From c2d46e0e6cfea1927875219bd5e03962cef7b010 Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Mon, 29 Jan 2018 16:31:18 +0000 Subject: Fix doc issue for utilities part on the web site git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@3176 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 3bafd9e13a5646ca93023144705d3ac7ed7c9b3a --- src/Alpha_complex/utilities/README | 148 ++++++++++++++++++------------------- 1 file changed, 70 insertions(+), 78 deletions(-) (limited to 'src/Alpha_complex/utilities') diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README index 1cd2ca95..56bce602 100644 --- a/src/Alpha_complex/utilities/README +++ b/src/Alpha_complex/utilities/README @@ -1,16 +1,35 @@ -# Alpha_complex # - -## `alpha_complex_3d_persistence` ## +--- +layout: page +title: "Alpha complex" +meta_title: "alphacomplex" +subheadline: "" +teaser: "" +permalink: "/alphacomplex/" +--- +{::comment} +These flags above are here for web site generation, please let them. +cf. https://gitlab.inria.fr/GUDHI/website +Must be in conformity with _data/navigation.yml +{:/comment} + + + +## 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` +``` +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). + +``` + 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** @@ -20,43 +39,38 @@ where * `-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 +alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45 ``` -Here we retrieve expected Betti numbers on a tore 3D: -``` -Betti numbers[0] = 1 -Betti numbers[1] = 2 -Betti numbers[2] = 1 -``` +N.B.: -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. -## `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 ## -## `weighted_alpha_complex_3d_persistence` ## Same as `alpha_complex_3d_persistence`, but using weighted points. **Usage** -`weighted_alpha_complex_3d_persistence [options] ` + +``` + 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). + +* `` 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** @@ -66,32 +80,33 @@ where * `-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 + 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` ## +## 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] ` + +``` + 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](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid). + +* `` 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](http://gudhi.gforge.inria.fr/doc/latest/fileformats.html#FileFormatsIsoCuboid). **Allowed options** @@ -102,46 +117,36 @@ where **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 +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 ``` -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.: -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 ## -## `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: +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` +``` + 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** -`alpha_complex_persistence [options] ` + +``` + 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). @@ -154,24 +159,11 @@ where * `-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 + alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off ``` N.B.: + * Filtration values are alpha square values. -- cgit v1.2.3