From 6ee77c3da821256459406e87024077c48419a493 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 20 Jan 2020 20:03:56 +0100 Subject: Shuffle the modules on the main page --- src/common/doc/main_page.md | 253 +++++++++++++++++++++----------------------- 1 file changed, 123 insertions(+), 130 deletions(-) (limited to 'src/common') diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 0b4bfb7a..768c5794 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -4,8 +4,8 @@ \image html "Gudhi_banner.png"



-## Complexes {#Complexes} -### Cubical complex +## Data structures for cell complexes {#Complexes} +### Cubical complexes @@ -29,246 +29,269 @@
-### Simplicial complex - -#### Alpha complex +### Simplicial complexes +#### Simplex tree
- \image html "alpha_complex_representation.png" + \image html "Simplex_tree_representation.png" - Alpha complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.
- The filtration value of each simplex is computed as the square of the circumradius of the simplex if the - circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration - values of the codimension 1 cofaces that make it not Gabriel otherwise. - All simplices that have a filtration value \f$ > \alpha^2 \f$ are removed from the Delaunay complex - when creating the simplicial complex if it is specified.
- For performances reasons, it is advised to use \ref cgal ≥ 5.0.0. + The simplex tree is an efficient and flexible + data structure for representing general (filtered) simplicial complexes. The data structure + is described in \cite boissonnatmariasimplextreealgorithmica . 		- Author: Vincent Rouvreau
- Introduced in: GUDHI 1.3.0
- Copyright: MIT [(GPL v3)](../../licensing/)
- Requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0 + Author: Clément Maria
+ Introduced in: GUDHI 1.0.0
+ Copyright: MIT
- User manual: \ref alpha_complex + User manual: \ref simplex_tree
-#### Čech complex +#### Skeleton blocker - +
- \image html "cech_complex_representation.png" + \image html "ds_representation.png" - The Čech complex is a simplicial complex constructed from a proximity graph. - The set of all simplices is filtered by the radius of their minimal enclosing ball. + The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* + representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the + 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice. + This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but + operations that are particularly efficient are operations that do not require simplex enumeration such as edge + iteration, link computation or simplex contraction. - Author: Vincent Rouvreau
- Introduced in: GUDHI 2.2.0
- Copyright: MIT [(GPL v3)](../../licensing/)
- Includes: [Miniball](https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html)
+ Author: David Salinas
+ Introduced in: GUDHI 1.1.0
+ Copyright: MIT
- User manual: \ref cech_complex + User manual: \ref skbl
-#### Rips complex +#### Toplex Map
- \image html "rips_complex_representation.png" + \image html "map.png" - Rips complex is a simplicial complex constructed from a one skeleton graph.
- The filtration value of each edge is computed from a user-given distance function and is inserted until a - user-given threshold value.
- This complex can be built from a point cloud and a distance function, or from a distance matrix. + The Toplex map data structure is composed firstly of a raw storage of toplices (the maximal simplices) + and secondly of a map which associate any vertex to a set of pointers toward all toplices + containing this vertex. 		- Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse
- Introduced in: GUDHI 2.0.0
+ Author: François Godi
+ Introduced in: GUDHI 2.1.0
Copyright: MIT
- User manual: \ref rips_complex + User manual: \ref toplex_map
-#### Witness complex +#### Basic operation: contraction
- \image html "Witness_complex_representation.png" + \image html "sphere_contraction_representation.png" - Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$. - The data structure is described in \cite boissonnatmariasimplextreealgorithmica . + The purpose of this package is to offer a user-friendly interface for edge contraction simplification of huge + simplicial complexes. It uses the \ref skbl data-structure whose size remains small during simplification of most + used geometrical complexes of topological data analysis such as the Rips or the Delaunay complexes. In practice, + the size of this data-structure is even much lower than the total number of simplices. - Author: Siargey Kachanovich
- Introduced in: GUDHI 1.3.0
- Copyright: MIT ([GPL v3](../../licensing/) for Euclidean version)
- Euclidean version requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0 + Author: David Salinas
+ Introduced in: GUDHI 1.1.0
+ Copyright: MIT [(LGPL v3)](../../licensing/)
+ Requires: \ref cgal ≥ 4.11.0
- User manual: \ref witness_complex + User manual: \ref contr
-### Cover Complexes +## Filtrations and reconstructions +### Alpha complex +
- \image html "gicvisu.jpg" + \image html "alpha_complex_representation.png" - Nerves and Graph Induced Complexes are cover complexes, i.e. simplicial complexes that provably contain - topological information about the input data. They can be computed with a cover of the - data, that comes i.e. from the preimage of a family of intervals covering the image - of a scalar-valued function defined on the data.
+ Alpha complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.
+ The filtration value of each simplex is computed as the square of the circumradius of the simplex if the + circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration + values of the codimension 1 cofaces that make it not Gabriel otherwise. + All simplices that have a filtration value \f$ > \alpha^2 \f$ are removed from the Delaunay complex + when creating the simplicial complex if it is specified.
+ For performances reasons, it is advised to use \ref cgal ≥ 5.0.0. 		- Author: Mathieu Carrière
- Introduced in: GUDHI 2.1.0
+ Author: Vincent Rouvreau
+ Introduced in: GUDHI 1.3.0
Copyright: MIT [(GPL v3)](../../licensing/)
- Requires: \ref cgal ≥ 4.11.0 + Requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0
- User manual: \ref cover_complex + User manual: \ref alpha_complex
-## Data structures and basic operations {#DataStructuresAndBasicOperations} +### Čech complex + + + + + + + + + + +
+ \image html "cech_complex_representation.png" + + The Čech complex is a simplicial complex constructed from a proximity graph. + The set of all simplices is filtered by the radius of their minimal enclosing ball. + + Author: Vincent Rouvreau
+ Introduced in: GUDHI 2.2.0
+ Copyright: MIT [(GPL v3)](../../licensing/)
+ Includes: [Miniball](https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html)
+
+ User manual: \ref cech_complex +
-### Data structures +### Rips complex -#### Simplex tree
- \image html "Simplex_tree_representation.png" + \image html "rips_complex_representation.png" - The simplex tree is an efficient and flexible - data structure for representing general (filtered) simplicial complexes. The data structure - is described in \cite boissonnatmariasimplextreealgorithmica . + Rips complex is a simplicial complex constructed from a one skeleton graph.
+ The filtration value of each edge is computed from a user-given distance function and is inserted until a + user-given threshold value.
+ This complex can be built from a point cloud and a distance function, or from a distance matrix. 		- Author: Clément Maria
- Introduced in: GUDHI 1.0.0
+ Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse
+ Introduced in: GUDHI 2.0.0
Copyright: MIT
- User manual: \ref simplex_tree + User manual: \ref rips_complex
-#### Skeleton blocker +### Witness complex
- \image html "ds_representation.png" + \image html "Witness_complex_representation.png" - The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* - representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the - 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice. - This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but - operations that are particularly efficient are operations that do not require simplex enumeration such as edge - iteration, link computation or simplex contraction. + Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$. + The data structure is described in \cite boissonnatmariasimplextreealgorithmica . - Author: David Salinas
- Introduced in: GUDHI 1.1.0
- Copyright: MIT
+ Author: Siargey Kachanovich
+ Introduced in: GUDHI 1.3.0
+ Copyright: MIT ([GPL v3](../../licensing/) for Euclidean version)
+ Euclidean version requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0
- User manual: \ref skbl + User manual: \ref witness_complex
-#### Toplex Map - +### Cover Complexes
- \image html "map.png" + \image html "gicvisu.jpg" - The Toplex map data structure is composed firstly of a raw storage of toplices (the maximal simplices) - and secondly of a map which associate any vertex to a set of pointers toward all toplices - containing this vertex. + Nerves and Graph Induced Complexes are cover complexes, i.e. simplicial complexes that provably contain + topological information about the input data. They can be computed with a cover of the + data, that comes i.e. from the preimage of a family of intervals covering the image + of a scalar-valued function defined on the data.
- Author: François Godi
+ Author: Mathieu Carrière
Introduced in: GUDHI 2.1.0
- Copyright: MIT
+ Copyright: MIT [(GPL v3)](../../licensing/)
+ Requires: \ref cgal ≥ 4.11.0
- User manual: \ref toplex_map + User manual: \ref cover_complex
-### Basic operations - -#### Contraction +### Tangential complex
- \image html "sphere_contraction_representation.png" + \image html "tc_examples.png" - The purpose of this package is to offer a user-friendly interface for edge contraction simplification of huge - simplicial complexes. It uses the \ref skbl data-structure whose size remains small during simplification of most - used geometrical complexes of topological data analysis such as the Rips or the Delaunay complexes. In practice, - the size of this data-structure is even much lower than the total number of simplices. + A Tangential Delaunay complex is a simplicial complex + designed to reconstruct a \f$ k \f$-dimensional manifold embedded in \f$ d \f$-dimensional Euclidean space. + The input is a point sample coming from an unknown manifold. + The running time depends only linearly on the extrinsic dimension \f$ d \f$ + and exponentially on the intrinsic dimension \f$ k \f$. - Author: David Salinas
- Introduced in: GUDHI 1.1.0
- Copyright: MIT [(LGPL v3)](../../licensing/)
- Requires: \ref cgal ≥ 4.11.0 + Author: Clément Jamin
+ Introduced in: GUDHI 2.0.0
+ Copyright: MIT [(GPL v3)](../../licensing/)
+ Requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0
- User manual: \ref contr + User manual: \ref tangential_complex
@@ -305,36 +328,6 @@ -## Manifold reconstruction {#ManifoldReconstruction} - -### Tangential complex - - - - - - - - - - -
- \image html "tc_examples.png" - - A Tangential Delaunay complex is a simplicial complex - designed to reconstruct a \f$ k \f$-dimensional manifold embedded in \f$ d \f$-dimensional Euclidean space. - The input is a point sample coming from an unknown manifold. - The running time depends only linearly on the extrinsic dimension \f$ d \f$ - and exponentially on the intrinsic dimension \f$ k \f$. - - Author: Clément Jamin
- Introduced in: GUDHI 2.0.0
- Copyright: MIT [(GPL v3)](../../licensing/)
- Requires: \ref eigen ≥ 3.1.0 and \ref cgal ≥ 4.11.0 -
- User manual: \ref tangential_complex -
- ## Topological descriptors tools {#TopologicalDescriptorsTools} ### Bottleneck distance -- cgit v1.2.3 From 82b4a1e765adc6ec9d37b1bfb09ce443f642cb08 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 20 Jan 2020 20:11:28 +0100 Subject: Missing entry in TOC --- src/common/doc/main_page.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'src/common') diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 768c5794..90afb05d 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -135,7 +135,7 @@ -## Filtrations and reconstructions +## Filtrations and reconstructions {#FiltrationsReconstructions} ### Alpha complex -- cgit v1.2.3 From 8c85fa3f6dcb47346f3070adc46d44c9afca2f2c Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 20 Jan 2020 20:26:18 +0100 Subject: Reorder skbl and toplexmap so that skbl is next to contractions --- src/common/doc/main_page.md | 38 +++++++++++++++++++------------------- 1 file changed, 19 insertions(+), 19 deletions(-) (limited to 'src/common') diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 90afb05d..23dd3fde 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -55,55 +55,55 @@
-#### Skeleton blocker +#### Toplex Map
- \image html "ds_representation.png" + \image html "map.png" - The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* - representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the - 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice. - This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but - operations that are particularly efficient are operations that do not require simplex enumeration such as edge - iteration, link computation or simplex contraction. + The Toplex map data structure is composed firstly of a raw storage of toplices (the maximal simplices) + and secondly of a map which associate any vertex to a set of pointers toward all toplices + containing this vertex. - Author: David Salinas
- Introduced in: GUDHI 1.1.0
+ Author: François Godi
+ Introduced in: GUDHI 2.1.0
Copyright: MIT
- User manual: \ref skbl + User manual: \ref toplex_map
-#### Toplex Map +#### Skeleton blocker
- \image html "map.png" + \image html "ds_representation.png" - The Toplex map data structure is composed firstly of a raw storage of toplices (the maximal simplices) - and secondly of a map which associate any vertex to a set of pointers toward all toplices - containing this vertex. + The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* + representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the + 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice. + This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but + operations that are particularly efficient are operations that do not require simplex enumeration such as edge + iteration, link computation or simplex contraction. - Author: François Godi
- Introduced in: GUDHI 2.1.0
+ Author: David Salinas
+ Introduced in: GUDHI 1.1.0
Copyright: MIT
- User manual: \ref toplex_map + User manual: \ref skbl
-- cgit v1.2.3 From dc3d21f55d3e0de311f56b2706629483f50b0258 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 20 Jan 2020 20:36:58 +0100 Subject: Link kd-tree and subsampling from the main doc --- src/common/doc/main_page.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) (limited to 'src/common') diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 23dd3fde..72bf1cef 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -383,3 +383,26 @@ + +## Point cloud utilities {#PointCloudUtils} + + + + + + + + + + +
+ \f$(x_1,\ldots\x_d)\f$ + + This contains various tools to handle point clouds: spatial searching, subsampling, etc. + + Author: Clément Jamin
+ Introduced in: GUDHI 1.3.0
+ Copyright: MIT [(GPL v3)](../../licensing/)
+
+ Manuals: \ref spatial_searching, \ref subsampling +
-- cgit v1.2.3 From 43b6452cf36e92595e4fd05bdeca6c5eeaf95e86 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 20 Jan 2020 20:55:33 +0100 Subject: Typo --- src/common/doc/main_page.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'src/common') diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 72bf1cef..6ea10b88 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -389,7 +389,7 @@
- \f$(x_1,\ldots\x_d)\f$ + \f$(x_1,\ldots,x_d)\f$ This contains various tools to handle point clouds: spatial searching, subsampling, etc. -- cgit v1.2.3