layout: page title: "Alpha complex" meta_title: "Alpha complex" teaser: ""

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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.

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.
-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.
-f [ --fast ] for the fast computation version.

Example

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

N.B.:

Filtration values are alpha square values.
Weights values are explained on CGAL dD Triangulations and Regular triangulation documentation.

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 for more details).

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