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+---
+layout: page
+title: "Alpha complex"
+meta_title: "Alpha complex"
+teaser: ""
+permalink: /alphacomplex/
+---
+{::comment}
+Leave the lines above as it is required by the web site generator 'Jekyll'
+{:/comment}
+
+
+## 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:
+
+```
+   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_persistence [options] <input OFF file>
+```
+
+where
+`<input OFF file>` is the path to the input point cloud in
+[nOFF ASCII format]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsOFF).
+
+**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.
+
+**Example**
+
+```
+   alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off
+```
+
+N.B.:
+
+* Filtration values are alpha square values.
+
+
+## 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.
+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).
+
+**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]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsOFF).
+
+**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.
+* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain.
+It must be in the format described
+[here]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsIsoCuboid).
+Default version is not periodic.
+* `-w [ --weight-file ]` is the path to the file containing the weights of the
+points (one value per line).
+Default version is not weighted.
+* `-e [ --exact ]` for the exact computation version (not compatible with
+weight and periodic version).
+* `-f [ --fast ]` for the fast computation version.
+
+**Example**
+
+```
+alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45
+```
+
+N.B.:
+
+* `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
+* Filtration values are alpha square values.
+* 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.