From 9fe2e4671b2f1564a65a590702718100a9b93b8c Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Mon, 9 Apr 2018 09:13:56 +0000 Subject: Doc review : Fix links to Gudhi::Minimal_enclosing_ball_radius Improve the doc git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/cechcomplex_vincent@3356 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 886022b4addfe0b0993fbe2675adb527a0f57700 --- src/Cech_complex/doc/Intro_cech_complex.h | 15 +++++++-------- src/Cech_complex/utilities/cechcomplex.md | 17 +++++++++++------ 2 files changed, 18 insertions(+), 14 deletions(-) diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h index ec0d35e2..a1d6f5dd 100644 --- a/src/Cech_complex/doc/Intro_cech_complex.h +++ b/src/Cech_complex/doc/Intro_cech_complex.h @@ -33,7 +33,7 @@ namespace cech_complex { * * @{ * - * \section cechdefinition Cech complex definition + * \section cechdefinition Čech complex definition * * Cech_complex * (Wikipedia) is a @@ -42,7 +42,8 @@ namespace cech_complex { * from it. * The input shall be a point cloud in an Euclidean space. * - * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from `Gudhi::Radius_distance` function. + * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from + * `Gudhi::Minimal_enclosing_ball_radius` function. * * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$, * are not inserted into the complex. @@ -51,8 +52,8 @@ namespace cech_complex { * * \image html "cech_one_skeleton.png" "Cech complex proximity graph representation" * - * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the simplicial - * complex data structure, and then expands the simplicial complex when required. + * When creating a simplicial complex from this proximity graph, Cech_complex inserts the proximity graph into the + * simplicial complex data structure, and then expands the simplicial complex when required. * * On this example, as edges \f$(x,y)\f$, \f$(y,z)\f$ and \f$(z,y)\f$ are in the complex, the minimal ball radius * containing the points \f$(x,y,z)\f$ is computed. @@ -62,7 +63,7 @@ namespace cech_complex { * * And so on for higher dimensions. * - * \image html "cech_complex_representation.png" "Cech complex expansion" + * \image html "cech_complex_representation.png" "Čech complex expansion" * * The minimal ball radius computation is insured by * @@ -78,8 +79,6 @@ namespace cech_complex { * * cech_complex_step_by_step.cpp example, where the graph construction over the Simplex_tree is more detailed. * - * \section cechpointsdistance Point cloud - * * \subsection cechpointscloudexample Example from a point cloud * * This example builds the proximity graph from the given points, and maximal radius values. @@ -89,7 +88,7 @@ namespace cech_complex { * * \include Cech_complex/cech_complex_example_from_points.cpp * - * When launching (Cech maximal distance between 2 points is 1., is expanded until dimension 2): + * When launching (maximal enclosing ball radius is 1., is expanded until dimension 2): * * \code $> ./Cech_complex_example_from_points * \endcode diff --git a/src/Cech_complex/utilities/cechcomplex.md b/src/Cech_complex/utilities/cechcomplex.md index 6330727a..f7817dbb 100644 --- a/src/Cech_complex/utilities/cechcomplex.md +++ b/src/Cech_complex/utilities/cechcomplex.md @@ -1,13 +1,18 @@ -# Cech complex # +# Čech complex # ## cech_persistence ## -This program computes the persistent homology with coefficient field *Z/pZ* of a Cech complex defined on a set of input points, using Euclidean distance. The output diagram contains one bar per line, written with the convention: +This program computes the persistent homology with coefficient field *Z/pZ* of +a Čech complex defined on a set of input points, using Euclidean distance. 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** @@ -17,9 +22,9 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are * `-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-edge-length ]` (default = inf) Maximal length of an edge for the Cech complex construction. -* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Cech complex we want to compute. -* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology. +* `-r [ --max-edge-length ]` (default = inf) Maximal length of an edge for the Čech complex construction. +* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Čech complex we want to compute. +* `-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. Beware: this program may use a lot of RAM and take a lot of time if `max-edge-length` is set to a large value. -- cgit v1.2.3