merge_en.tex

% \documentclass[]{minimal}
% \usepackage{tikz}
% \usetikzlibrary{positioning}
% \usetikzlibrary{arrows}
% \usetikzlibrary{patterns}

% \begin{document}

% \pagestyle{empty}

% \begin{tikzpicture}[scale=2.2]


%legend
\uncover<1->{
\draw[] (3.25,.25) rectangle (4.75, 1.65);

\begin{scope}[anchor=west]
    \node[] at (3.8,1.45) {\(\mathcal{F}\)};
    \node[] at (3.8,1.25) {\(\mathcal{G}\)};
    \node[] at (3.8,.95) {$i_k$};
    \node[] at (3.8,.75) {$i_{k+1}$};
    \node[] at (3.8,.45) {\small correction};
\end{scope}

\draw[-, dotted,very thick] (3.4,1.45) -- (3.7,1.45);
\draw[-, loosely dotted,very thick] (3.4,1.25) -- (3.7,1.25);
\draw[pattern color=blue,pattern=north east lines] (3.4,.9) rectangle (3.7, 1);
\draw[pattern color=orange,pattern=north east lines] (3.4,.7) rectangle (3.7, .8);
\draw[->,red, ultra thick] (3.4,.45) -- (3.7,.45);

% coordinates
\draw[->] (0,0) -- (0,3) node[pos=1,below left] {y};

\draw[-] (0,0) -- (.25,0);
\draw[dotted] (.25,0) -- (.5,0);
\draw[-] (.5,0) -- (5.5,0);
\draw[dotted] (5.5,0) -- (5.75,0);
\draw[->] (5.75,0) -- (6,0) node[pos=1,below left] {x};

% threads
\draw[loosely dashed] (1,0) -- (1,3.3);
\draw[loosely dashed] (3,0) -- (3,3.3);
\draw[loosely dashed] (5,0) -- (5,3.3);
\node[below] at (1,0) {$t_{i-1}$};
\node[below] at (3,0) {$t_{i}$};
\node[below] at (5,0) {$t_{i+1}$};

% exact
\draw[thick] (.5,-.3) parabola  bend +(5,2.6) (5.5,2.3);
}
\begin{scope}[very thick]
\uncover<2->{
% pCoarse
\begin{scope}[loosely dotted, color=blue]
\draw (1,.8) to[out=45,in=215] (3,2.6);
\draw (3,2.15) to[out=39,in=192] (5,2.95);
\end{scope}
}
% pFine
\uncover<3->{
\begin{scope}[densely dotted, color=blue]
\draw (1,.8) to[out=44,in=212] (3,2.35);
\draw (3,2.15) to[out=28,in=186] (5,2.75);
\end{scope}
}
% coarse

\begin{scope}[loosely dotted, color=orange]
\uncover<4->{\draw (1,.5) to[out=45,in=215] (3,2.2);}
\uncover<7->{\draw (3,1.95) to[out=32,in=188] (5,2.7);}
\end{scope}

\end{scope}

% merges
\begin{scope}[red, ultra thick]
\uncover<5->{\draw[->, dashed] (2.96,2.6) -- (2.96,2.2);}
\uncover<6->{\draw[->] (3.04,2.35) -- (3.04,1.95);}
\uncover<8->{
\draw[->, dashed] (4.96,2.95) -- (4.96,2.7);
\draw[->] (5.04,2.75) -- (5.04,2.5);
}
\end{scope}


% \end{tikzpicture}

% \end{document}