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+---

+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

+```

+

+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).

+

+**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**

+

+```

+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.

+

+

+## 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 ##

+

+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 ##

+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>

+```

+

+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).

+

+**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**

+

+```

+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

+```

+

+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 ##

+

+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](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.

+

+**Example**

+

+```

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

+```

+

+N.B.:

+

+* Filtration values are alpha square values.