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| author | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2017-03-08 22:05:14 +0000 |
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| committer | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2017-03-08 22:05:14 +0000 |
| commit | fd06f7f93f69b7d31645b1f198ebedc957f3adf1 (patch) | |
| tree | 34f1371a5437521320d37d7c9b5544d4514499f3 /src/cython/doc/witness_complex_sum.rst | |
| parent | fe917a0676a7b819782f5294565951dca8212776 (diff) | |
New revision of witness and its documentation
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@2181 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 5f002c1a58b2daff6c6826a2552d1c101f6810e1
Diffstat (limited to 'src/cython/doc/witness_complex_sum.rst')
| -rw-r--r-- | src/cython/doc/witness_complex_sum.rst | 20 |
1 files changed, 6 insertions, 14 deletions
diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst index 1b20d4bc..b65522ba 100644 --- a/src/cython/doc/witness_complex_sum.rst +++ b/src/cython/doc/witness_complex_sum.rst @@ -1,25 +1,17 @@ ================================================================= =================================== =================================== :Author: Siargey Kachanovich :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 +:Euclidean version requires: CGAL :math:`\geq` 4.6.0 Eigen3 ================================================================= =================================== =================================== +-----------------------------------------------------------------+----------------------------------------------------------------------+ | .. image:: | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on | -| img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`:Wit(W,L)` is a simplicial | -| | complex defined on two sets of points in :math:`\mathbb{R}^D`: | -| | | -| | * :math:`W` set of **witnesses** and | -| | * :math:`L \subseteq W` set of **landmarks**. | -| | | -| | The simplices are based on landmarks and a simplex belongs to the | -| | witness complex if and only if it is witnessed, that is: | -| | | -| | :math:`\sigma \subset L` is witnessed if there exists a point | -| | :math:`w \in W` such that w is closer to the vertices of | -| | :math:`\sigma` than other points in :math:`L` and all of its faces | -| | are witnessed as well. | +| img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`. | | | | | | The data structure is described in | | | :cite:`boissonnatmariasimplextreealgorithmica`. | +-----------------------------------------------------------------+----------------------------------------------------------------------+ -| :doc:`witness_complex_user` | :doc:`witness_complex_ref` | +| :doc:`witness_complex_user` | * :doc:`witness_complex_ref` | +| | * :doc:`strong_witness_complex_ref` | +| | * :doc:`euclidean_witness_complex_ref` | +| | * :doc:`euclidean_strong_witness_complex_ref` | +-----------------------------------------------------------------+----------------------------------------------------------------------+ |