layout: page title: "Alpha complex" meta_title: "Alpha complex" teaser: ""
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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:
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
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
N.B.:
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:
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
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.-c [ --cuboid-file ]
is the path to the file describing the periodic domain. It must be in the format described here. 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
N.B.:
alpha_complex_3d_persistence
only accepts OFF files in dimension 3.GUDHIdev Version 3.5.0 - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. - Copyright : MIT | Generated on Fri Jan 14 2022 18:28:42 for GUDHIdev by Doxygen 1.9.1 |