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Diffstat (limited to 'src/Tangential_complex/doc/Intro_tangential_complex.h')
| -rw-r--r-- | src/Tangential_complex/doc/Intro_tangential_complex.h | 5 |
1 files changed, 3 insertions, 2 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" |