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diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst new file mode 100644 index 00000000..005a5a41 --- /dev/null +++ b/src/cython/doc/witness_complex_sum.rst @@ -0,0 +1,25 @@ +===================================== ===================================== ===================================== +: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` | ++---------------------------------------------+----------------------------------------------------------------------+ |