\section{Graphes}

%double tiret dans le texte
\newcommand{\dd}{-{}-}

\subsection{Noeuds}


%création de noeud
\begin{frame}[fragile, t]
\frametitle{Créer des noeuds}

\begin{tikzpicture}
\tikzstyle{element} = [outer sep=0,inner sep=1]
\node[element] (node) at (0,0) {\verb|\node|};
\node[element] (options) at (1.8,0) {\verb|[<options>]|};
\node[element] (nom) at (3.8,0) {\verb|(<nom>)|};
\node[element] (pos) at (6,0) {\verb|at (<X>,<Y>) |};
\node[element] (texte) at (8.2,0) {\verb|{texte};|};

%\draw[decorate, decoration ={brace,raise=4pt}] (node.north west) -- (node.north east) node (nodedef) [midway, above=6pt] {Commande};
\draw[decorate, decoration ={brace,raise=4pt, mirror}, thick , blue] (options.south west) -- (options.south east) node (nodedef) [midway, below=6pt] {\begin{tabular}{c}Options \\du noeud\end{tabular}};

\draw[decorate, decoration ={brace,raise=4pt}, thick, blue] (nom.north west) -- (nom.north east) node (nodedef) [midway, above=6pt] {\begin{tabular}{c}Nom du noeud \\(optionnel)\end{tabular}};
\draw[decorate, decoration ={brace,raise=4pt, mirror}, thick,blue] (pos.south west) -- (pos.south east) node (nodedef) [midway, below=6pt] {Coordonnées};
\draw[decorate, decoration ={brace,raise=4pt}, thick, blue] (texte.north west) -- (texte.north east) node (nodedef) [midway, above=6pt] {\begin{tabular}{c}Texte \\(Obligatoire, \\peut être vide)\end{tabular}};

\end{tikzpicture}

\underline{\Large \textbf{Exemple:}}

\vspace{10pt}

\scriptsize{
\ttfamily
\textbackslash node [] (monNoeud) at (0,0) \{ceci est un noeud\};
}

\vspace{10pt}

\begin{center}
\begin{tikzpicture}
\node [] (monNoeud) at (0,0) {ceci est un noeud};
\end{tikzpicture}
\end{center}

\end{frame}




%Options de noeuds 1
\begin{frame}[fragile, t]
\frametitle{Options de noeuds}

\begin{tikzpicture}
\tikzstyle{element} = [outer sep=0,inner sep=1]
\node[element, text=gray] (node) at (0,0) {\verb|\node |};
\node[element] (options) at (2,0) {\verb|[<options>]|};
\node[element, text=gray] (nom) at (4.3,0) {\verb|(<nom>)|};
\node[element, text=gray] (pos) at (6.6,0) {\verb|at (<X>,<Y>) |};
\node[element, text=gray] (texte) at (9,0) {\verb|{texte};|};
\end{tikzpicture}

\vspace{10pt}

%\begin{tabular*}{\columnwidth}{@{\extracolsep{\stretch{1}}}*{3}{c}@{}}

\begin{tikzpicture}
	\uncover<1->{\node [draw, label={[gray]0:\texttt{[draw]} }]                             (n1) at (0,4) {1}; 	}
	\uncover<2->{\node [draw, circle, label={[gray]0:\texttt{[draw, circle]} }]                     (n2) at (0,3) {2}; }
	\uncover<3->{\node [draw, rounded corners=3pt, label={[gray]0:\texttt{\small \begin{tabular}{l}[draw,\\ rounded corners=3pt]\end{tabular}} }]        (n3) at (0,2) {3};}
	\uncover<4->{\node [draw, red, label={[gray, distance=20pt]0:\texttt{[draw, red]} }]                        (n4) at (0,1) {4};}
	\uncover<5->{\node [draw, text = blue, label={[gray, distance=20pt]0:\texttt{[draw, text=blue ]} }]                (n5) at (0,0) {5};}
	
	\uncover<6->{\node [draw, fill=red!30, label={[gray]0:\texttt{[draw, fill=red!30] }} ]                   (n6) at (5, 4) {6}; }
	\uncover<7->{\node [draw, ultra thick, label={[gray]0:\texttt{[draw, ultra thick] } }]                (n7) at (5,3) {7};}
	\uncover<8->{\node [draw, pattern = north east lines, label={[gray]0:\texttt{\small \begin{tabular}{l}[draw, pattern = \\north east lines] \end{tabular}}}] (n8) at (5,2) {8};}
	\uncover<9->{\node [draw, inner sep=1pt, label={[gray]0:\texttt{\small \begin{tabular}{l}[draw, \\inner sep=1pt]\end{tabular}}}]              (n9) at (5,1) {9};}
	\uncover<10->{\node [draw, minimum height = 30pt, label={[gray]0:\texttt{\small \begin{tabular}{l}[draw, \\minimum height = 30pt]\end{tabular} }}]      (n10) at (5, 0) {10};}
\end{tikzpicture}

\vspace{10pt}


\end{frame}



%astuces supplementaires (noeuds)
\begin{frame}[fragile]
\frametitle{Texte du noeud sur plusieurs lignes}


\vspace{30pt}

{\ttfamily 
\textbackslash node [draw] (monNoeud) at (0,0) \{ 

\qquad \textbackslash  begin\{tabular\}

\qquad \qquad ceci est \textbackslash \textbackslash un noeud 

 \qquad \textbackslash end\{tabular\}  

\};}


\vspace{30pt}

{\centering

\begin{tikzpicture}\node [draw] (monNoeud) at (0,0) {\begin{tabular}{c} ceci est \\ un noeud\end{tabular}}; \end{tikzpicture}

}

\end{frame}


%============================================
% Arcs
%============================================
\subsection{Arcs}

%base
\begin{frame}[fragile, t]

\small{
\ttfamily 
\textbackslash draw[<options>] (<noeud 1>) \dd (<noeud 2>);
}
\vspace{5pt}

\underline{\large \textbf{Exemple : }}
\frametitle{Arcs}
{\color{gray}
\begin{verbatim}
\node [draw, circle] (n1) at (0,0) {n1};
...
\end{verbatim}
}

\begin{verbatim}
	\draw[] (n1) -- (n2);
	\draw[dashed, ->] (n2) -| (n3);
\end{verbatim}
\begin{verbatim}
	\draw[red,  line width=4pt, diamond-stealth] 
	                           (n3) to (n1);
\end{verbatim}

\vspace{5pt}

\begin{center}
\begin{tikzpicture}
	\node [draw, circle] (n1) at (0,0) {n1};
	\node [draw, circle] (n2) at (2,2) {n2};
	\node [draw, circle] (n3) at (4,0) {n3};
	\draw[] (n1) -- (n2);
	\draw[dashed, ->] (n2) -| (n3);
	\draw[red, line width=4pt, diamond-stealth] (n3) to (n1);
\end{tikzpicture}
\end{center}



\end{frame}


%---------------------------------------------
% autre options d'arcs


%options d'arcs

\begin{frame}[t]
\only<handout:1>{
%	\only<1-1>{
\vspace{20pt}

%figure
\scalebox{0.41}{
\begin{tikzpicture}
\tikzstyle{monNoeud}=[draw, circle, inner sep=1pt, minimum size = 2em]
\tikzstyle{mafleche}=[-stealth, thick]


%source
\node [monNoeud, line width = 2pt] (s1) at (-8.5,0.5) {s1};

%col 1
\node [monNoeud] (n11) at (-4,3.5) {n11};
\node [monNoeud] (n12) at (-4,0.5) {n12};
\node [monNoeud] (n13) at (-4,-2.5) {n13};

%col 2
\node [monNoeud] (n21) at (1,3.5) {n21};
\node [monNoeud] (n22) at (1,0.5) {n22};
\node [monNoeud] (n23) at (1,-2.5) {n23};

%col 3
\node [monNoeud] (n31) at (5.5,3.5) {n31};
\node [monNoeud] (n32) at (5.5,0.5) {n32};
\node [monNoeud] (n33) at (5.5,-2.5) {n33};

%col 4
\node [monNoeud] (n41) at (9.5,3.5) {n41};
\node [monNoeud] (n42) at (9.5,0.5) {n42};
\node [monNoeud] (n43) at (9.5,-2.5) {n43};

%puit
\node [monNoeud, line width = 2pt] (s2) at (14.5,0.5) {s2};


%loops du haut

%premiere loop

\draw[mafleche, line width=3pt]  (n11) to[loop, looseness=20] node[midway, above=3pt, circle, inner sep =1pt, draw, line width = 1pt, scale=2, gray] {1} (n11);


%deuxieme loop
\draw[mafleche, line width=3pt]  (n21) to[loop above, looseness=40] node[midway, above=3pt, circle, inner sep =1pt, draw, line width = 1pt, scale=2, gray] {2} (n21);


%3e loop
\draw[mafleche]  (n31) to[loop, looseness=20] (n31);
%4e loop
\draw[mafleche]  (n41) to[loop, looseness=20] (n41);


%------------------------------
%loops du bas

\draw[mafleche, line width=3pt]  (n13) to[loop below, looseness=40] node[midway, below=3pt, circle, inner sep =1pt, draw, line width = 1pt, scale=2, gray] {3} (n13);


\draw[mafleche]  (n23) to[loop below, looseness=40] (n23);
\draw[mafleche]  (n33) to[loop below, looseness=40] (n33);
\draw[mafleche]  (n43) to[loop below, looseness=40] (n43);


%--------------------------------------
%depart de la source


%double depart vers le haut

\draw[mafleche]  (s1.45) to (n11.205);
\draw[mafleche]  (s1) to (n11);


%double depart vers le bas
\draw[mafleche]  (s1.-45) to (n13.160);
\draw[mafleche]  (s1) to (n13);



\draw[mafleche]  (s1) to (n12);

%-----------------------------------
%fleches qui bend
\draw[mafleche]  (s1) to (n22);


%autre fleche
\draw[mafleche]  (n11) to (n33);

%autre fleche
\draw[mafleche]  (n12) to (n32);

%bend left 10
\draw[mafleche]  (n13) to (n31);


%in=... ,out=...
\draw[mafleche]  (n31) to (s2);
\draw[mafleche]  (n41) to (s2);




\draw[mafleche]  (n11) to (n22);
\draw[mafleche]  (n11) to (n21);
\draw[mafleche]  (n12) to (n23);
\draw[mafleche]  (n12) to (n31);


\draw[mafleche]  (n22) to (n32);
\draw[mafleche]  (n32) to (n42);


\draw[mafleche]  (n32) to (n43);

\draw[mafleche]  (n32) to (n41);

\draw[mafleche]  (n13) to (n23);
\draw[mafleche]  (n23) to (n32);
\draw[mafleche]  (n33) to (n42);
\draw[mafleche]  (n33) to (n43);


%arrivee au puit
\draw[mafleche]  (n42) to (s2);
\draw[mafleche]  (n21) to (s2);



\draw[mafleche]  (n43) to (s2);

\end{tikzpicture}
}

\scriptsize{
\ttfamily

\tikz \node[draw, circle, inner sep=1pt]{1}; \textbackslash draw[]  (n11) to[{\color{red}loop, looseness=20}] (n11);

\tikz \node[draw, circle, inner sep=1pt]{2}; \textbackslash draw[]  (n21) to[{\color{red}loop above, looseness=40}] (n21);


\tikz \node[draw, circle, inner sep=1pt]{3}; \textbackslash draw[]  (n13) to[{\color{red}loop below, looseness=40}] (n13);

}
}
%\only<2-2>{
	\only<handout:2>{
\vspace{20pt}

%figure
\scalebox{0.41}{
\begin{tikzpicture}
\tikzstyle{monNoeud}=[draw, circle, inner sep=1pt, minimum size = 2em]
\tikzstyle{mafleche}=[-stealth, thick]
\tikzstyle{label}=[midway, above=3pt, circle, inner sep =1pt, draw, line width = 1pt, scale=2, gray]


%source
\node [monNoeud, line width = 2pt] (s1) at (-8.5,0.5) {s1};

%col 1
\node [monNoeud] (n11) at (-4,3.5) {n11};
\node [monNoeud] (n12) at (-4,0.5) {n12};
\node [monNoeud] (n13) at (-4,-2.5) {n13};

%col 2
\node [monNoeud] (n21) at (1,3.5) {n21};
\node [monNoeud] (n22) at (1,0.5) {n22};
\node [monNoeud] (n23) at (1,-2.5) {n23};

%col 3
\node [monNoeud] (n31) at (5.5,3.5) {n31};
\node [monNoeud] (n32) at (5.5,0.5) {n32};
\node [monNoeud] (n33) at (5.5,-2.5) {n33};

%col 4
\node [monNoeud] (n41) at (9.5,3.5) {n41};
\node [monNoeud] (n42) at (9.5,0.5) {n42};
\node [monNoeud] (n43) at (9.5,-2.5) {n43};

%puit
\node [monNoeud, line width = 2pt] (s2) at (14.5,0.5) {s2};


%loops du haut

%premiere loop

\draw[mafleche]  (n11) to[loop, looseness=20] (n11);


%deuxieme loop
\draw[mafleche]  (n21) to[loop above, looseness=40] (n21);


%3e loop
\draw[mafleche]  (n31) to[loop, looseness=20] (n31);
%4e loop
\draw[mafleche]  (n41) to[loop, looseness=20] (n41);


%------------------------------
%loops du bas
\draw[mafleche]  (n13) to[loop below, looseness=40] (n13);


\draw[mafleche]  (n23) to[loop below, looseness=40] (n23);
\draw[mafleche]  (n33) to[loop below, looseness=40] (n33);
\draw[mafleche]  (n43) to[loop below, looseness=40] (n43);


%--------------------------------------
%depart de la source


%double depart vers le haut
\draw[mafleche, line width = 3pt]  (s1) to[bend left] node[label]{1} (n11);
\draw[mafleche]  (s1) to (n11);


%double depart vers le bas

\draw[mafleche, bend right, line width = 3pt]  (s1) to node[label, below=3pt]{2} (n13);
\draw[mafleche]  (s1) to (n13);



\draw[mafleche]  (s1) to (n12);

%-----------------------------------
%fleches qui bend

\draw[mafleche, line width = 3pt ]  (s1) to[bend left] node[label]{3} (n22);

%autre fleche
\draw[mafleche]  (n11) to[bend left] (n33);


%autre fleche
\draw[mafleche]  (n12) to[bend right] (n32);


%bend left 10
\draw[mafleche, line width=3pt]  (n13) to[bend left=10] node[label, pos=0.3]{4} (n31);


%in=... ,out=...
\draw[mafleche, line width=3pt]  (n31) to[out = -10, in = 135] node[label, below]{5} (s2);
\draw[mafleche, line width=3pt]  (n41) to[out=0, in=90] node[label]{6} (s2);




\draw[mafleche]  (n11) to (n22);
\draw[mafleche]  (n11) to (n21);
\draw[mafleche]  (n12) to (n23);
\draw[mafleche]  (n12) to (n31);


\draw[mafleche]  (n22) to (n32);
\draw[mafleche]  (n32) to (n42);


\draw[mafleche]  (n32) to (n43);

\draw[mafleche]  (n32) to (n41);

\draw[mafleche]  (n13) to (n23);
\draw[mafleche]  (n23) to (n32);
\draw[mafleche]  (n33) to (n42);
\draw[mafleche]  (n33) to (n43);


%arrivee au puit
\draw[mafleche]  (n42) to (s2);
\draw[mafleche]  (n21) to (s2);



\draw[mafleche]  (n43) to (s2);

\end{tikzpicture}
}


\scriptsize{
\ttfamily



\tikz \node[draw, circle, inner sep=1pt]{1}; \textbackslash draw[]  (s1) to[{\color{red}bend left}] (n11);

\tikz \node[draw, circle, inner sep=1pt]{2}; \textbackslash draw[{\color{red}bend right}]  (s1) to (n13);

\tikz \node[draw, circle, inner sep=1pt]{3}; \textbackslash draw[]  (s1) to[{\color{red}bend left}] (n22);

\tikz \node[draw, circle, inner sep=1pt]{4}; \textbackslash draw[]  (n13) to[{\color{red}bend left=10}] (n31);

\tikz \node[draw, circle, inner sep=1pt]{5}; \textbackslash draw[]  (n31) to[{\color{red}out = -10, in = 135}] (s2);

\tikz \node[draw, circle, inner sep=1pt]{6}; \textbackslash draw[]  (n41) to[{\color{red}out=0, in=90}] (s2);

}
}

\end{frame}


%============================================
% Étiquettes
%============================================

\subsection{Étiquettes}

%les labels
\begin{frame}[fragile]

\frametitle{Étiquettes de noeuds}


\scriptsize{
\ttfamily
	\textbackslash node [draw, {\color{red} label = Étiquette du noeud n1}] (n1) at (0,0) \{\};

	\vspace{10pt}

	\textbackslash node [draw, {\color{red} label = \{[red]45:n2\}}] (n2) at (2,0) \{\};
}
	\vspace{20pt}

\begin{tikzpicture}
	\node [draw, label = Étiquette du noeud n1] (n1) at (0,0) {};
	\node [draw, label ={[red]45:n2}] (n2) at (6,0) {};
	\draw[->] (n1) -- (n2);
\end{tikzpicture}


\end{frame}




\begin{frame}[t]
\frametitle{Étiquettes d'arcs}
\vspace{-15pt}

\scalebox{0.8}{
\begin{tikzpicture}
\node [draw] (n1) at (-6,4) {n1};
\node [draw] (n2) at (1.5,4) {n2};
\node [draw] (n3) at (-6,-1.5) {n3};
\node [draw] (n4) at (-1,2.5) {n4};

%arc 1-2
\draw [] (n1) -- (n2) node[midway, above=10pt, gray]{[midway, above]} node[midway, above]{L};


%arc 1-3
\draw [] (n1) -- (n3) 
node[gray, left, very near start]{[very near start]} node[very near start]{A} 
node[gray, left, near start]{[near start]} node[near start]{B} 
node[gray, left, near end]{[near end]} node[near end]{C}
node[gray, left, very near end]{[very near end]} node[very near end]{D}
;

%arc 3-2
\draw [bend right = 60] (n3) to node[gray, pos=0.2, below right]{[pos=0.2]}  node[pos=0.2]{F} 
node[gray, pos=0.5, below right]{[pos=0.5]}  node[pos=0.5]{G}  
node[gray, pos=0.7, below right]{[pos=0.7]}  node[pos=0.7]{H} 
(n2);


%arc 1-4
\draw [] (n1) -- (n4) node[sloped, below, gray, pos=0.3]{[sloped]} node[sloped, pos=0.3]{N}  
 node[sloped, above, gray, pos=0.65]{[rotate=-45]} node[rotate=-45, pos=0.65]{M} ;


%arc 4-3
\draw [] (n4) -- (n3) node[pos=0.2, left]{W} node[pos=0.2, left= 10pt, gray]{[left]}
node[pos=0.7, right]{K} node[pos=0.7, right= 10pt, gray]{[right]}
;


%arc 4-2
\draw [] (n4) -- (n2) node[pos=0.3, scale = 2]{X} node[gray, pos=0.3, right=5pt]{[scale=2]};








\end{tikzpicture}
}

\vspace{-15pt}


\scriptsize{
\underline{Avec la commande \dd}
\ttfamily


\textbackslash draw [] (n1) \dd (n2) node[midway, above]\{L\};
}


\underline{Avec la commande to}
\scriptsize{
\ttfamily

\textbackslash node[bend right = 60] (n3) to 

node[pos=0.2]\{F\} 

node[pos=0.5]\{G\}  

node[pos=0.7]\{H\} 

(n2);

}




\end{frame}


%========================================
% Autres astuces
%========================================


%ancres
\begin{frame}

\frametitle{Ancres}

\begin{tikzpicture}

\node[draw, rounded corners=10pt, very thick, minimum size = 60pt] (n1) at (0,0) {\large noeud n};

\draw[->] (-2, -2) node[below left = -3pt]{n.south west} -- (n1.south west);
\draw[->] (-2, 2) node[above left = -3pt]{n.north west} -- (n1.north west);
\draw[->] (2, -2) node[below right = -3pt]{n.south east} -- (n1.south east);
\draw[->] (2, 2) node[above right = -3pt]{n.north east} -- (n1.north east);

\draw[->] (2, -1) node[right]{n.center} -- (n1.center);
\draw[->] (-2,-1) node[left]{n.text} -- (n1.text);

\draw[->] (2, 1) node[right]{n.30} -- (n1.30);


\draw[->] (0, 2) node[above]{n.north} -- (n1.north);
\draw[->] (0, -2) node[below]{n.south} -- (n1.south);
\draw[->] (2, 0) node[right]{n.east} -- (n1.east);
\draw[->] (-2, 0) node[left]{n.west} -- (n1.west);
\end{tikzpicture}

\end{frame}

%ancres 2
\begin{frame}
\frametitle{Ancres}
\begin{columns}

\column{3cm}
\begin{tikzpicture}

\node[draw, very thick, minimum size = 30] (n1) at (2,-2) {n1};

\node[draw, very thick, minimum size = 30] (n2) at (2,2) {n2};

\node[draw, very thick, minimum size = 30] (n3) at (0,0) {n3};


\draw[] (n1.north west) -- (n2.south east);

\draw[] (n1.north east) -- (n2.south west);

\draw[] (n3.north east) -- (n2.west);
\draw[] (n3.south east) -- (n1.center);



\end{tikzpicture}

\column{6.5cm}

\scriptsize{
\ttfamily
{\textbackslash draw[] (n1.north west) \dd (n2.south east);}

{\textbackslash draw[] (n1.north east) \dd (n2.south west);}

{\textbackslash draw[] (n3.north east) \dd (n2.west);}

{\textbackslash draw[] (n3.south east) \dd (n1.center);}
}

\end{columns}
\end{frame}


%graphes faciles

\begin{frame}
\frametitle{Une librairie pour des graphes simples}
\begin{columns}[t]

\column{4cm}

\scalebox{0.4}{
\begin{tikzpicture}[scale=3]

\GraphInit[vstyle=Normal]
\uncover<2->{
	\Vertex{A}
}
\uncover<3->{
\NOEA(A){C}
}
\uncover<4->{
\NO(C){B}
\EA(A){D}
\SO(D){E}
\EA(B){F}
\EA(C){G}
\EA(D){O}
\EA(E){I}
%\EA(F){J}
\EA(G){K}
\EA(O){L}
\EA(I){M}
%\EA(M){N}
%\NOEA(L){H}
%\NO(F){P}
\SO(I){Q}
}
\uncover<5->{
\tikzset{EdgeStyle/.style = {->,ultra thick}}
\Edge[label=1/1](A)(B)
}
\uncover<6->{
\Edge[label=1/1](A)(C)
\Edge[label=1/1](A)(D)
\Edge[label=1/1](A)(E)
%\Edge[label=1/1](B)(P)
\Edge[label=0/1](B)(F)
\Edge[label=0/1](C)(G)
\Edge[label=1/1](C)(O)
\Edge[label=0/1](C)(I)
\Edge[label=0/1](D)(M)
\Edge[label=1/1](E)(Q)
\Edge[label=0/1](F)(K)
%\Edge[label=0/1](G)(J)
\Edge[label=1/1](O)(K)
\Edge[label=0/1](I)(L)
\Edge[label=0/1](I)(M)
%\Edge[label=1/1](J)(H)
%\Edge[label=1/1](K)(H)
%\Edge[label=1/1](L)(H)
%\Edge[label=1/1](M)(N)
%\Edge[label=1/1](N)(H)
%\Edge[label=1/1](P)(J)
\Edge[label=0/1](Q)(L)
\Edge[label=1/1](Q)(M)

\tikzset{EdgeStyle/.style = {->,bend left=35, ultra thick}}
\Edge[label=1/1](D)(L)

}
\end{tikzpicture}
}
\column{6cm}

\scriptsize{
\ttfamily

\uncover<2->{
\textbackslash usepackage\{tkz-graph\} {\color{gray} dans le préambule}

\textbackslash GraphInit[vstyle=Normal]

\textbackslash Vertex\{A\}
}
\uncover<3->{
\textbackslash NOEA(A)\{C\} {\color{gray} 

\textbackslash NOEA pour NOrth EAst}
}

\uncover<4->{
\textbackslash NO(C)\{B\}

\textbackslash EA(A)\{D\}

\textbackslash SO(D)\{E\}

\textbackslash EA(B)\{F\}

\textbackslash EA(C)\{G\}

\textbackslash EA(D)\{O\}

\textbackslash EA(E)\{I\}

\textbackslash EA(G)\{K\}

\textbackslash EA(O)\{L\}

\textbackslash EA(I)\{M\}

\textbackslash SO(I)\{Q\}
}

\uncover<5->{
\vspace{10pt}
\textbackslash Edge[label=1/1](A)(B)
}

\uncover<6->{
\textbackslash Edge[label=1/1](A)(D)

\textbackslash Edge[label=1/1](A)(E)

...
}

}

\end{columns}

\end{frame}

%============================================
% 2D/3D
%============================================

\subsection{2D/3D}
%graphes 2D/3D

\begin{frame}[fragile, t]
\frametitle{Graphes 2D/3D et animation avec tikz}
\bigskip
\tiny{
\ttfamily{http://www.texample.net/tikz/examples/tag/3d/}
\begin{figure}
\includegraphics[width=2cm]{Figures/2D3D.jpg}
\caption{\tiny Circumscribed Parallepiped by Axel Pavillet \url{http://www.texample.net/tikz/examples/parallelepiped/}}	
\end{figure}
\vspace{10pt}
%
\begin{figure}
	\includegraphics[width=4cm]{andler.png}
	\caption{\tiny Animation of the Optimal Lot-Size with the Andler Formula by Felix Lindemann \url{http://www.texample.net/tikz/examples/andler-optimal-lot-size/}}	
\end{figure}
}
\end{frame}

\begin{frame}
	\begin{animateinline}[autoplay,palindrome,
		begin={\begin{tikzpicture}[domain=0.3:8.4]},
		end={\end{tikzpicture}}]{3}
		\ANDLER{5}{20}{5}{50}; \newframe
		\ANDLER{6}{20}{5}{50}; \newframe
		\ANDLER{7}{20}{5}{50}; \newframe
		\ANDLER{8}{20}{5}{50}; \newframe
		\ANDLER{9}{20}{5}{50}; \newframe
		\ANDLER{10}{20}{5}{50}; \newframe
		\ANDLER{11}{20}{5}{50}; \newframe
		\ANDLER{12}{20}{5}{50}; 
	\end{animateinline}
\end{frame}


\begin{frame}
%  Development of total cost function by varying the storing cost parameter

\vspace*{-1em}
\begin{animateinline}[autoplay,palindrome,
	begin={\begin{tikzpicture}[domain=0.3:8.4]},
	end={\end{tikzpicture}}]{3}
	\ANDLER{5}{20}{3.5}{50};\newframe
	\ANDLER{5}{20}{4.0}{50};\newframe
	\ANDLER{5}{20}{4.5}{50};\newframe
	\ANDLER{5}{20}{5.0}{50};\newframe
	\ANDLER{5}{20}{5.5}{50};\newframe
	\ANDLER{5}{20}{6.0}{50};\newframe
	\ANDLER{5}{20}{6.5}{50}  ;
\end{animateinline}
\end{frame}