phd-defence-fr/otb.ppm.tex

318 lines
12 KiB
TeX
Raw Normal View History

2017-07-06 15:54:32 +02:00
\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
{Le problème de la dépendance aux cellules voisines}
\vfill
\centering
\begin{tikzpicture}
\clip (-17mm,-17mm) rectangle (17mm,17mm);
\draw[xshift=5mm,yshift=5mm] ( -3cm, -3cm) grid ( 3cm, 3cm);
\node (x) at (0,0) {$x_i$};
\foreach[count=\n] \p in {(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)} {
\node (v\n) at \p {$v_{\n_i}$};
}
\begin{scope}[on background layer]
\clip (-17mm,-17mm) rectangle (17mm,17mm);
\only<1>{%
\fill[black!10] (v6.south west) rectangle (v2.north east);
\fill[white] (v6.north east) rectangle (v2.south west);
\fill[red!60] (x) circle (3mm);
}
\only<2>{%
\fill[black!10] (v3.north east) rectangle ($(v7.south east)+(-10cm,0)$);
\fill[white] (v3.south west) rectangle ($(v7.north east)+(-10cm,0)$);
\fill[red!60] (v5) circle (3mm);
}
\end{scope}
\end{tikzpicture}
\alt<1>{%
$$ x_{i,1} = f(x_i , v_{1_i} , v_{2_i} , \ldots , v_{8_i}) $$
}{%
$$ v_{5_{i,1}} = f(v_{5_i} , x_i , v_{3_i}, v_{4_i} ,
\alert{? , ? , ?} , v_{6_i} , v_{7_i}) $$
}
\vfill~
\uncover<2>{Une partie du \structure{contexte} est manquant.}
\end{frame}
\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
{Le voisinage de margolus}
\vfill
\centering
\begin{tikzpicture}
\clip (-27mm,-27mm) rectangle (27mm,27mm);
\draw[xshift=5mm,yshift=5mm] ( -5cm, -5cm) grid ( 5cm, 5cm);
\fill[red] (0,0) circle (3mm);
\only<1>{\draw[xshift=5mm,yshift=5mm, step=2cm, very thick]%
( -5cm, -5cm) grid ( 5cm, 5cm);}
\only<2>{\draw[xshift=-5mm,yshift=-5mm, step=2cm, very thick]%
( -5cm, -5cm) grid ( 5cm, 5cm);}
\begin{scope}[on background layer]
\only<1>{%
\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
\only<2>{%
\fill[red!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
\end{scope}
\end{tikzpicture}
\vfill~
\end{frame}
\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
{Mise à jour \emph{indépendante} d'un bloc}
\vfill
\centering
\begin{tikzpicture}[
cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\TINY},
neighbor cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\small},
center cell/.style={cell,white,fill=black},
spy using outlines={circle,red,size=58mm,magnification=4,connect spies}]
\begin{scope}[scale=.5]
\clip (-27mm,-27mm) rectangle (27mm,27mm);
% Background
\only<1-3>{%
\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
}
\only<4->{%
\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
}
\begin{scope}
\clip (-3mm,-3mm) rectangle (3mm,3mm);
\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
\end{scope}
\only<1-3>{
\begin{scope}[shift={(-1cm,0)}]
\clip (-3mm,-3mm) rectangle (3mm,3mm);
\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
\end{scope}
\begin{scope}[shift={(-1cm,-1cm)}]
\clip (-3mm,-3mm) rectangle (3mm,3mm);
\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
\end{scope}
\begin{scope}[shift={(0cm,-1cm)}]
\clip (-3mm,-3mm) rectangle (3mm,3mm);
\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
\end{scope}
}
\only<1>{
% Voisins
\node[neighbor cell] at ( 1cm, 0cm) {$v_{A,1}$};
\node[neighbor cell] at ( 1cm, 1cm) {$v_{A,2}$};
\node[neighbor cell] at ( 0cm, 1cm) {$v_{A,3}$};
\node[neighbor cell] at (-1cm, 1cm) {$v_{B,1}$};
\node[neighbor cell] at (-2cm, 1cm) {$v_{B,2}$};
\node[neighbor cell] at (-2cm, 0cm) {$v_{B,3}$};
\node[neighbor cell] at (-2cm,-1cm) {$v_{C,1}$};
\node[neighbor cell] at (-2cm,-2cm) {$v_{C,2}$};
\node[neighbor cell] at (-1cm,-2cm) {$v_{C,3}$};
\node[neighbor cell] at ( 0cm,-2cm) {$v_{D,1}$};
\node[neighbor cell] at ( 1cm,-2cm) {$v_{D,2}$};
\node[neighbor cell] at ( 1cm,-1cm) {$v_{D,3}$};
\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
\node[center cell] at ( -0mm, -0mm) {$A$};
\node[cell] at (-10mm, -0mm) {$B$};
\node[cell] at (-10mm,-10mm) {$C$};
\node[cell] at ( -0mm,-10mm) {$D$};
\node[cell] at ( 1cm, 0cm) {$v_{A,1}$};
\node[cell] at ( 1cm, 1cm) {$v_{A,2}$};
\node[cell] at ( 0cm, 1cm) {$v_{A,3}$};
\node[cell] at (-1cm, 1cm) {$v_{B,1}$};
\node[cell] at (-2cm, 1cm) {$v_{B,2}$};
\node[cell] at (-2cm, 0cm) {$v_{B,3}$};
\node[cell] at (-2cm,-1cm) {$v_{C,1}$};
\node[cell] at (-2cm,-2cm) {$v_{C,2}$};
\node[cell] at (-1cm,-2cm) {$v_{C,3}$};
\node[cell] at ( 0cm,-2cm) {$v_{D,1}$};
\node[cell] at ( 1cm,-2cm) {$v_{D,2}$};
\node[cell] at ( 1cm,-1cm) {$v_{D,3}$};
\end{scope}
}
\only<2>{
\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
\node[center cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
}
\only<3>{
\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
\node[center cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
\begin{scope}[scale=0.5,shift={(-15mm,5mm)}]
\node[cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
\begin{scope}[scale=0.5,shift={(-15mm,-15mm)}]
\node[cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
\begin{scope}[scale=0.5,shift={(5mm,-15mm)}]
\node[cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
}
\only<4>{
\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
\node[center cell] at ( -0mm, -0mm) {$A'$};
\node[cell] at (-10mm, -0mm) {$B'$};
\node[cell] at (-10mm,-10mm) {$C'$};
\node[cell] at ( -0mm,-10mm) {$D'$};
\end{scope}
}
% Grilles:
\draw[xshift=5mm,yshift=5mm,thin] ( -5cm, -5cm) grid ( 5cm, 5cm);
\only<1-3>{\draw[xshift=5mm,yshift=5mm, step=2cm, thick]%
( -5cm, -5cm) grid ( 5cm, 5cm);}
\only<4>{\draw[xshift=-5mm,yshift=-5mm, step=2cm, thick]%
( -5cm, -5cm) grid ( 5cm, 5cm);}
\only<1-3>{
\coordinate (spyhook) at (-5mm,-5mm);
}
\only<4>{
\coordinate (spyhook) at (5mm,5mm);
}
\end{scope}
\spy on (spyhook) in node (zoom) at (5cm,0);
\end{tikzpicture}
%\only<1-2>{
%Toute l'information \emph{nécessaire} est disponible pour mettre à jour $A$.
%$$ A' = f( A, v_{A_1}, v_{A_2}, v_{A_3}, v_{B_1}, B, C, D, v_{D_3} ) $$
%ainsi que $B$, $C$ et $D$, symétriquement.
%}
%\only<3>{
%Le bloc $(A',B',C',D')$ est répliqué 4 fois.}
%\only<4>{
%Au décalage de la grille, le nouveau bloc est prêt pour une mise à jour.
%}
\vfill~
\end{frame}
%\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
% {Mise à jour \emph{indépendante} d'un bloc}
% \vfill
%
% \begin{columns}[c]
% \column{.4\textwidth}\centering
% \begin{tikzpicture}[scale=.5]
% \clip (-27mm,-27mm) rectangle (27mm,27mm);
% \draw[xshift=5mm,yshift=5mm] ( -5cm, -5cm) grid ( 5cm, 5cm);
% \fill[red] (0,0) circle (3mm);
% \only<1-3>{\draw[xshift=5mm,yshift=5mm, step=2cm, very thick]%
% ( -5cm, -5cm) grid ( 5cm, 5cm);}
% \only<4->{\draw[xshift=-5mm,yshift=-5mm, step=2cm, very thick]%
% ( -5cm, -5cm) grid ( 5cm, 5cm);}
% \begin{scope}[on background layer]
% \only<1-3>{%
% \fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
% \fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
% \only<4->{%
% \fill[red!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
% \end{scope}
% \end{tikzpicture}
% \column{.6\textwidth}\centering
% \begin{tikzpicture}
% \only<1-2,4>{%
% \fill[red!50] (-1cm,-1cm) rectangle (1cm,1cm);}
% \only<3>{%
% \fill[red!50, shift={(1cm,1cm)}] (0cm,0cm) rectangle (1cm,1cm);
% \fill[red!50, shift={(1cm,-2cm)}] (0cm,0cm) rectangle (1cm,1cm);
% \fill[red!50, shift={(-2cm,1cm)}] (0cm,0cm) rectangle (1cm,1cm);
% \fill[red!50, shift={(-2cm,-2cm)}] (0cm,0cm) rectangle (1cm,1cm);}
% \only<1>{%
% \fill[blue!50] (0cm,1cm) -- (0cm,2cm) -- (2cm,2cm) -- (2cm,0cm) -- (1cm,0cm) -- (1cm,1cm) -- cycle;}
% \draw[very thin,dashed] (-2,-2) grid (2,2);
% \draw[step=2cm] (-2,-2) grid (2,2);
% \draw[step=4cm, very thick, shift={(-2cm,-2cm)}] (-4mm,-4mm) grid (44mm,44mm);
% \only<1>{%
% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A) at (5mm,5mm) {A};%
% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (B) at (-5mm,5mm) {B};%
% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (C) at (-5mm,-5mm) {C};%
% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (D) at (5mm,-5mm) {D};%
% \node (va1) at (15mm,5mm) {$v_{A_1}$};%
% \node (va2) at (15mm,15mm) {$v_{A_2}$};%
% \node (va3) at (5mm,15mm) {$v_{A_3}$};%
% \node (vb1) at (-5mm,15mm) {$v_{B_1}$};%
% \node (vd3) at (15mm,-5mm) {$v_{D_3}$};%
% }
% \only<2>{%
% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (5mm,5mm) {A'};%
% \node (B') at (-5mm,5mm) {B'};%
% \node (C') at (-5mm,-5mm) {C'};%
% \node (D') at (5mm,-5mm) {D'};%
% }
% \only<3>{%
% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (15mm,15mm) {A'};%
% \node (B') at ( 5mm,15mm) {B'};%
% \node (C') at ( 5mm, 5mm) {C'};%
% \node (D') at (15mm, 5mm) {D'};%
% \begin{scope}[shift={(-15mm,5mm)}]
% \node (A') at (10mm,10mm) {A'};%
% \node (B') at ( 0mm,10mm) {B'};%
% \node (C') at ( 0mm, 0mm) {C'};%
% \node (D') at (10mm, 0mm) {D'};%
% \end{scope}
% \begin{scope}[shift={(5mm,-15mm)}]
% \node (A') at (10mm,10mm) {A'};%
% \node (B') at ( 0mm,10mm) {B'};%
% \node (C') at ( 0mm, 0mm) {C'};%
% \node (D') at (10mm, 0mm) {D'};%
% \end{scope}
% \begin{scope}[shift={(-15mm,-15mm)}]
% \node (A') at (10mm,10mm) {A'};%
% \node (B') at ( 0mm,10mm) {B'};%
% \node (C') at ( 0mm, 0mm) {C'};%
% \node (D') at (10mm, 0mm) {D'};%
% \end{scope}
% }
% \only<4>{
% \begin{scope}[shift={(-15mm,-15mm)}]
% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (10mm,10mm) {A};%
% \node (B') at ( 0mm,10mm) {B};%
% \node (C') at ( 0mm, 0mm) {C};%
% \node (D') at (10mm, 0mm) {D};%
% \end{scope}
% }
% \end{tikzpicture}
% \end{columns}
%
% \centering
% \only<1-2>{
% Toute l'information \emph{nécessaire} est disponible pour mettre à jour $A$.
% $$ A' = f( A, v_{A_1}, v_{A_2}, v_{A_3}, v_{B_1}, B, C, D, v_{D_3} ) $$
% ainsi que $B$, $C$ et $D$, symétriquement.
% }
% \only<3>{
% Le bloc $(A',B',C',D')$ est répliqué 4 fois.}
% \only<4>{
% Au décalage de la grille, le nouveau bloc est prêt pour une mise à jour.
% }
%
%
% \vfill~
%\end{frame}