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Diffstat (limited to 'src/cython/doc/tangential_complex_user.rst')
| -rw-r--r-- | src/cython/doc/tangential_complex_user.rst | 17 |
1 files changed, 10 insertions, 7 deletions
diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst index 5ce69e86..ebfe1e29 100644 --- a/src/cython/doc/tangential_complex_user.rst +++ b/src/cython/doc/tangential_complex_user.rst @@ -23,8 +23,10 @@ What is a Tangential Complex? ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Let us start with the description of the Tangential complex of a simple -example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points -:math:`P` located on a curve embedded in 2D. +example, with :math:`k = 1` and :math:`d = 2`. The point set +:math:`\mathscr P` is located on a closed curve embedded in 2D. +Only 4 points will be displayed (more are required for PCA) to simplify the +figures. .. figure:: ../../doc/Tangential_complex/tc_example_01.png :alt: The input @@ -32,8 +34,7 @@ example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points The input -For each point :math:`p`, estimate its tangent subspace :math:`T_p` (e.g. -using PCA). +For each point :math:`P`, estimate its tangent subspace :math:`T_P` using PCA. .. figure:: ../../doc/Tangential_complex/tc_example_02.png :alt: The estimated normals @@ -43,8 +44,8 @@ using PCA). Let us add the Voronoi diagram of the points in orange. For each point -:math:`p`, construct its star in the Delaunay triangulation of :math:`P` -restricted to :math:`T_p`. +:math:`P`, construct its star in the Delaunay triangulation of +:math:`\mathscr P` restricted to :math:`T_P`. .. figure:: ../../doc/Tangential_complex/tc_example_03.png :alt: The Voronoi diagram @@ -72,7 +73,7 @@ Let us take the same example. Before -Let us slightly move the tangent subspace :math:`T_q` +Let us slightly move the tangent subspace :math:`T_Q` .. figure:: ../../doc/Tangential_complex/tc_example_07_after.png :alt: After @@ -128,6 +129,7 @@ This example builds the Tangential complex of point set read in an OFF file. import gudhi tc = gudhi.TangentialComplex(intrisic_dim = 1, off_file=gudhi.__root_source_dir__ + '/data/points/alphacomplexdoc.off') + tc.compute_tangential_complex() result_str = 'Tangential contains ' + repr(tc.num_simplices()) + \ ' simplices - ' + repr(tc.num_vertices()) + ' vertices.' print(result_str) @@ -175,6 +177,7 @@ simplices. import gudhi tc = gudhi.TangentialComplex(intrisic_dim = 1, points=[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]) + tc.compute_tangential_complex() result_str = 'Tangential contains ' + repr(tc.num_vertices()) + ' vertices.' print(result_str) |