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Diffstat (limited to 'src/cython/doc/tangential_complex_user.rst')
| -rw-r--r-- | src/cython/doc/tangential_complex_user.rst | 7 |
1 files changed, 7 insertions, 0 deletions
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 |