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authorvrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2017-02-02 07:58:53 +0000
committervrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2017-02-02 07:58:53 +0000
commit0921d31dec497b21a3b2805790ef295e90566e3d (patch)
treeaef9fa89544ba58c9365382f2d5374402dabb5e2 /src/cython/doc/tangential_complex_user.rst
parente5345d29ca69d318f8c9b39cab21d79944ed69bb (diff)
Change doc html theme.
Change tables git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@2047 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: aaa29b8f610d506efc3762ad17c4fd768e74d399
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diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst
index 7b6c9e79..2679528c 100644
--- a/src/cython/doc/tangential_complex_user.rst
+++ b/src/cython/doc/tangential_complex_user.rst
@@ -26,6 +26,7 @@ example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points
.. figure:: img/tc_example_01.png
:alt: The input
:figclass: align-center
+
The input
For each point :math:`p`, estimate its tangent subspace :math:`T_p` (e.g.
@@ -34,8 +35,10 @@ using PCA).
.. figure:: img/tc_example_02.png
:alt: The estimated normals
:figclass: align-center
+
The estimated normals
+
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`.
@@ -43,6 +46,7 @@ restricted to :math:`T_p`.
.. figure:: img/tc_example_03.png
:alt: The Voronoi diagram
:figclass: align-center
+
The Voronoi diagram
The Tangential Delaunay complex is the union of those stars.
@@ -62,6 +66,7 @@ Let us take the same example.
.. figure:: img/tc_example_07_before.png
:alt: Before
:figclass: align-center
+
Before
Let us slightly move the tangent subspace :math:`T_q`
@@ -69,6 +74,7 @@ Let us slightly move the tangent subspace :math:`T_q`
.. figure:: img/tc_example_07_after.png
:alt: After
:figclass: align-center
+
After
Now, the star of :math:`Q` contains :math:`QP`, but the star of :math:`P` does
@@ -77,6 +83,7 @@ not contain :math:`QP`. We have an inconsistency.
.. figure:: img/tc_example_08.png
:alt: After
:figclass: align-center
+
After
One way to solve inconsistencies is to randomly perturb the positions of the