# how to fill the area under a curve

I can not find a way to fill the area under these 3 curves and the legend doesn't seem to show the correct line colours (the red one is missing?). Thanks.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[hide axis,clip=false,
xmin=-1,xmax=5,
ymin=-1,ymax=5,
ticks=none,
%axis line style={draw=none},
tick style={draw=none},
legend pos=outer north east,
scale=1.7
]

\addplot[no marks,color=blue!20,fill=blue!20,domain=-0:3.3,samples=200,scale=0.3,transform canvas={rotate around={22:(0,4)}},color=gray]plot[smooth] {-sqrt(x)+4-0.2*sin(deg(x^2))} \closedcycle;

\addplot[no marks,color=lime!20,fill=lime!20,domain=0:4.95,samples=200,transform canvas={rotate around={37:(0,0)}},scale=0.3,color=blue] plot[smooth]{0.75*sin(deg(x^2))/x} \closedcycle;

\node at (axis cs:1,1) {$\Omega_1$};
\node at (axis cs:1,2.5) {$\Omega_2$};
\node at (axis cs:1.3,3.6) {$\Omega_3$};
\draw (0,0) rectangle (4,4);
\draw (0,4) node[left]{$b$} ;
\draw (0,0) node[below]{$t_0$} ;
\draw (0,0) node[above left]{$1$} ;
\draw (4,0) node[below]{$t_1$} ;
\draw (2.21,0.6) node[below] {$(\tau,\sigma)$}  node[color=red] {$\times$};
\draw (1.5,0) node[below] {$\xi^{\tau}(\sigma)$}  node[rotate=41,color=red] {$>$};
\draw [blue] (4,3.3) node[above right] {$\Phi_{(t_0,1)}$};
\draw [red] (4,1.1) node[below right] {$\Phi_{(\tau,\sigma)}$};
\draw [gray] (3.7,4) node[above] {$\Phi_{(t_0,b)}$};
\addlegendentry{$\Phi_{(t_0,b)}$};
\addlegendentry{$\Phi_{(t_0,1)}$};
\addlegendentry{$\Phi_{(\tau,\sigma)}$};
\end{axis}
\end{tikzpicture}
\end{document}

• Welcome to TeX-SE! Which curves do you want to get filled. (The fillbetween library allows you to fill pretty much any curve.) – marmot Mar 7 at 21:35
• Gray between {y=4} and {y=sqrt{x}+4-0.2*\sin{x^2)}, lime between {y=sqrt{x}+4-0.2*sin{x^2)} and {y=0.75*sin(x^2)/x}, blue between {y=0.75*sin(x^2)/x} and {y-0} – Abe Mar 7 at 22:37
• A large fraction of the difficulties stems from you using transform canvas. Have you tried to produce the plots without it (and e.g. just using rotate around or changing the parametrization of the plots)? – marmot Mar 7 at 22:50
• I used rotate around and fillbetween but the problem still. – Abe Mar 7 at 23:14

I do not know what your target picture is. And I am not claiming that the additional terms I add precisely correspond to your rotate around statements (but to a low approximation they do). Anyway, I am wondering if the following goes in the right direction.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}
%\usepgfplotslibrary{fillbetween} %<- for more delicate fills
\begin{document}
\begin{tikzpicture}
\begin{axis}[hide axis,clip=false,
xmin=-1,xmax=5,
ymin=-1,ymax=5,
ticks=none,
%axis line style={draw=none},
tick style={draw=none},
legend pos=outer north east,
scale=1.7
]

%rotate around={22:(0,4)},
color=gray]  {-sqrt(x)+4-0.2*sin(deg(x^2))+tan(22)*x} \closedcycle;

%rotate around={37:(0,0)},scale=0.3,
color=blue]
{0.75*sin(deg(x^2))/x+tan(37)*x} \closedcycle;

color=red,fill=red] {0.5*sin(deg((x-1.5)*(x-1.5)))/(x-1.5)+tan(15)*x}
\closedcycle;
\node at (axis cs:1,1) {$\Omega_1$};
\node at (axis cs:1,2.5) {$\Omega_2$};
\node at (axis cs:1.3,3.6) {$\Omega_3$};
\draw (0,0) rectangle (4,4);
\draw (0,4) node[left]{$b$} ;
\draw (0,0) node[below]{$t_0$} ;
\draw (0,0) node[above left]{$1$} ;
\draw (4,0) node[below]{$t_1$} ;
\draw (2.21,0.6) node[below] {$(\tau,\sigma)$}  node[color=red] {$\times$};
\draw (1.5,0) node[below] {$\xi^{\tau}(\sigma)$}  node[rotate=41,color=red] {$>$};
\draw [blue] (4,3.3) node[above right] {$\Phi_{(t_0,1)}$};
\draw [red] (4,1.1) node[below right] {$\Phi_{(\tau,\sigma)}$};
\draw [gray] (3.7,4) node[above] {$\Phi_{(t_0,b)}$};
\addlegendentry{$\Phi_{(t_0,b)}$};
\addlegendentry{$\Phi_{(t_0,1)}$};
\addlegendentry{$\Phi_{(\tau,\sigma)}$};
\end{axis}
\end{tikzpicture}
\end{document}