Alpha complex
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:
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.
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
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 and Regular triangulation documentation.