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| author | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2019-03-13 07:37:33 +0100 |
|---|---|---|
| committer | ROUVREAU Vincent <vincent.rouvreau@inria.fr> | 2019-03-13 07:37:33 +0100 |
| commit | 481718886577973385f657484c124456890ffa76 (patch) | |
| tree | 3dafb05d5808a0110d16d181ba08c81e3789ffb1 /src | |
| parent | 6112bd15d73b00a07edd54eeaf9c94cdff93aa9e (diff) | |
Improve documentation for Tangential complex (Fix #16)
Diffstat (limited to 'src')
| -rw-r--r-- | src/Tangential_complex/doc/Intro_tangential_complex.h | 5 | ||||
| -rw-r--r-- | src/cython/doc/tangential_complex_user.rst | 8 |
2 files changed, 7 insertions, 6 deletions
diff --git a/src/Tangential_complex/doc/Intro_tangential_complex.h b/src/Tangential_complex/doc/Intro_tangential_complex.h index f4fc8ac7..649ec389 100644 --- a/src/Tangential_complex/doc/Intro_tangential_complex.h +++ b/src/Tangential_complex/doc/Intro_tangential_complex.h @@ -46,9 +46,10 @@ An extensive description of the Tangential complex can be found in \cite tangent \subsection whatisthetc What is a Tangential Complex? Let us start with the description of the Tangential complex of a simple example, with \f$ k=1 \f$ and \f$ d=2 \f$. -The input data is 4 points \f$ P \f$ located on a curve embedded in 2D. +Only 4 points will be displayed (more are required for PCA) to simplify the figures. \f$ P \f$ located on a closed +curve embedded in 2D. \image html "tc_example_01.png" "The input" -For each point \f$ p \f$, estimate its tangent subspace \f$ T_p \f$ (e.g. 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$, construct its star in the Delaunay triangulation of \f$ P \f$ restricted to \f$ T_p \f$. \image html "tc_example_03.png" "The Voronoi diagram" diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst index 97471baf..5147797c 100644 --- a/src/cython/doc/tangential_complex_user.rst +++ b/src/cython/doc/tangential_complex_user.rst @@ -23,8 +23,9 @@ 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`. Only 4 points will be displayed +(more are required for PCA) to simplify the figures. :math:`P` located +on a closed curve embedded in 2D. .. figure:: ../../doc/Tangential_complex/tc_example_01.png :alt: The input @@ -32,8 +33,7 @@ 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 |