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diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README new file mode 100644 index 00000000..c3dd170b --- /dev/null +++ b/src/Alpha_complex/utilities/README @@ -0,0 +1,172 @@ +# Alpha_complex # + +## `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 b d` + +where `dim` is the dimension of the homological feature, `b` and `d` 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] <OFF input file>` + +**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` + +outputs: +``` +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 +``` + +Here we retrieve expected Betti numbers on a tore 3D: +``` +Betti numbers[0] = 1 +Betti numbers[1] = 2 +Betti numbers[2] = 1 +``` + +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] <OFF input file> <weights input file>` + +**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` + +outputs: +``` +Simplex_tree dim: 3 +2 0 -1 inf +2 1 -0.931784 0.000103311 +2 1 -0.906588 2.60165e-05 +2 2 -0.43556 0.0393798 +``` + +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. + +**Usage** +`periodic_alpha_complex_3d_persistence <input OFF file> <cuboid file> <p> <min_persistence>` +where +`<input OFF file>` is the path to the input point cloud in OFF format. +`<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). +`<p>` is the characteristic p of the coefficient field *Z/pZ* for computing homology. It must be a stricly positive integer. +`<min_persistence>` is the minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals. + +**Usage** +`./periodic_alpha_complex_3d_persistence [options] input-file cuboid-file` + +**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` + +outputs: +``` +Periodic Delaunay computed. +Simplex_tree dim: 3 +3 0 0 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 2 0.005 inf +3 2 0.005 inf +3 2 0.005 inf +3 3 0.0075 inf +``` + +Here we retrieve expected Betti numbers on an 3D iso-oriented cuboids: +``` +Betti numbers[0] = 1 +Betti numbers[1] = 3 +Betti numbers[2] = 3 +Betti numbers[3] = 1 +``` + +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 b d` + +where `dim` is the dimension of the homological feature, `b` and `d` 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] <OFF input file>` + +**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` + +outputs: +``` +Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 +``` + +Here we retrieve expected Betti numbers on a tore 3D: +``` +Betti numbers[0] = 1 +Betti numbers[1] = 2 +Betti numbers[2] = 1 +``` + +N.B.: +* `alpha_complex_persistence` only accepts OFF files in dimension d. +* Filtration values are alpha square values. |