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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.