diff options
Diffstat (limited to 'src/Alpha_complex/doc')
-rw-r--r-- | src/Alpha_complex/doc/Intro_alpha_complex.h | 87 |
1 files changed, 60 insertions, 27 deletions
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index 3ffdae7f..cf1a946a 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -71,7 +71,7 @@ namespace alpha_complex { * * When launching: * - * \code $> ./alphapoints + * \code $> ./Alpha_complex_example_from_points * \endcode * * the program output is: @@ -89,31 +89,64 @@ namespace alpha_complex { * \image html "alpha_complex_doc.png" "Simplicial complex structure construction example" * * \subsection filtrationcomputation Filtration value computation algorithm - * - * \f{algorithm}{ - * \caption{Filtration value computation algorithm}\label{alpha} - * \begin{algorithmic} - * \For{i : dimension $\rightarrow$ 0} - * \ForAll{$\sigma$ of dimension i} - * \If {filtration($\sigma$) is NaN} - * \State filtration($\sigma$) = $\alpha^2(\sigma)$ - * \EndIf - * \ForAll{$\tau$ face of $\sigma$} \Comment{propagate alpha filtration value} - * \If {filtration($\tau$) is not NaN} - * \State filtration($\tau$) = min (filtration($\tau$), filtration($\sigma$)) - * \Else - * \If {$\tau$ is not Gabriel for $\sigma$} - * \State filtration($\tau$) = filtration($\sigma$) - * \EndIf - * \EndIf - * \EndFor - * \EndFor - * \EndFor - * \State make\_filtration\_non\_decreasing() - * \State prune\_above\_filtration() - * \end{algorithmic} - * \f} - * + * + * + * + * <ul> + * <li style="list-style-type: none;">\f$ \textbf{for } i : dimension \rightarrow 0 \textbf{ do} \f$ + * <ul> + * <li style="list-style-type: none;">\f$\textbf{for all } \sigma of dimension i \f$ + * <ul> + * <li style="list-style-type: none;">\f$\textbf{if } filtration( \sigma ) is NaN \textbf{ then} \f$ + * <ul> + * <li style="list-style-type: none;">\f$ filtration( \sigma ) = \alpha^2( \sigma ) \f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end if}\f$ + * </li> + * <li style="list-style-type: none;">\f$\textbf{for all } \tau face of \sigma \textbf{ do} \f$ + * // propagate alpha filtration value + * <ul> + * <li style="list-style-type: none;">\f$\textbf{if } filtration( \tau ) is not NaN \textbf{ then} \f$ + * <ul> + * <li style="list-style-type: none;">\f$ filtration( \tau ) = min ( filtration( \tau ), filtration( \sigma ) ) \f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{else}\f$ + * <ul> + * <li style="list-style-type: none;">\f$\textbf{if } \tau is not Gabriel for \sigma \textbf{ then} \f$ + * <ul> + * <li style="list-style-type: none;">\f$ filtration( \tau ) = filtration( \sigma ) \f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end if}\f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end if}\f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end for}\f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end for}\f$ + * </li> + * </ul> + * </li> + * <li style="list-style-type: none;">\f$\textbf{end for}\f$ + * </li> + * <li style="list-style-type: none;">\f$make\_filtration\_non\_decreasing()\f$ + * </li> + * <li style="list-style-type: none;">\f$prune\_above\_filtration()\f$ + * </li> + * </ul> + * + * * \subsubsection dimension2 Dimension 2 * * From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...), @@ -155,7 +188,7 @@ namespace alpha_complex { * * When launching: * - * \code $> ./alphaoffreader ../../data/points/alphacomplexdoc.off 32.0 + * \code $> ./Alpha_complex_example_from_off ../../data/points/alphacomplexdoc.off 32.0 * \endcode * * the program output is: |