From 9899ae167f281d10b1684dfcd02c6838c5bf28df Mon Sep 17 00:00:00 2001 From: Gard Spreemann Date: Fri, 2 Feb 2018 13:51:45 +0100 Subject: GUDHI 2.1.0 as released by upstream in a tarball. --- utilities/Alpha_complex/alphacomplex.md | 158 ++++++++++++++++++++++++++++++++ 1 file changed, 158 insertions(+) create mode 100644 utilities/Alpha_complex/alphacomplex.md (limited to 'utilities/Alpha_complex/alphacomplex.md') diff --git a/utilities/Alpha_complex/alphacomplex.md b/utilities/Alpha_complex/alphacomplex.md new file mode 100644 index 00000000..aace85d3 --- /dev/null +++ b/utilities/Alpha_complex/alphacomplex.md @@ -0,0 +1,158 @@ + + +# 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] +``` + +where +`` 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. + + +## 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] +``` + +where `` 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] +``` + +where + +* `` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html). +* `` 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] +``` + +where + +* `` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html). +* `` is the path to the file describing the periodic domain. It must be in the format described +[here](/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](/doc/latest/fileformats.html#FileFormatsIsoCuboid). +* Filtration values are alpha square values. -- cgit v1.2.3