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author | Gard Spreemann <gspreemann@gmail.com> | 2017-10-09 10:47:31 +0200 |
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committer | Gard Spreemann <gspreemann@gmail.com> | 2017-10-09 10:47:31 +0200 |
commit | 673b6bb63befd7e591e52c13f43e5db53e5b29bd (patch) | |
tree | 3f15d96ef39bf0c6cf656d176ff1c437cacf5988 /doc/Alpha_complex/Intro_alpha_complex.h | |
parent | 9466ce44e348487fc04a1fda493ed659ae92b775 (diff) | |
parent | 866f6ce614e9c09c97fed12c8c0c2c9fb84fad3f (diff) |
Merge tag 'upstream/2.0.1' into dfsg/latest
Upstream's 2.0.1 release.
Diffstat (limited to 'doc/Alpha_complex/Intro_alpha_complex.h')
-rw-r--r-- | doc/Alpha_complex/Intro_alpha_complex.h | 83 |
1 files changed, 58 insertions, 25 deletions
diff --git a/doc/Alpha_complex/Intro_alpha_complex.h b/doc/Alpha_complex/Intro_alpha_complex.h index 69959fc5..cf1a946a 100644 --- a/doc/Alpha_complex/Intro_alpha_complex.h +++ b/doc/Alpha_complex/Intro_alpha_complex.h @@ -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], ...), |