Documentation for Alpha complex 3d

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alpha_complex_3d_module_vincent@3664 636b058d-ea47-450e-bf9e-a15bfbe3eedb

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diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md
index 0fe98837..7ae5f913 100644
--- a/src/Alpha_complex/utilities/alphacomplex.md
+++ b/src/Alpha_complex/utilities/alphacomplex.md
@@ -12,15 +12,18 @@ Leave the lines above as it is required by the web site generator 'Jekyll'
 

 ## 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.

+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

 ```

 

-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**

 

@@ -29,15 +32,20 @@ and `p` is the characteristic of the field *Z/pZ* used for homology coefficients
 ```

 

 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 OFF file>` is the path to the input point cloud in

+[nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).

 

 **Allowed options**

 

 * `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.

-* `-p [ --field-charac ]` (default = 11)     Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

+* `-o [ --output-file ]` Name of file in which the persistence diagram is

+written. Default print in standard output.

+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value

+for the Alpha complex construction.

+* `-p [ --field-charac ]` (default = 11)     Characteristic p of the

+coefficient field Z/pZ for computing homology.

+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature

+to be recorded. Enter a negative value to see zero length intervals.

 

 **Example**

 

@@ -51,13 +59,26 @@ N.B.:
 

 

 ## 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:

+This program computes the persistent homology with coefficient field Z/pZ of

+the 3D alpha complex built from a 3D point cloud.

+One can use exact computation. It is slower, but it is necessary when points

+are on a grid for instance.

+Alpha complex 3d can be weighted and/or periodic (refer to the

+[CGAL's 3D Periodic Triangulations User Manual](

+https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html)

+for more details).

+

+The output diagram contains

+one bar per line, written with the convention:

 

 ```

 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**

 

@@ -65,14 +86,25 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are
    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).

+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**

 

 * `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.

+* `-o [ --output-file ]` Name of file in which the persistence diagram is

+written. Default print in standard output.

+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient

+field Z/pZ for computing homology.

+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature

+to be recorded. Enter a negative value to see zero length intervals.

+* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain.

+It must be in the format described

+[here](/doc/latest/fileformats.html#FileFormatsIsoCuboid).

+* `-w [ --weight-file ]` is the path to the file containing the weights of the

+points (one value per line).

+* `-e [ --exact ]` for the exact computation version (not compatible with

+weight and periodic version).

 

 **Example**

 

@@ -84,49 +116,16 @@ 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.

+* 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.

 

 

 

-## 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>

-```

-

-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).

 

-**Allowed options**

-

-* `-h [ --help ]` Produce help message

-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.

-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.

-* `-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

-```

-

-

-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 ##