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Filling an area between two curves


How to draw a decorated rectangle with rounded corners?TikZ: Cropping the Bounding BoxRotate a node but not its content: the case of the ellipse decorationHow to define the default vertical distance between nodes?Area between curves tikzGraphics: Area between curvesFilling an area between curvesFill area between two curvesFilling the area between two circlesFilling Area between two Bezier Curves with tikzFill the area between two curves













3















I would like to draw the following figure:
enter image description here



To do this I have used the following codes : 



documentclass[10pt]{article}

usepackage{pgf,tikz}

usetikzlibrary{arrows}

pagestyle{empty}

begin{document}



begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]

draw [rotate around={15.05:(6.07,0.75)}] (6.07,0.75) ellipse (1.11cm and 0.56cm);

draw [rotate around={-13.74:(8.9,0.78)}] (8.9,0.78) ellipse (1.07cm and 0.53cm);

draw  (4.58,2.02)-- (11,2);

draw  (11,2)-- (10.48,-1);

draw  (10.48,-1)-- (4,-1);

draw  (4,-1)-- (4.58,2.02);

draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});

draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});

draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);

draw [rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);

draw [rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);

draw [->] (8.96,6.46) -- (8.8,1.62);

draw [->] (6.7,6.38) -- (6.46,1.62);

draw [->] (7.3,0.98) -- (7.76,0.98);





draw (9.54,9.82) node {$M$};

draw (6.8,7.3) node {$U_i$};

draw (8.8,7.3) node {$U_j$};

draw (6.24,4.34) node {$psi_i$};

draw (9.52,4.2) node {$psi_j$};

draw (8.94,-1.3) node {$mathbf{R}^n$};

draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};



end{tikzpicture}

end{document}


It produces:
enter image description here



How can I shade this figure?






tikz-pgf tikz-3dplot







share|improve this question





























    3















    I would like to draw the following figure:
    enter image description here



    To do this I have used the following codes : 



    documentclass[10pt]{article}
    
usepackage{pgf,tikz}
    
usetikzlibrary{arrows}
    
pagestyle{empty}
    
begin{document}
    

    
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
    
draw [rotate around={15.05:(6.07,0.75)}] (6.07,0.75) ellipse (1.11cm and 0.56cm);
    
draw [rotate around={-13.74:(8.9,0.78)}] (8.9,0.78) ellipse (1.07cm and 0.53cm);
    
draw  (4.58,2.02)-- (11,2);
    
draw  (11,2)-- (10.48,-1);
    
draw  (10.48,-1)-- (4,-1);
    
draw  (4,-1)-- (4.58,2.02);
    
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
    
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
    
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
    
draw [rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
    
draw [rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
    
draw [->] (8.96,6.46) -- (8.8,1.62);
    
draw [->] (6.7,6.38) -- (6.46,1.62);
    
draw [->] (7.3,0.98) -- (7.76,0.98);
    

    

    
draw (9.54,9.82) node {$M$};
    
draw (6.8,7.3) node {$U_i$};
    
draw (8.8,7.3) node {$U_j$};
    
draw (6.24,4.34) node {$psi_i$};
    
draw (9.52,4.2) node {$psi_j$};
    
draw (8.94,-1.3) node {$mathbf{R}^n$};
    
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
    

    
end{tikzpicture}
    
end{document}


    It produces:
    enter image description here



    How can I shade this figure?






    tikz-pgf tikz-3dplot







    share|improve this question



























      3












      3








      3








      I would like to draw the following figure:
      enter image description here



      To do this I have used the following codes : 



      documentclass[10pt]{article}
      
usepackage{pgf,tikz}
      
usetikzlibrary{arrows}
      
pagestyle{empty}
      
begin{document}
      

      
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
      
draw [rotate around={15.05:(6.07,0.75)}] (6.07,0.75) ellipse (1.11cm and 0.56cm);
      
draw [rotate around={-13.74:(8.9,0.78)}] (8.9,0.78) ellipse (1.07cm and 0.53cm);
      
draw  (4.58,2.02)-- (11,2);
      
draw  (11,2)-- (10.48,-1);
      
draw  (10.48,-1)-- (4,-1);
      
draw  (4,-1)-- (4.58,2.02);
      
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
      
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
      
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
      
draw [rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
      
draw [rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
      
draw [->] (8.96,6.46) -- (8.8,1.62);
      
draw [->] (6.7,6.38) -- (6.46,1.62);
      
draw [->] (7.3,0.98) -- (7.76,0.98);
      

      

      
draw (9.54,9.82) node {$M$};
      
draw (6.8,7.3) node {$U_i$};
      
draw (8.8,7.3) node {$U_j$};
      
draw (6.24,4.34) node {$psi_i$};
      
draw (9.52,4.2) node {$psi_j$};
      
draw (8.94,-1.3) node {$mathbf{R}^n$};
      
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
      

      
end{tikzpicture}
      
end{document}


      It produces:
      enter image description here



      How can I shade this figure?






      tikz-pgf tikz-3dplot







      share|improve this question
















      I would like to draw the following figure:
      enter image description here



      To do this I have used the following codes : 



      documentclass[10pt]{article}
      
usepackage{pgf,tikz}
      
usetikzlibrary{arrows}
      
pagestyle{empty}
      
begin{document}
      

      
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
      
draw [rotate around={15.05:(6.07,0.75)}] (6.07,0.75) ellipse (1.11cm and 0.56cm);
      
draw [rotate around={-13.74:(8.9,0.78)}] (8.9,0.78) ellipse (1.07cm and 0.53cm);
      
draw  (4.58,2.02)-- (11,2);
      
draw  (11,2)-- (10.48,-1);
      
draw  (10.48,-1)-- (4,-1);
      
draw  (4,-1)-- (4.58,2.02);
      
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
      
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
      
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
      
draw [rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
      
draw [rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
      
draw [->] (8.96,6.46) -- (8.8,1.62);
      
draw [->] (6.7,6.38) -- (6.46,1.62);
      
draw [->] (7.3,0.98) -- (7.76,0.98);
      

      

      
draw (9.54,9.82) node {$M$};
      
draw (6.8,7.3) node {$U_i$};
      
draw (8.8,7.3) node {$U_j$};
      
draw (6.24,4.34) node {$psi_i$};
      
draw (9.52,4.2) node {$psi_j$};
      
draw (8.94,-1.3) node {$mathbf{R}^n$};
      
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
      

      
end{tikzpicture}
      
end{document}


      It produces:
      enter image description here



      How can I shade this figure?






      tikz-pgf tikz-3dplot




      tikz-pgf tikz-3dplot






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 3 hours ago







      MKS

















      asked 3 hours ago









      MKSMKS

      834




      834






















          1 Answer
          1






          active

          oldest

          votes


















          4














          There are two basic tricks that allow you to fill the area bounded by two different curves/contours:




          1. clip against one curve and fill the other;

          2. use even odd rule.


          And there are combinations of the two and other possibilities. This answer focuses on possibility 1. Then there is the question how on could recycle curves for the fill. Out of several possibilities, this answer will utilize the use path trick in the first part and insert path in the second path.



          The first path modifies your code such as to shade the correct (?) areas.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows}
          
makeatletter % https://tex.stackexchange.com/a/38995/121799
          
tikzset{
          
  use path/.code={pgfsyssoftpath@setcurrentpath{#1}}
          
}
          
makeatother
          

          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
          
draw [rotate around={15.05:(6.07,0.75)},save path=pathA] (6.07,0.75) ellipse (1.11cm and 0.56cm);
          
draw [rotate around={-13.74:(8.9,0.78)},save path=pathB] (8.9,0.78) ellipse (1.07cm and 0.53cm);
          
draw  (4.58,2.02)-- (11,2);
          
draw  (11,2)-- (10.48,-1);
          
draw  (10.48,-1)-- (4,-1);
          
draw  (4,-1)-- (4.58,2.02);
          
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
          
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
          
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
          
draw [save path=pathC,rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
          
draw [save path=pathD,rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
          
draw [->] (8.96,6.46) -- (8.8,1.62);
          
draw [->] (6.7,6.38) -- (6.46,1.62);
          
draw [->] (7.3,0.98) -- (7.76,0.98);
          

          

          
draw (9.54,9.82) node {$M$};
          
draw (6.8,7.3) node {$U_i$};
          
draw (8.8,7.3) node {$U_j$};
          
draw (6.24,4.34) node {$psi_i$};
          
draw (9.52,4.2) node {$psi_j$};
          
draw (8.94,-1.3) node {$mathbf{R}^n$};
          
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
          
begin{scope}
          
clip[use path=pathA];
          
path[fill=blue,shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)})
          
-- ++ (1,0) |- cycle;
          
end{scope}
          
begin{scope}
          
clip[use path=pathB];
          
path[fill=blue,shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)})
          
-- ++ (-1,0) |- cycle;
          
end{scope}
          
clip[use path=pathC];
          
fill[blue,use path=pathD];
          
end{tikzpicture}
          
end{document}


          enter image description here



          However, I am wondering if you are willing to consider an arguably simpler code yielding a similar picture. Advantages include more relative positioning such that you can move complete parts around without having to redo all coordinates.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows,patterns}
          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle
          
45,x=1.0cm,y=1.0cm,standard ellipse around/.style args={#1 rotated by #2}{%
          
insert path={[rotate around={#2:#1}] #1 circle[x radius=1.2cm,y radius=0.6cm]}}]
          
  begin{scope}[yshift=6.5cm]
          
    draw (0,0) circle[x radius=3.5cm,y radius=1.9cm];
          
    node at (2,2.3) {$M$};
          
    draw (-0.7,-0.2) node[left] (Ui) {$U_i$}
          
     [standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
    draw (0.7,-0.2) node[right] (Uj) {$U_i$}
          
     [standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    clip[standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    path[pattern=north east lines, 
          
     standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
  end{scope}
          
  begin{scope}[local bounding box=b]
          
    begin{scope}[xshift=-4mm,local bounding box=bl]
          
      draw[clip,standard ellipse around={(-1.2,0) rotated by 15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by -15}];
          
    end{scope}
          
    begin{scope}[xshift=4mm,local bounding box=br]
          
      draw[clip,standard ellipse around={(1.2,0) rotated by -15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by 15}];
          
    end{scope}
          
    draw [->] (bl) -- (br) node[midway,below=8mm]{$psi_jcirc psi_i^{-1}$};
          
  end{scope}
          
  draw[->] ([yshift=-0.5cm]Ui.south) -- ([yshift=2mm]bl.north-|Ui.south)
          
   node[midway,left]{$psi_i$};
          
  draw[->] ([yshift=-0.5cm]Uj.south) -- ([yshift=2mm]br.north-|Uj.south)
          
   node[midway,right]{$psi_j$};
          
  draw ([xshift=-1.5cm,yshift=-1cm]b.south west)
          
   -- ([xshift=-1cm,yshift=1cm]b.north west)
          
   -- ([xshift=1.5cm,yshift=1cm]b.north east)
          
   -- ([xshift=1cm,yshift=-1cm]b.south east) -- cycle;
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer


























          • Thank you very much for your answer@marmot

            – MKS
            36 mins ago













          • @MKS You're welcome!

            – marmot
            33 mins ago












          Your Answer








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          1 Answer
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          active

          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          4














          There are two basic tricks that allow you to fill the area bounded by two different curves/contours:




          1. clip against one curve and fill the other;

          2. use even odd rule.


          And there are combinations of the two and other possibilities. This answer focuses on possibility 1. Then there is the question how on could recycle curves for the fill. Out of several possibilities, this answer will utilize the use path trick in the first part and insert path in the second path.



          The first path modifies your code such as to shade the correct (?) areas.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows}
          
makeatletter % https://tex.stackexchange.com/a/38995/121799
          
tikzset{
          
  use path/.code={pgfsyssoftpath@setcurrentpath{#1}}
          
}
          
makeatother
          

          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
          
draw [rotate around={15.05:(6.07,0.75)},save path=pathA] (6.07,0.75) ellipse (1.11cm and 0.56cm);
          
draw [rotate around={-13.74:(8.9,0.78)},save path=pathB] (8.9,0.78) ellipse (1.07cm and 0.53cm);
          
draw  (4.58,2.02)-- (11,2);
          
draw  (11,2)-- (10.48,-1);
          
draw  (10.48,-1)-- (4,-1);
          
draw  (4,-1)-- (4.58,2.02);
          
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
          
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
          
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
          
draw [save path=pathC,rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
          
draw [save path=pathD,rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
          
draw [->] (8.96,6.46) -- (8.8,1.62);
          
draw [->] (6.7,6.38) -- (6.46,1.62);
          
draw [->] (7.3,0.98) -- (7.76,0.98);
          

          

          
draw (9.54,9.82) node {$M$};
          
draw (6.8,7.3) node {$U_i$};
          
draw (8.8,7.3) node {$U_j$};
          
draw (6.24,4.34) node {$psi_i$};
          
draw (9.52,4.2) node {$psi_j$};
          
draw (8.94,-1.3) node {$mathbf{R}^n$};
          
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
          
begin{scope}
          
clip[use path=pathA];
          
path[fill=blue,shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)})
          
-- ++ (1,0) |- cycle;
          
end{scope}
          
begin{scope}
          
clip[use path=pathB];
          
path[fill=blue,shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)})
          
-- ++ (-1,0) |- cycle;
          
end{scope}
          
clip[use path=pathC];
          
fill[blue,use path=pathD];
          
end{tikzpicture}
          
end{document}


          enter image description here



          However, I am wondering if you are willing to consider an arguably simpler code yielding a similar picture. Advantages include more relative positioning such that you can move complete parts around without having to redo all coordinates.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows,patterns}
          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle
          
45,x=1.0cm,y=1.0cm,standard ellipse around/.style args={#1 rotated by #2}{%
          
insert path={[rotate around={#2:#1}] #1 circle[x radius=1.2cm,y radius=0.6cm]}}]
          
  begin{scope}[yshift=6.5cm]
          
    draw (0,0) circle[x radius=3.5cm,y radius=1.9cm];
          
    node at (2,2.3) {$M$};
          
    draw (-0.7,-0.2) node[left] (Ui) {$U_i$}
          
     [standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
    draw (0.7,-0.2) node[right] (Uj) {$U_i$}
          
     [standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    clip[standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    path[pattern=north east lines, 
          
     standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
  end{scope}
          
  begin{scope}[local bounding box=b]
          
    begin{scope}[xshift=-4mm,local bounding box=bl]
          
      draw[clip,standard ellipse around={(-1.2,0) rotated by 15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by -15}];
          
    end{scope}
          
    begin{scope}[xshift=4mm,local bounding box=br]
          
      draw[clip,standard ellipse around={(1.2,0) rotated by -15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by 15}];
          
    end{scope}
          
    draw [->] (bl) -- (br) node[midway,below=8mm]{$psi_jcirc psi_i^{-1}$};
          
  end{scope}
          
  draw[->] ([yshift=-0.5cm]Ui.south) -- ([yshift=2mm]bl.north-|Ui.south)
          
   node[midway,left]{$psi_i$};
          
  draw[->] ([yshift=-0.5cm]Uj.south) -- ([yshift=2mm]br.north-|Uj.south)
          
   node[midway,right]{$psi_j$};
          
  draw ([xshift=-1.5cm,yshift=-1cm]b.south west)
          
   -- ([xshift=-1cm,yshift=1cm]b.north west)
          
   -- ([xshift=1.5cm,yshift=1cm]b.north east)
          
   -- ([xshift=1cm,yshift=-1cm]b.south east) -- cycle;
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer


























          • Thank you very much for your answer@marmot

            – MKS
            36 mins ago













          • @MKS You're welcome!

            – marmot
            33 mins ago
















          4














          There are two basic tricks that allow you to fill the area bounded by two different curves/contours:




          1. clip against one curve and fill the other;

          2. use even odd rule.


          And there are combinations of the two and other possibilities. This answer focuses on possibility 1. Then there is the question how on could recycle curves for the fill. Out of several possibilities, this answer will utilize the use path trick in the first part and insert path in the second path.



          The first path modifies your code such as to shade the correct (?) areas.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows}
          
makeatletter % https://tex.stackexchange.com/a/38995/121799
          
tikzset{
          
  use path/.code={pgfsyssoftpath@setcurrentpath{#1}}
          
}
          
makeatother
          

          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
          
draw [rotate around={15.05:(6.07,0.75)},save path=pathA] (6.07,0.75) ellipse (1.11cm and 0.56cm);
          
draw [rotate around={-13.74:(8.9,0.78)},save path=pathB] (8.9,0.78) ellipse (1.07cm and 0.53cm);
          
draw  (4.58,2.02)-- (11,2);
          
draw  (11,2)-- (10.48,-1);
          
draw  (10.48,-1)-- (4,-1);
          
draw  (4,-1)-- (4.58,2.02);
          
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
          
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
          
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
          
draw [save path=pathC,rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
          
draw [save path=pathD,rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
          
draw [->] (8.96,6.46) -- (8.8,1.62);
          
draw [->] (6.7,6.38) -- (6.46,1.62);
          
draw [->] (7.3,0.98) -- (7.76,0.98);
          

          

          
draw (9.54,9.82) node {$M$};
          
draw (6.8,7.3) node {$U_i$};
          
draw (8.8,7.3) node {$U_j$};
          
draw (6.24,4.34) node {$psi_i$};
          
draw (9.52,4.2) node {$psi_j$};
          
draw (8.94,-1.3) node {$mathbf{R}^n$};
          
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
          
begin{scope}
          
clip[use path=pathA];
          
path[fill=blue,shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)})
          
-- ++ (1,0) |- cycle;
          
end{scope}
          
begin{scope}
          
clip[use path=pathB];
          
path[fill=blue,shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)})
          
-- ++ (-1,0) |- cycle;
          
end{scope}
          
clip[use path=pathC];
          
fill[blue,use path=pathD];
          
end{tikzpicture}
          
end{document}


          enter image description here



          However, I am wondering if you are willing to consider an arguably simpler code yielding a similar picture. Advantages include more relative positioning such that you can move complete parts around without having to redo all coordinates.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows,patterns}
          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle
          
45,x=1.0cm,y=1.0cm,standard ellipse around/.style args={#1 rotated by #2}{%
          
insert path={[rotate around={#2:#1}] #1 circle[x radius=1.2cm,y radius=0.6cm]}}]
          
  begin{scope}[yshift=6.5cm]
          
    draw (0,0) circle[x radius=3.5cm,y radius=1.9cm];
          
    node at (2,2.3) {$M$};
          
    draw (-0.7,-0.2) node[left] (Ui) {$U_i$}
          
     [standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
    draw (0.7,-0.2) node[right] (Uj) {$U_i$}
          
     [standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    clip[standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    path[pattern=north east lines, 
          
     standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
  end{scope}
          
  begin{scope}[local bounding box=b]
          
    begin{scope}[xshift=-4mm,local bounding box=bl]
          
      draw[clip,standard ellipse around={(-1.2,0) rotated by 15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by -15}];
          
    end{scope}
          
    begin{scope}[xshift=4mm,local bounding box=br]
          
      draw[clip,standard ellipse around={(1.2,0) rotated by -15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by 15}];
          
    end{scope}
          
    draw [->] (bl) -- (br) node[midway,below=8mm]{$psi_jcirc psi_i^{-1}$};
          
  end{scope}
          
  draw[->] ([yshift=-0.5cm]Ui.south) -- ([yshift=2mm]bl.north-|Ui.south)
          
   node[midway,left]{$psi_i$};
          
  draw[->] ([yshift=-0.5cm]Uj.south) -- ([yshift=2mm]br.north-|Uj.south)
          
   node[midway,right]{$psi_j$};
          
  draw ([xshift=-1.5cm,yshift=-1cm]b.south west)
          
   -- ([xshift=-1cm,yshift=1cm]b.north west)
          
   -- ([xshift=1.5cm,yshift=1cm]b.north east)
          
   -- ([xshift=1cm,yshift=-1cm]b.south east) -- cycle;
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer


























          • Thank you very much for your answer@marmot

            – MKS
            36 mins ago













          • @MKS You're welcome!

            – marmot
            33 mins ago














          4












          4








          4







          There are two basic tricks that allow you to fill the area bounded by two different curves/contours:




          1. clip against one curve and fill the other;

          2. use even odd rule.


          And there are combinations of the two and other possibilities. This answer focuses on possibility 1. Then there is the question how on could recycle curves for the fill. Out of several possibilities, this answer will utilize the use path trick in the first part and insert path in the second path.



          The first path modifies your code such as to shade the correct (?) areas.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows}
          
makeatletter % https://tex.stackexchange.com/a/38995/121799
          
tikzset{
          
  use path/.code={pgfsyssoftpath@setcurrentpath{#1}}
          
}
          
makeatother
          

          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
          
draw [rotate around={15.05:(6.07,0.75)},save path=pathA] (6.07,0.75) ellipse (1.11cm and 0.56cm);
          
draw [rotate around={-13.74:(8.9,0.78)},save path=pathB] (8.9,0.78) ellipse (1.07cm and 0.53cm);
          
draw  (4.58,2.02)-- (11,2);
          
draw  (11,2)-- (10.48,-1);
          
draw  (10.48,-1)-- (4,-1);
          
draw  (4,-1)-- (4.58,2.02);
          
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
          
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
          
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
          
draw [save path=pathC,rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
          
draw [save path=pathD,rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
          
draw [->] (8.96,6.46) -- (8.8,1.62);
          
draw [->] (6.7,6.38) -- (6.46,1.62);
          
draw [->] (7.3,0.98) -- (7.76,0.98);
          

          

          
draw (9.54,9.82) node {$M$};
          
draw (6.8,7.3) node {$U_i$};
          
draw (8.8,7.3) node {$U_j$};
          
draw (6.24,4.34) node {$psi_i$};
          
draw (9.52,4.2) node {$psi_j$};
          
draw (8.94,-1.3) node {$mathbf{R}^n$};
          
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
          
begin{scope}
          
clip[use path=pathA];
          
path[fill=blue,shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)})
          
-- ++ (1,0) |- cycle;
          
end{scope}
          
begin{scope}
          
clip[use path=pathB];
          
path[fill=blue,shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)})
          
-- ++ (-1,0) |- cycle;
          
end{scope}
          
clip[use path=pathC];
          
fill[blue,use path=pathD];
          
end{tikzpicture}
          
end{document}


          enter image description here



          However, I am wondering if you are willing to consider an arguably simpler code yielding a similar picture. Advantages include more relative positioning such that you can move complete parts around without having to redo all coordinates.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows,patterns}
          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle
          
45,x=1.0cm,y=1.0cm,standard ellipse around/.style args={#1 rotated by #2}{%
          
insert path={[rotate around={#2:#1}] #1 circle[x radius=1.2cm,y radius=0.6cm]}}]
          
  begin{scope}[yshift=6.5cm]
          
    draw (0,0) circle[x radius=3.5cm,y radius=1.9cm];
          
    node at (2,2.3) {$M$};
          
    draw (-0.7,-0.2) node[left] (Ui) {$U_i$}
          
     [standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
    draw (0.7,-0.2) node[right] (Uj) {$U_i$}
          
     [standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    clip[standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    path[pattern=north east lines, 
          
     standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
  end{scope}
          
  begin{scope}[local bounding box=b]
          
    begin{scope}[xshift=-4mm,local bounding box=bl]
          
      draw[clip,standard ellipse around={(-1.2,0) rotated by 15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by -15}];
          
    end{scope}
          
    begin{scope}[xshift=4mm,local bounding box=br]
          
      draw[clip,standard ellipse around={(1.2,0) rotated by -15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by 15}];
          
    end{scope}
          
    draw [->] (bl) -- (br) node[midway,below=8mm]{$psi_jcirc psi_i^{-1}$};
          
  end{scope}
          
  draw[->] ([yshift=-0.5cm]Ui.south) -- ([yshift=2mm]bl.north-|Ui.south)
          
   node[midway,left]{$psi_i$};
          
  draw[->] ([yshift=-0.5cm]Uj.south) -- ([yshift=2mm]br.north-|Uj.south)
          
   node[midway,right]{$psi_j$};
          
  draw ([xshift=-1.5cm,yshift=-1cm]b.south west)
          
   -- ([xshift=-1cm,yshift=1cm]b.north west)
          
   -- ([xshift=1.5cm,yshift=1cm]b.north east)
          
   -- ([xshift=1cm,yshift=-1cm]b.south east) -- cycle;
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer















          There are two basic tricks that allow you to fill the area bounded by two different curves/contours:




          1. clip against one curve and fill the other;

          2. use even odd rule.


          And there are combinations of the two and other possibilities. This answer focuses on possibility 1. Then there is the question how on could recycle curves for the fill. Out of several possibilities, this answer will utilize the use path trick in the first part and insert path in the second path.



          The first path modifies your code such as to shade the correct (?) areas.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows}
          
makeatletter % https://tex.stackexchange.com/a/38995/121799
          
tikzset{
          
  use path/.code={pgfsyssoftpath@setcurrentpath{#1}}
          
}
          
makeatother
          

          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
          
draw [rotate around={15.05:(6.07,0.75)},save path=pathA] (6.07,0.75) ellipse (1.11cm and 0.56cm);
          
draw [rotate around={-13.74:(8.9,0.78)},save path=pathB] (8.9,0.78) ellipse (1.07cm and 0.53cm);
          
draw  (4.58,2.02)-- (11,2);
          
draw  (11,2)-- (10.48,-1);
          
draw  (10.48,-1)-- (4,-1);
          
draw  (4,-1)-- (4.58,2.02);
          
draw [shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)});
          
draw [shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)});
          
draw [rotate around={-3.74:(8.09,7.47)}] (8.09,7.47) ellipse (3.48cm and 1.89cm);
          
draw [save path=pathC,rotate around={13.37:(7.03,7.4)}] (7.03,7.4) ellipse (1.2cm and 0.59cm);
          
draw [save path=pathD,rotate around={-18.43:(8.48,7.38)}] (8.48,7.38) ellipse (1.23cm and 0.59cm);
          
draw [->] (8.96,6.46) -- (8.8,1.62);
          
draw [->] (6.7,6.38) -- (6.46,1.62);
          
draw [->] (7.3,0.98) -- (7.76,0.98);
          

          

          
draw (9.54,9.82) node {$M$};
          
draw (6.8,7.3) node {$U_i$};
          
draw (8.8,7.3) node {$U_j$};
          
draw (6.24,4.34) node {$psi_i$};
          
draw (9.52,4.2) node {$psi_j$};
          
draw (8.94,-1.3) node {$mathbf{R}^n$};
          
draw (7.6,0) node {$psi_jcirc psi_i^{-1}$};
          
begin{scope}
          
clip[use path=pathA];
          
path[fill=blue,shift={(6.76,0.91)}] plot[domain=1.71:4.85,variable=t]({1*0.43*cos(t r)+0*0.43*sin(t r)},{0*0.43*cos(t r)+1*0.43*sin(t r)})
          
-- ++ (1,0) |- cycle;
          
end{scope}
          
begin{scope}
          
clip[use path=pathB];
          
path[fill=blue,shift={(8.25,0.9)}] plot[domain=-1.6:1.54,variable=t]({1*0.42*cos(t r)+0*0.42*sin(t r)},{0*0.42*cos(t r)+1*0.42*sin(t r)})
          
-- ++ (-1,0) |- cycle;
          
end{scope}
          
clip[use path=pathC];
          
fill[blue,use path=pathD];
          
end{tikzpicture}
          
end{document}


          enter image description here



          However, I am wondering if you are willing to consider an arguably simpler code yielding a similar picture. Advantages include more relative positioning such that you can move complete parts around without having to redo all coordinates.



          documentclass[10pt]{article}
          
usepackage{tikz}
          
usetikzlibrary{arrows,patterns}
          
pagestyle{empty}
          
begin{document}
          

          
begin{tikzpicture}[line cap=round,line join=round,>=triangle
          
45,x=1.0cm,y=1.0cm,standard ellipse around/.style args={#1 rotated by #2}{%
          
insert path={[rotate around={#2:#1}] #1 circle[x radius=1.2cm,y radius=0.6cm]}}]
          
  begin{scope}[yshift=6.5cm]
          
    draw (0,0) circle[x radius=3.5cm,y radius=1.9cm];
          
    node at (2,2.3) {$M$};
          
    draw (-0.7,-0.2) node[left] (Ui) {$U_i$}
          
     [standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
    draw (0.7,-0.2) node[right] (Uj) {$U_i$}
          
     [standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    clip[standard ellipse around={(0.7,-0.2) rotated by -15}];
          
    path[pattern=north east lines, 
          
     standard ellipse around={(-0.7,-0.2) rotated by 15}];
          
  end{scope}
          
  begin{scope}[local bounding box=b]
          
    begin{scope}[xshift=-4mm,local bounding box=bl]
          
      draw[clip,standard ellipse around={(-1.2,0) rotated by 15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by -15}];
          
    end{scope}
          
    begin{scope}[xshift=4mm,local bounding box=br]
          
      draw[clip,standard ellipse around={(1.2,0) rotated by -15}];
          
      draw[pattern=north east lines,standard ellipse around={(0,0) rotated by 15}];
          
    end{scope}
          
    draw [->] (bl) -- (br) node[midway,below=8mm]{$psi_jcirc psi_i^{-1}$};
          
  end{scope}
          
  draw[->] ([yshift=-0.5cm]Ui.south) -- ([yshift=2mm]bl.north-|Ui.south)
          
   node[midway,left]{$psi_i$};
          
  draw[->] ([yshift=-0.5cm]Uj.south) -- ([yshift=2mm]br.north-|Uj.south)
          
   node[midway,right]{$psi_j$};
          
  draw ([xshift=-1.5cm,yshift=-1cm]b.south west)
          
   -- ([xshift=-1cm,yshift=1cm]b.north west)
          
   -- ([xshift=1.5cm,yshift=1cm]b.north east)
          
   -- ([xshift=1cm,yshift=-1cm]b.south east) -- cycle;
          
end{tikzpicture}
          
end{document}


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 1 hour ago

























          answered 2 hours ago









          marmotmarmot

          116k5147277




          116k5147277













          • Thank you very much for your answer@marmot

            – MKS
            36 mins ago













          • @MKS You're welcome!

            – marmot
            33 mins ago



















          • Thank you very much for your answer@marmot

            – MKS
            36 mins ago













          • @MKS You're welcome!

            – marmot
            33 mins ago

















          Thank you very much for your answer@marmot

          – MKS
          36 mins ago







          Thank you very much for your answer@marmot

          – MKS
          36 mins ago















          @MKS You're welcome!

          – marmot
          33 mins ago





          @MKS You're welcome!

          – marmot
          33 mins ago


















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