighted_alpha_complex_3d_persistence [options] <input OFF file> <weights input file>

+```

+

 where

-`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

-`<input weights file>` is the path to the file containing the weights of the points (one value per line).

+

+* `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

+* `<input weights file>` is the path to the file containing the weights of the points (one value per line).

 

 **Allowed options**

 

@@ -66,32 +80,33 @@ where
 * `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

 

 **Example**

-`weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45`

 

-outputs:

 ```

-Simplex_tree dim: 3

-2  0 -1 inf

-2  1 -0.931784 0.000103311

-2  1 -0.906588 2.60165e-05

-2  2 -0.43556 0.0393798

+   weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45

 ```

 

+

 N.B.:

+

 * Weights values are explained on CGAL [Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)

 and [Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.

 * Filtration values are alpha square values.

 

 

-## `periodic_alpha_complex_3d_persistence` ##

+## periodic_alpha_complex_3d_persistence ##

 Same as `alpha_complex_3d_persistence`, but using periodic alpha shape 3d.

 Refer to the [CGAL's 3D Periodic Triangulations User Manual](https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html) for more details.

 

 **Usage**

-`periodic_alpha_complex_3d_persistence [options] <input OFF file> <cuboid file>`

+

+```

+   periodic_alpha_complex_3d_persistence [options] <input OFF file> <cuboid file>

+```

+

 where

-`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

-`<cuboid file>` is the path to the file describing the periodic domain. It must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).

+

+* `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

+* `<cuboid file>` is the path to the file describing the periodic domain. It must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).

 

 **Allowed options**

 

@@ -102,46 +117,36 @@ where
 

 

 **Example**

-`periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0`

 

-outputs:

 ```

-Periodic Delaunay computed.

-Simplex_tree dim: 3

-3  0 0 inf

-3  1 0.0025 inf

-3  1 0.0025 inf

-3  1 0.0025 inf

-3  2 0.005 inf

-3  2 0.005 inf

-3  2 0.005 inf

-3  3 0.0075 inf

+periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0

 ```

 

-Here we retrieve expected Betti numbers on an 3D iso-oriented cuboids:

-```

-Betti numbers[0] = 1

-Betti numbers[1] = 3

-Betti numbers[2] = 3

-Betti numbers[3] = 1

-```

+N.B.:

 

-N.B.: 

 * Cuboid file must be in the format described [here](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid).

 * Filtration values are alpha square values.

 

 

 

+## alpha_complex_persistence ##

 

-## `alpha_complex_persistence` ##

-This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud. The output diagram contains one bar per line, written with the convention:

+This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud.

+The output diagram contains one bar per line, written with the convention:

 

-`p dim birth death`

+```

+   p dim birth death

+```

 

-where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).

+where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature,

+and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).

 

 **Usage**

-`alpha_complex_persistence [options] <input OFF file>`

+

+```

+   alpha_complex_persistence [options] <input OFF file>

+```

+

 where

 `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

 

@@ -154,24 +159,11 @@ where
 * `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

 

 **Example**

-`alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off`

 

-outputs:

 ```

-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

+   alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off

 ```

 

 N.B.:

+

 * Filtration values are alpha square values.