Kdtyjb

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}

pgfplotsset{compat=newest}



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=gray!20,fill=gray!20,domain=0:4,samples=200] {4} closedcycle;



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;



addplot[no marks,domain=1.5:4.05,samples,scale=0.3,transform canvas={rotate around={15:(1.5,0)}},color=red] plot[smooth]{0.5*sin(deg((x-1.5)*(x-1.5)))/(x-1.5)};

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}

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}

pgfplotsset{compat=newest}

%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

      ]



addplot[no marks,color=gray!20,fill=gray!20,domain=0:4,samples=2,forget plot] {4} closedcycle;



addplot[no marks,color=blue!20,fill=blue!20,domain=-0:4,samples=200,%scale=0.3,

%rotate around={22:(0,4)},

color=gray]  {-sqrt(x)+4-0.2*sin(deg(x^2))+tan(22)*x} closedcycle;



addplot[no marks,color=lime!20,fill=lime!20,domain=0:4,samples=200,

%rotate around={37:(0,0)},scale=0.3,

color=blue] 

{0.75*sin(deg(x^2))/x+tan(37)*x} closedcycle;



addplot[no marks,domain=1.5:4,samples,%scale=0.3,rotate around={15:(1.5,0)},

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}