diff options
-rw-r--r-- | src/Tangential_complex/doc/Intro_tangential_complex.h | 6 | ||||
-rw-r--r-- | src/cython/doc/tangential_complex_user.rst | 6 |
2 files changed, 6 insertions, 6 deletions
diff --git a/src/Tangential_complex/doc/Intro_tangential_complex.h b/src/Tangential_complex/doc/Intro_tangential_complex.h index 2b019021..501f4a8b 100644 --- a/src/Tangential_complex/doc/Intro_tangential_complex.h +++ b/src/Tangential_complex/doc/Intro_tangential_complex.h @@ -51,10 +51,10 @@ Let us start with the description of the Tangential complex of a simple example, The point set \f$ \mathscr P \f$ is located on a closed curve embedded in 2D. Only 4 points will be displayed (more are required for PCA) to simplify the figures. \image html "tc_example_01.png" "The input" -For each point \f$ P \f$, estimate its tangent subspace \f$ T_p \f$ using PCA. +For each point \f$ P \f$, estimate its tangent subspace \f$ T_P \f$ using PCA. \image html "tc_example_02.png" "The estimated normals" Let us add the Voronoi diagram of the points in orange. For each point \f$ P \f$, construct its star in the Delaunay -triangulation of \f$ \mathscr P \f$ restricted to \f$ T_p \f$. +triangulation of \f$ \mathscr P \f$ restricted to \f$ T_P \f$. \image html "tc_example_03.png" "The Voronoi diagram" The Tangential Delaunay complex is the union of those stars. @@ -69,7 +69,7 @@ An inconsistency occurs when a simplex is not in the star of all its vertices. Let us take the same example. \image html "tc_example_07_before.png" "Before" -Let us slightly move the tangent subspace \f$ T_q \f$ +Let us slightly move the tangent subspace \f$ T_Q \f$ \image html "tc_example_07_after.png" "After" Now, the star of \f$ Q \f$ contains \f$ QP \f$, but the star of \f$ P \f$ does not contain \f$ QP \f$. We have an inconsistency. \image html "tc_example_08.png" "After" diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst index 11b37009..ebfe1e29 100644 --- a/src/cython/doc/tangential_complex_user.rst +++ b/src/cython/doc/tangential_complex_user.rst @@ -34,7 +34,7 @@ figures. The input -For each point :math:`P`, estimate its tangent subspace :math:`T_p` 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 @@ -45,7 +45,7 @@ For each point :math:`P`, estimate its tangent subspace :math:`T_p` 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:`\mathscr P` restricted to :math:`T_p`. +:math:`\mathscr P` restricted to :math:`T_P`. .. figure:: ../../doc/Tangential_complex/tc_example_03.png :alt: The Voronoi diagram @@ -73,7 +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 |