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Diffstat (limited to 'src/cython/doc/witness_complex_sum.rst')
| -rw-r--r-- | src/cython/doc/witness_complex_sum.rst | 48 |
1 files changed, 24 insertions, 24 deletions
diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst index 005a5a41..22ef36ea 100644 --- a/src/cython/doc/witness_complex_sum.rst +++ b/src/cython/doc/witness_complex_sum.rst @@ -1,25 +1,25 @@ -===================================== ===================================== ===================================== -:Author: Siargey Kachanovich :Introduced in: GUDHI 1.3.0 :Copyright: GPL v3 -===================================== ===================================== ===================================== +================================================================= =================================== =================================== +:Author: Siargey Kachanovich :Introduced in: GUDHI 1.3.0 :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` | -+---------------------------------------------+----------------------------------------------------------------------+ ++-----------------------------------------------------------------+----------------------------------------------------------------------+ +| .. 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` | ++-----------------------------------------------------------------+----------------------------------------------------------------------+ |