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Filling an area between two curves



The 2019 Stack Overflow Developer Survey Results Are In
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar Manara
Do we need more moderators?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










8















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



To do this I have used the following codes :



documentclass[10pt]article
usepackagepgf,tikz
usetikzlibraryarrows
pagestyleempty
begindocument

begintikzpicture[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 $mathbfR^n$;
draw (7.6,0) node $psi_jcirc psi_i^-1$;

endtikzpicture
enddocument


It produces:
enter image description here



How can I shade this figure?










share|improve this question




























    8















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



    To do this I have used the following codes :



    documentclass[10pt]article
    usepackagepgf,tikz
    usetikzlibraryarrows
    pagestyleempty
    begindocument

    begintikzpicture[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 $mathbfR^n$;
    draw (7.6,0) node $psi_jcirc psi_i^-1$;

    endtikzpicture
    enddocument


    It produces:
    enter image description here



    How can I shade this figure?










    share|improve this question


























      8












      8








      8








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



      To do this I have used the following codes :



      documentclass[10pt]article
      usepackagepgf,tikz
      usetikzlibraryarrows
      pagestyleempty
      begindocument

      begintikzpicture[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 $mathbfR^n$;
      draw (7.6,0) node $psi_jcirc psi_i^-1$;

      endtikzpicture
      enddocument


      It produces:
      enter image description here



      How can I shade this figure?










      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
      usepackagepgf,tikz
      usetikzlibraryarrows
      pagestyleempty
      begindocument

      begintikzpicture[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 $mathbfR^n$;
      draw (7.6,0) node $psi_jcirc psi_i^-1$;

      endtikzpicture
      enddocument


      It produces:
      enter image description here



      How can I shade this figure?







      tikz-pgf tikz-3dplot






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Apr 9 at 2:31







      MKS

















      asked Apr 9 at 2:16









      MKSMKS

      1084




      1084




















          1 Answer
          1






          active

          oldest

          votes


















          14














          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
          usepackagetikz
          usetikzlibraryarrows
          makeatletter % https://tex.stackexchange.com/a/38995/121799
          tikzset
          use path/.code=pgfsyssoftpath@setcurrentpath#1

          makeatother

          pagestyleempty
          begindocument

          begintikzpicture[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 $mathbfR^n$;
          draw (7.6,0) node $psi_jcirc psi_i^-1$;
          beginscope
          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;
          endscope
          beginscope
          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;
          endscope
          clip[use path=pathC];
          fill[blue,use path=pathD];
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows,patterns
          pagestyleempty
          begindocument

          begintikzpicture[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]]
          beginscope[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];
          endscope
          beginscope[local bounding box=b]
          beginscope[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];
          endscope
          beginscope[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];
          endscope
          draw [->] (bl) -- (br) node[midway,below=8mm]$psi_jcirc psi_i^-1$;
          endscope
          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;
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer

























          • Thank you very much for your answer@marmot

            – MKS
            Apr 9 at 5:09












          • @MKS You're welcome!

            – marmot
            Apr 9 at 5:11











          • You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

            – Kpym
            Apr 9 at 13:52











          Your Answer








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          1 Answer
          1






          active

          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          14














          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
          usepackagetikz
          usetikzlibraryarrows
          makeatletter % https://tex.stackexchange.com/a/38995/121799
          tikzset
          use path/.code=pgfsyssoftpath@setcurrentpath#1

          makeatother

          pagestyleempty
          begindocument

          begintikzpicture[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 $mathbfR^n$;
          draw (7.6,0) node $psi_jcirc psi_i^-1$;
          beginscope
          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;
          endscope
          beginscope
          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;
          endscope
          clip[use path=pathC];
          fill[blue,use path=pathD];
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows,patterns
          pagestyleempty
          begindocument

          begintikzpicture[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]]
          beginscope[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];
          endscope
          beginscope[local bounding box=b]
          beginscope[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];
          endscope
          beginscope[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];
          endscope
          draw [->] (bl) -- (br) node[midway,below=8mm]$psi_jcirc psi_i^-1$;
          endscope
          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;
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer

























          • Thank you very much for your answer@marmot

            – MKS
            Apr 9 at 5:09












          • @MKS You're welcome!

            – marmot
            Apr 9 at 5:11











          • You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

            – Kpym
            Apr 9 at 13:52















          14














          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
          usepackagetikz
          usetikzlibraryarrows
          makeatletter % https://tex.stackexchange.com/a/38995/121799
          tikzset
          use path/.code=pgfsyssoftpath@setcurrentpath#1

          makeatother

          pagestyleempty
          begindocument

          begintikzpicture[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 $mathbfR^n$;
          draw (7.6,0) node $psi_jcirc psi_i^-1$;
          beginscope
          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;
          endscope
          beginscope
          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;
          endscope
          clip[use path=pathC];
          fill[blue,use path=pathD];
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows,patterns
          pagestyleempty
          begindocument

          begintikzpicture[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]]
          beginscope[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];
          endscope
          beginscope[local bounding box=b]
          beginscope[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];
          endscope
          beginscope[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];
          endscope
          draw [->] (bl) -- (br) node[midway,below=8mm]$psi_jcirc psi_i^-1$;
          endscope
          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;
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer

























          • Thank you very much for your answer@marmot

            – MKS
            Apr 9 at 5:09












          • @MKS You're welcome!

            – marmot
            Apr 9 at 5:11











          • You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

            – Kpym
            Apr 9 at 13:52













          14












          14








          14







          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
          usepackagetikz
          usetikzlibraryarrows
          makeatletter % https://tex.stackexchange.com/a/38995/121799
          tikzset
          use path/.code=pgfsyssoftpath@setcurrentpath#1

          makeatother

          pagestyleempty
          begindocument

          begintikzpicture[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 $mathbfR^n$;
          draw (7.6,0) node $psi_jcirc psi_i^-1$;
          beginscope
          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;
          endscope
          beginscope
          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;
          endscope
          clip[use path=pathC];
          fill[blue,use path=pathD];
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows,patterns
          pagestyleempty
          begindocument

          begintikzpicture[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]]
          beginscope[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];
          endscope
          beginscope[local bounding box=b]
          beginscope[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];
          endscope
          beginscope[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];
          endscope
          draw [->] (bl) -- (br) node[midway,below=8mm]$psi_jcirc psi_i^-1$;
          endscope
          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;
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows
          makeatletter % https://tex.stackexchange.com/a/38995/121799
          tikzset
          use path/.code=pgfsyssoftpath@setcurrentpath#1

          makeatother

          pagestyleempty
          begindocument

          begintikzpicture[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 $mathbfR^n$;
          draw (7.6,0) node $psi_jcirc psi_i^-1$;
          beginscope
          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;
          endscope
          beginscope
          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;
          endscope
          clip[use path=pathC];
          fill[blue,use path=pathD];
          endtikzpicture
          enddocument


          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
          usepackagetikz
          usetikzlibraryarrows,patterns
          pagestyleempty
          begindocument

          begintikzpicture[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]]
          beginscope[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];
          endscope
          beginscope[local bounding box=b]
          beginscope[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];
          endscope
          beginscope[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];
          endscope
          draw [->] (bl) -- (br) node[midway,below=8mm]$psi_jcirc psi_i^-1$;
          endscope
          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;
          endtikzpicture
          enddocument


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Apr 9 at 4:35

























          answered Apr 9 at 3:13









          marmotmarmot

          117k5150283




          117k5150283












          • Thank you very much for your answer@marmot

            – MKS
            Apr 9 at 5:09












          • @MKS You're welcome!

            – marmot
            Apr 9 at 5:11











          • You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

            – Kpym
            Apr 9 at 13:52

















          • Thank you very much for your answer@marmot

            – MKS
            Apr 9 at 5:09












          • @MKS You're welcome!

            – marmot
            Apr 9 at 5:11











          • You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

            – Kpym
            Apr 9 at 13:52
















          Thank you very much for your answer@marmot

          – MKS
          Apr 9 at 5:09






          Thank you very much for your answer@marmot

          – MKS
          Apr 9 at 5:09














          @MKS You're welcome!

          – marmot
          Apr 9 at 5:11





          @MKS You're welcome!

          – marmot
          Apr 9 at 5:11













          You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

          – Kpym
          Apr 9 at 13:52





          You can use pgfsetpath instead of the low level pgfsyssoftpath@setcurrentpath (as they are identical) and avoid makeatletter ... makeatother.

          – Kpym
          Apr 9 at 13:52

















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