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| author | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-08-12 15:29:48 +0000 |
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| committer | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-08-12 15:29:48 +0000 |
| commit | 5b6bebd9a8072d8998b0c741e5b40de0cfe5dc8e (patch) | |
| tree | 995194307af2d09f44dcdd9fd1494f3ada6e966a /src/cython/doc/witness_complex_sum.rst | |
| parent | 46566db4452be7dee8398e1ed5a25add7f80ac39 (diff) | |
Move cython/src/* in cython/
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@1436 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 8f971ef16ef6df597d5d3667db0eecbca94233b2
Diffstat (limited to 'src/cython/doc/witness_complex_sum.rst')
| -rw-r--r-- | src/cython/doc/witness_complex_sum.rst | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst new file mode 100644 index 00000000..0d65d420 --- /dev/null +++ b/src/cython/doc/witness_complex_sum.rst @@ -0,0 +1,25 @@ +===================================== ===================================== ===================================== +:Author: Siargey Kachanovich :Introduced in: GUDHI PYTHON 1.4.0 :Copyright: GPL v3 +===================================== ===================================== ===================================== + ++---------------------------------------------+----------------------------------------------------------------------+ +| .. 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. | +| | | +| | The data structure is described in | +| | :cite:`boissonnatmariasimplextreealgorithmica`. | ++---------------------------------------------+----------------------------------------------------------------------+ +| :doc:`witness_complex_user` | :doc:`witness_complex_ref` | ++---------------------------------------------+----------------------------------------------------------------------+ |