From 9b8bb34ff06b08119b8fa1e78c260886287c5a92 Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Tue, 3 Jul 2018 16:08:32 +0000 Subject: Documentation for Alpha complex 3d git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alpha_complex_3d_module_vincent@3664 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: c6d824cdab7ac5ea79ce458dac666d35a9a21ab7 --- src/Alpha_complex/utilities/alphacomplex.md | 101 ++++++++++++++-------------- 1 file changed, 50 insertions(+), 51 deletions(-) (limited to 'src/Alpha_complex/utilities/alphacomplex.md') diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md index 0fe98837..7ae5f913 100644 --- a/src/Alpha_complex/utilities/alphacomplex.md +++ b/src/Alpha_complex/utilities/alphacomplex.md @@ -12,15 +12,18 @@ Leave the lines above as it is required by the web site generator 'Jekyll' ## 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. +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). +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** @@ -29,15 +32,20 @@ and `p` is the characteristic of the field *Z/pZ* used for homology coefficients ``` 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 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. +* `-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** @@ -51,13 +59,26 @@ N.B.: ## 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: +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]( +https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html) +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). +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** @@ -65,14 +86,25 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are 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). +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. +* `-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. +* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain. +It must be in the format described +[here](/doc/latest/fileformats.html#FileFormatsIsoCuboid). +* `-w [ --weight-file ]` is the path to the file containing the weights of the +points (one value per line). +* `-e [ --exact ]` for the exact computation version (not compatible with +weight and periodic version). **Example** @@ -84,49 +116,16 @@ 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. +* 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. -## 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 ## -- cgit v1.2.3