Drawing a perspective ellipse with TikZ











up vote
4
down vote

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I made the following ellipse in Inkscape



enter image description here



But I would like to draw it within TikZ environment.My final goal is to put this ellipse inside a coordinate system. Using the image from Inkscape, here is my try



documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,shapes.geometric,shadows.blur}

usepackage{graphicx}

% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799

makeatletter

tikzoption{canvas is xy plane at z}{%

    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%

    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%

    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%

    tikz@canvas@is@plane}

makeatother

begin{document}

tdplotsetmaincoords{60}{130}

begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]

    coordinate (O) at (0,0,0);

    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};

    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};

    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};

    draw[dashed] (O) -- (-1.2,0,0);



    pgfmathsetmacro{rvec}{1.5}

    pgfmathsetmacro{thetavec}{40}

    pgfmathsetmacro{phivec}{60}

    tdplotsetcoord{P}{rvec}{thetavec}{phivec}

   node[anchor=south west,color=red] at (P) {$B$};

   draw[-stealth,color=red,very thick] (O) -- (P);



   begin{scope}[canvas is yz plane at x=0]

   node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image.eps}}; 

   end{scope}  

end{tikzpicture}

end{document}


enter image description here



Using Tikz my best attempt was 



 documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,shapes.geometric,shadows.blur}

usepackage{graphicx}

% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799

makeatletter

tikzoption{canvas is xy plane at z}{%

    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%

    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%

    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%

    tikz@canvas@is@plane}

makeatother

begin{document}

tdplotsetmaincoords{60}{130}

begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]

    coordinate (O) at (0,0,0);

    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};

    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};

    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};

    draw[dashed] (O) -- (-1.2,0,0);



    pgfmathsetmacro{rvec}{1.5}

    pgfmathsetmacro{thetavec}{40}

    pgfmathsetmacro{phivec}{60}

    tdplotsetcoord{P}{rvec}{thetavec}{phivec}

   node[anchor=south west,color=red] at (P) {};

   draw[-stealth,color=red,very thick] (O) -- (P);



   begin{scope}[canvas is xz plane at y=0]

   node[ellipse,fill=gray,fill opacity=0.3,draw,minimum width=2cm,minimum height=1cm,rotate=90] (elliL) at (0,0) {};

   end{scope}  

end{tikzpicture}

end{document}


enter image description here






tikz-pgf







share|improve this question


























    up vote
    4
    down vote

    favorite












    I made the following ellipse in Inkscape



    enter image description here



    But I would like to draw it within TikZ environment.My final goal is to put this ellipse inside a coordinate system. Using the image from Inkscape, here is my try



    documentclass[tikz,border=3.14mm]{standalone}
    
usepackage{tikz-3dplot}
    
usetikzlibrary{3d,shapes.geometric,shadows.blur}
    
usepackage{graphicx}
    
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
    
makeatletter
    
tikzoption{canvas is xy plane at z}{%
    
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
    
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
    
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
    
    tikz@canvas@is@plane}
    
makeatother
    
begin{document}
    
tdplotsetmaincoords{60}{130}
    
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
    
    coordinate (O) at (0,0,0);
    
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
    
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
    
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
    
    draw[dashed] (O) -- (-1.2,0,0);
    

    
    pgfmathsetmacro{rvec}{1.5}
    
    pgfmathsetmacro{thetavec}{40}
    
    pgfmathsetmacro{phivec}{60}
    
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
    
   node[anchor=south west,color=red] at (P) {$B$};
    
   draw[-stealth,color=red,very thick] (O) -- (P);
    

    
   begin{scope}[canvas is yz plane at x=0]
    
   node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image.eps}}; 
    
   end{scope}  
    
end{tikzpicture}
    
end{document}


    enter image description here



    Using Tikz my best attempt was 



     documentclass[tikz,border=3.14mm]{standalone}
    
usepackage{tikz-3dplot}
    
usetikzlibrary{3d,shapes.geometric,shadows.blur}
    
usepackage{graphicx}
    
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
    
makeatletter
    
tikzoption{canvas is xy plane at z}{%
    
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
    
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
    
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
    
    tikz@canvas@is@plane}
    
makeatother
    
begin{document}
    
tdplotsetmaincoords{60}{130}
    
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
    
    coordinate (O) at (0,0,0);
    
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
    
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
    
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
    
    draw[dashed] (O) -- (-1.2,0,0);
    

    
    pgfmathsetmacro{rvec}{1.5}
    
    pgfmathsetmacro{thetavec}{40}
    
    pgfmathsetmacro{phivec}{60}
    
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
    
   node[anchor=south west,color=red] at (P) {};
    
   draw[-stealth,color=red,very thick] (O) -- (P);
    

    
   begin{scope}[canvas is xz plane at y=0]
    
   node[ellipse,fill=gray,fill opacity=0.3,draw,minimum width=2cm,minimum height=1cm,rotate=90] (elliL) at (0,0) {};
    
   end{scope}  
    
end{tikzpicture}
    
end{document}


    enter image description here






    tikz-pgf







    share|improve this question
























      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite











      I made the following ellipse in Inkscape



      enter image description here



      But I would like to draw it within TikZ environment.My final goal is to put this ellipse inside a coordinate system. Using the image from Inkscape, here is my try



      documentclass[tikz,border=3.14mm]{standalone}
      
usepackage{tikz-3dplot}
      
usetikzlibrary{3d,shapes.geometric,shadows.blur}
      
usepackage{graphicx}
      
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
      
makeatletter
      
tikzoption{canvas is xy plane at z}{%
      
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
      
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
      
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
      
    tikz@canvas@is@plane}
      
makeatother
      
begin{document}
      
tdplotsetmaincoords{60}{130}
      
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
      
    coordinate (O) at (0,0,0);
      
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
      
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
      
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
      
    draw[dashed] (O) -- (-1.2,0,0);
      

      
    pgfmathsetmacro{rvec}{1.5}
      
    pgfmathsetmacro{thetavec}{40}
      
    pgfmathsetmacro{phivec}{60}
      
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
      
   node[anchor=south west,color=red] at (P) {$B$};
      
   draw[-stealth,color=red,very thick] (O) -- (P);
      

      
   begin{scope}[canvas is yz plane at x=0]
      
   node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image.eps}}; 
      
   end{scope}  
      
end{tikzpicture}
      
end{document}


      enter image description here



      Using Tikz my best attempt was 



       documentclass[tikz,border=3.14mm]{standalone}
      
usepackage{tikz-3dplot}
      
usetikzlibrary{3d,shapes.geometric,shadows.blur}
      
usepackage{graphicx}
      
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
      
makeatletter
      
tikzoption{canvas is xy plane at z}{%
      
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
      
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
      
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
      
    tikz@canvas@is@plane}
      
makeatother
      
begin{document}
      
tdplotsetmaincoords{60}{130}
      
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
      
    coordinate (O) at (0,0,0);
      
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
      
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
      
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
      
    draw[dashed] (O) -- (-1.2,0,0);
      

      
    pgfmathsetmacro{rvec}{1.5}
      
    pgfmathsetmacro{thetavec}{40}
      
    pgfmathsetmacro{phivec}{60}
      
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
      
   node[anchor=south west,color=red] at (P) {};
      
   draw[-stealth,color=red,very thick] (O) -- (P);
      

      
   begin{scope}[canvas is xz plane at y=0]
      
   node[ellipse,fill=gray,fill opacity=0.3,draw,minimum width=2cm,minimum height=1cm,rotate=90] (elliL) at (0,0) {};
      
   end{scope}  
      
end{tikzpicture}
      
end{document}


      enter image description here






      tikz-pgf







      share|improve this question













      I made the following ellipse in Inkscape



      enter image description here



      But I would like to draw it within TikZ environment.My final goal is to put this ellipse inside a coordinate system. Using the image from Inkscape, here is my try



      documentclass[tikz,border=3.14mm]{standalone}
      
usepackage{tikz-3dplot}
      
usetikzlibrary{3d,shapes.geometric,shadows.blur}
      
usepackage{graphicx}
      
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
      
makeatletter
      
tikzoption{canvas is xy plane at z}{%
      
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
      
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
      
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
      
    tikz@canvas@is@plane}
      
makeatother
      
begin{document}
      
tdplotsetmaincoords{60}{130}
      
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
      
    coordinate (O) at (0,0,0);
      
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
      
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
      
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
      
    draw[dashed] (O) -- (-1.2,0,0);
      

      
    pgfmathsetmacro{rvec}{1.5}
      
    pgfmathsetmacro{thetavec}{40}
      
    pgfmathsetmacro{phivec}{60}
      
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
      
   node[anchor=south west,color=red] at (P) {$B$};
      
   draw[-stealth,color=red,very thick] (O) -- (P);
      

      
   begin{scope}[canvas is yz plane at x=0]
      
   node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image.eps}}; 
      
   end{scope}  
      
end{tikzpicture}
      
end{document}


      enter image description here



      Using Tikz my best attempt was 



       documentclass[tikz,border=3.14mm]{standalone}
      
usepackage{tikz-3dplot}
      
usetikzlibrary{3d,shapes.geometric,shadows.blur}
      
usepackage{graphicx}
      
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
      
makeatletter
      
tikzoption{canvas is xy plane at z}{%
      
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
      
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
      
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
      
    tikz@canvas@is@plane}
      
makeatother
      
begin{document}
      
tdplotsetmaincoords{60}{130}
      
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
      
    coordinate (O) at (0,0,0);
      
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
      
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
      
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
      
    draw[dashed] (O) -- (-1.2,0,0);
      

      
    pgfmathsetmacro{rvec}{1.5}
      
    pgfmathsetmacro{thetavec}{40}
      
    pgfmathsetmacro{phivec}{60}
      
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
      
   node[anchor=south west,color=red] at (P) {};
      
   draw[-stealth,color=red,very thick] (O) -- (P);
      

      
   begin{scope}[canvas is xz plane at y=0]
      
   node[ellipse,fill=gray,fill opacity=0.3,draw,minimum width=2cm,minimum height=1cm,rotate=90] (elliL) at (0,0) {};
      
   end{scope}  
      
end{tikzpicture}
      
end{document}


      enter image description here






      tikz-pgf




      tikz-pgf






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Dec 12 at 19:21









      Dinesh Shankar

      1725




      1725






















          2 Answers
          2






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          oldest

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          up vote
          7
          down vote













          tikz has ellipse shape, so you can use it with desired x radius and y radius. 



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{3d,shapes.geometric,shadows.blur}
          
usepackage{graphicx}
          
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
          
makeatletter
          
tikzoption{canvas is xy plane at z}{%
          
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
          
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
          
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
          
    tikz@canvas@is@plane}
          
makeatother
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
   begin{scope}%[canvas is yz plane at x=0]
          
%    node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image}}; 
          
    draw [fill=gray!40, gray!40]  (0,0) ellipse [x radius=5pt, y radius=11pt];
          
    draw [gray] (0,0) ellipse [x radius=2pt, y radius=11pt,];
          
    draw [gray] (0,0) ellipse [x radius=5pt, y radius=2pt,];
          
   end{scope}  
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          

          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {$B$};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer





















          • Wol. Very easy! Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:27


















          up vote
          6
          down vote













          This problem is actually less innocent than it might seem. The visible part of the ellipse is not obtained by just drawing an ellipse of the dimensions of the ellipsoid in the screen coordinates or, say, the xy plane. The problem as AFAIK only been used for the sphere, see e.g. the nice macros by Alain Matthes provided for a sphere and, in particular, this great answer by Fritz. Let me start by providing a brute force way to shade the relevant area.



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    pgfmathtruncatemacro{Xstart}{tdplotmainphi-180}
          
    pgfmathtruncatemacro{DeltaX}{10}
          
    pgfmathtruncatemacro{Xnext}{Xstart+DeltaX}
          
    pgfmathtruncatemacro{Xend}{tdplotmainphi+180}
          
    begin{scope}[transparency group,opacity=0.5]
          
    foreach X in {Xstart,Xnext,...,Xend}
          
    {tdplotsetrotatedcoords{0}{0}{X}
          
    begin{scope}[tdplot_rotated_coords]
          
    path[fill=gray!40] plot[variable=x,domain=-90:90,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          A somewhat more analytic variant thereof is



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{intersections,backgrounds}
          
makeatletter
          
%from https://tex.stackexchange.com/a/375604/121799
          
%along x axis
          
define@key{x sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{x sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{x sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
          
    setkeys{x sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along y axis
          
define@key{y sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{y sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{y sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
          
    setkeys{y sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along z axis
          
define@key{z sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{z sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{z sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
          
    setkeys{z sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}
          

          

          
makeatother % https://tex.stackexchange.com/a/438695/121799
          

          
% definitions to make your life easier
          
tikzset{rotate axes about y axis/.code={
          
path (y spherical cs:radius=1,theta=90,phi=0+#1) coordinate(xpp)
          
(y spherical cs:radius=1,theta=00,phi=90+#1) coordinate(ypp) 
          
(y spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},rotate axes about x axis/.code={
          
path (x spherical cs:radius=1,theta=00,phi=90+#1) coordinate(xpp)
          
(x spherical cs:radius=1,theta=90,phi=00+#1) coordinate(ypp) 
          
(x spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},
          
pitch/.style={rotate axes about y axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}},
          
roll/.style={rotate axes about x axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}}
          
}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    tdplotsetrotatedcoords{0}{0}{tdplotmainphi}   
          
    begin{scope}[tdplot_rotated_coords]
          
    begin{scope}[roll=-5]
          
    fill[gray!40,opacity=0.6] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetrotatedcoords{0}{0}{phivec}  
          
    begin{scope}[tdplot_rotated_coords]
          
    path[name path=elli] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
    node[anchor=south west,color=red] at (P) {P};
          
    begin{scope}[on background layer]
          
    draw[-stealth,color=red,very thick,name path global=P] (O) -- (P);
          
    end{scope}
          
    draw[-stealth,color=red,very thick,name intersections={of=P and elli}] 
          
    (intersection-1) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here



          This is an ellipsoid in perspective, see e.g.



          enter image description here



          to note that you view on the ellipsoid from the top, as dictated by the angle theta=60 in tdplotsetmaincoords{60}{130}.






          share|improve this answer























          • This is wonderful! I really appreciate your answer. Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:31











          Your Answer








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          up vote
          7
          down vote













          tikz has ellipse shape, so you can use it with desired x radius and y radius. 



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{3d,shapes.geometric,shadows.blur}
          
usepackage{graphicx}
          
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
          
makeatletter
          
tikzoption{canvas is xy plane at z}{%
          
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
          
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
          
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
          
    tikz@canvas@is@plane}
          
makeatother
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
   begin{scope}%[canvas is yz plane at x=0]
          
%    node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image}}; 
          
    draw [fill=gray!40, gray!40]  (0,0) ellipse [x radius=5pt, y radius=11pt];
          
    draw [gray] (0,0) ellipse [x radius=2pt, y radius=11pt,];
          
    draw [gray] (0,0) ellipse [x radius=5pt, y radius=2pt,];
          
   end{scope}  
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          

          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {$B$};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer





















          • Wol. Very easy! Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:27















          up vote
          7
          down vote













          tikz has ellipse shape, so you can use it with desired x radius and y radius. 



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{3d,shapes.geometric,shadows.blur}
          
usepackage{graphicx}
          
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
          
makeatletter
          
tikzoption{canvas is xy plane at z}{%
          
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
          
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
          
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
          
    tikz@canvas@is@plane}
          
makeatother
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
   begin{scope}%[canvas is yz plane at x=0]
          
%    node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image}}; 
          
    draw [fill=gray!40, gray!40]  (0,0) ellipse [x radius=5pt, y radius=11pt];
          
    draw [gray] (0,0) ellipse [x radius=2pt, y radius=11pt,];
          
    draw [gray] (0,0) ellipse [x radius=5pt, y radius=2pt,];
          
   end{scope}  
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          

          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {$B$};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer





















          • Wol. Very easy! Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:27













          up vote
          7
          down vote










          up vote
          7
          down vote









          tikz has ellipse shape, so you can use it with desired x radius and y radius. 



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{3d,shapes.geometric,shadows.blur}
          
usepackage{graphicx}
          
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
          
makeatletter
          
tikzoption{canvas is xy plane at z}{%
          
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
          
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
          
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
          
    tikz@canvas@is@plane}
          
makeatother
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
   begin{scope}%[canvas is yz plane at x=0]
          
%    node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image}}; 
          
    draw [fill=gray!40, gray!40]  (0,0) ellipse [x radius=5pt, y radius=11pt];
          
    draw [gray] (0,0) ellipse [x radius=2pt, y radius=11pt,];
          
    draw [gray] (0,0) ellipse [x radius=5pt, y radius=2pt,];
          
   end{scope}  
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          

          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {$B$};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer












          tikz has ellipse shape, so you can use it with desired x radius and y radius. 



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{3d,shapes.geometric,shadows.blur}
          
usepackage{graphicx}
          
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
          
makeatletter
          
tikzoption{canvas is xy plane at z}{%
          
    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%
          
    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%
          
    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%
          
    tikz@canvas@is@plane}
          
makeatother
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
   begin{scope}%[canvas is yz plane at x=0]
          
%    node (elliL) at (0,0) {includegraphics[width=.1textwidth]{image}}; 
          
    draw [fill=gray!40, gray!40]  (0,0) ellipse [x radius=5pt, y radius=11pt];
          
    draw [gray] (0,0) ellipse [x radius=2pt, y radius=11pt,];
          
    draw [gray] (0,0) ellipse [x radius=5pt, y radius=2pt,];
          
   end{scope}  
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          

          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {$B$};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Dec 12 at 19:38









          javadr

          1,570313




          1,570313












          • Wol. Very easy! Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:27


















          • Wol. Very easy! Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:27
















          Wol. Very easy! Thank you a lot.
          – Dinesh Shankar
          Dec 13 at 2:27




          Wol. Very easy! Thank you a lot.
          – Dinesh Shankar
          Dec 13 at 2:27










          up vote
          6
          down vote













          This problem is actually less innocent than it might seem. The visible part of the ellipse is not obtained by just drawing an ellipse of the dimensions of the ellipsoid in the screen coordinates or, say, the xy plane. The problem as AFAIK only been used for the sphere, see e.g. the nice macros by Alain Matthes provided for a sphere and, in particular, this great answer by Fritz. Let me start by providing a brute force way to shade the relevant area.



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    pgfmathtruncatemacro{Xstart}{tdplotmainphi-180}
          
    pgfmathtruncatemacro{DeltaX}{10}
          
    pgfmathtruncatemacro{Xnext}{Xstart+DeltaX}
          
    pgfmathtruncatemacro{Xend}{tdplotmainphi+180}
          
    begin{scope}[transparency group,opacity=0.5]
          
    foreach X in {Xstart,Xnext,...,Xend}
          
    {tdplotsetrotatedcoords{0}{0}{X}
          
    begin{scope}[tdplot_rotated_coords]
          
    path[fill=gray!40] plot[variable=x,domain=-90:90,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          A somewhat more analytic variant thereof is



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{intersections,backgrounds}
          
makeatletter
          
%from https://tex.stackexchange.com/a/375604/121799
          
%along x axis
          
define@key{x sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{x sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{x sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
          
    setkeys{x sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along y axis
          
define@key{y sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{y sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{y sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
          
    setkeys{y sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along z axis
          
define@key{z sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{z sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{z sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
          
    setkeys{z sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}
          

          

          
makeatother % https://tex.stackexchange.com/a/438695/121799
          

          
% definitions to make your life easier
          
tikzset{rotate axes about y axis/.code={
          
path (y spherical cs:radius=1,theta=90,phi=0+#1) coordinate(xpp)
          
(y spherical cs:radius=1,theta=00,phi=90+#1) coordinate(ypp) 
          
(y spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},rotate axes about x axis/.code={
          
path (x spherical cs:radius=1,theta=00,phi=90+#1) coordinate(xpp)
          
(x spherical cs:radius=1,theta=90,phi=00+#1) coordinate(ypp) 
          
(x spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},
          
pitch/.style={rotate axes about y axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}},
          
roll/.style={rotate axes about x axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}}
          
}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    tdplotsetrotatedcoords{0}{0}{tdplotmainphi}   
          
    begin{scope}[tdplot_rotated_coords]
          
    begin{scope}[roll=-5]
          
    fill[gray!40,opacity=0.6] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetrotatedcoords{0}{0}{phivec}  
          
    begin{scope}[tdplot_rotated_coords]
          
    path[name path=elli] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
    node[anchor=south west,color=red] at (P) {P};
          
    begin{scope}[on background layer]
          
    draw[-stealth,color=red,very thick,name path global=P] (O) -- (P);
          
    end{scope}
          
    draw[-stealth,color=red,very thick,name intersections={of=P and elli}] 
          
    (intersection-1) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here



          This is an ellipsoid in perspective, see e.g.



          enter image description here



          to note that you view on the ellipsoid from the top, as dictated by the angle theta=60 in tdplotsetmaincoords{60}{130}.






          share|improve this answer























          • This is wonderful! I really appreciate your answer. Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:31















          up vote
          6
          down vote













          This problem is actually less innocent than it might seem. The visible part of the ellipse is not obtained by just drawing an ellipse of the dimensions of the ellipsoid in the screen coordinates or, say, the xy plane. The problem as AFAIK only been used for the sphere, see e.g. the nice macros by Alain Matthes provided for a sphere and, in particular, this great answer by Fritz. Let me start by providing a brute force way to shade the relevant area.



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    pgfmathtruncatemacro{Xstart}{tdplotmainphi-180}
          
    pgfmathtruncatemacro{DeltaX}{10}
          
    pgfmathtruncatemacro{Xnext}{Xstart+DeltaX}
          
    pgfmathtruncatemacro{Xend}{tdplotmainphi+180}
          
    begin{scope}[transparency group,opacity=0.5]
          
    foreach X in {Xstart,Xnext,...,Xend}
          
    {tdplotsetrotatedcoords{0}{0}{X}
          
    begin{scope}[tdplot_rotated_coords]
          
    path[fill=gray!40] plot[variable=x,domain=-90:90,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          A somewhat more analytic variant thereof is



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{intersections,backgrounds}
          
makeatletter
          
%from https://tex.stackexchange.com/a/375604/121799
          
%along x axis
          
define@key{x sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{x sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{x sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
          
    setkeys{x sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along y axis
          
define@key{y sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{y sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{y sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
          
    setkeys{y sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along z axis
          
define@key{z sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{z sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{z sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
          
    setkeys{z sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}
          

          

          
makeatother % https://tex.stackexchange.com/a/438695/121799
          

          
% definitions to make your life easier
          
tikzset{rotate axes about y axis/.code={
          
path (y spherical cs:radius=1,theta=90,phi=0+#1) coordinate(xpp)
          
(y spherical cs:radius=1,theta=00,phi=90+#1) coordinate(ypp) 
          
(y spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},rotate axes about x axis/.code={
          
path (x spherical cs:radius=1,theta=00,phi=90+#1) coordinate(xpp)
          
(x spherical cs:radius=1,theta=90,phi=00+#1) coordinate(ypp) 
          
(x spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},
          
pitch/.style={rotate axes about y axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}},
          
roll/.style={rotate axes about x axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}}
          
}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    tdplotsetrotatedcoords{0}{0}{tdplotmainphi}   
          
    begin{scope}[tdplot_rotated_coords]
          
    begin{scope}[roll=-5]
          
    fill[gray!40,opacity=0.6] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetrotatedcoords{0}{0}{phivec}  
          
    begin{scope}[tdplot_rotated_coords]
          
    path[name path=elli] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
    node[anchor=south west,color=red] at (P) {P};
          
    begin{scope}[on background layer]
          
    draw[-stealth,color=red,very thick,name path global=P] (O) -- (P);
          
    end{scope}
          
    draw[-stealth,color=red,very thick,name intersections={of=P and elli}] 
          
    (intersection-1) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here



          This is an ellipsoid in perspective, see e.g.



          enter image description here



          to note that you view on the ellipsoid from the top, as dictated by the angle theta=60 in tdplotsetmaincoords{60}{130}.






          share|improve this answer























          • This is wonderful! I really appreciate your answer. Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:31













          up vote
          6
          down vote










          up vote
          6
          down vote









          This problem is actually less innocent than it might seem. The visible part of the ellipse is not obtained by just drawing an ellipse of the dimensions of the ellipsoid in the screen coordinates or, say, the xy plane. The problem as AFAIK only been used for the sphere, see e.g. the nice macros by Alain Matthes provided for a sphere and, in particular, this great answer by Fritz. Let me start by providing a brute force way to shade the relevant area.



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    pgfmathtruncatemacro{Xstart}{tdplotmainphi-180}
          
    pgfmathtruncatemacro{DeltaX}{10}
          
    pgfmathtruncatemacro{Xnext}{Xstart+DeltaX}
          
    pgfmathtruncatemacro{Xend}{tdplotmainphi+180}
          
    begin{scope}[transparency group,opacity=0.5]
          
    foreach X in {Xstart,Xnext,...,Xend}
          
    {tdplotsetrotatedcoords{0}{0}{X}
          
    begin{scope}[tdplot_rotated_coords]
          
    path[fill=gray!40] plot[variable=x,domain=-90:90,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          A somewhat more analytic variant thereof is



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{intersections,backgrounds}
          
makeatletter
          
%from https://tex.stackexchange.com/a/375604/121799
          
%along x axis
          
define@key{x sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{x sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{x sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
          
    setkeys{x sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along y axis
          
define@key{y sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{y sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{y sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
          
    setkeys{y sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along z axis
          
define@key{z sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{z sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{z sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
          
    setkeys{z sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}
          

          

          
makeatother % https://tex.stackexchange.com/a/438695/121799
          

          
% definitions to make your life easier
          
tikzset{rotate axes about y axis/.code={
          
path (y spherical cs:radius=1,theta=90,phi=0+#1) coordinate(xpp)
          
(y spherical cs:radius=1,theta=00,phi=90+#1) coordinate(ypp) 
          
(y spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},rotate axes about x axis/.code={
          
path (x spherical cs:radius=1,theta=00,phi=90+#1) coordinate(xpp)
          
(x spherical cs:radius=1,theta=90,phi=00+#1) coordinate(ypp) 
          
(x spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},
          
pitch/.style={rotate axes about y axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}},
          
roll/.style={rotate axes about x axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}}
          
}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    tdplotsetrotatedcoords{0}{0}{tdplotmainphi}   
          
    begin{scope}[tdplot_rotated_coords]
          
    begin{scope}[roll=-5]
          
    fill[gray!40,opacity=0.6] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetrotatedcoords{0}{0}{phivec}  
          
    begin{scope}[tdplot_rotated_coords]
          
    path[name path=elli] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
    node[anchor=south west,color=red] at (P) {P};
          
    begin{scope}[on background layer]
          
    draw[-stealth,color=red,very thick,name path global=P] (O) -- (P);
          
    end{scope}
          
    draw[-stealth,color=red,very thick,name intersections={of=P and elli}] 
          
    (intersection-1) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here



          This is an ellipsoid in perspective, see e.g.



          enter image description here



          to note that you view on the ellipsoid from the top, as dictated by the angle theta=60 in tdplotsetmaincoords{60}{130}.






          share|improve this answer














          This problem is actually less innocent than it might seem. The visible part of the ellipse is not obtained by just drawing an ellipse of the dimensions of the ellipsoid in the screen coordinates or, say, the xy plane. The problem as AFAIK only been used for the sphere, see e.g. the nice macros by Alain Matthes provided for a sphere and, in particular, this great answer by Fritz. Let me start by providing a brute force way to shade the relevant area.



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    pgfmathtruncatemacro{Xstart}{tdplotmainphi-180}
          
    pgfmathtruncatemacro{DeltaX}{10}
          
    pgfmathtruncatemacro{Xnext}{Xstart+DeltaX}
          
    pgfmathtruncatemacro{Xend}{tdplotmainphi+180}
          
    begin{scope}[transparency group,opacity=0.5]
          
    foreach X in {Xstart,Xnext,...,Xend}
          
    {tdplotsetrotatedcoords{0}{0}{X}
          
    begin{scope}[tdplot_rotated_coords]
          
    path[fill=gray!40] plot[variable=x,domain=-90:90,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
   node[anchor=south west,color=red] at (P) {};
          
   draw[-stealth,color=red,very thick] (O) -- (P);
          
end{tikzpicture}
          
end{document}


          A somewhat more analytic variant thereof is



          documentclass[tikz,border=3.14mm]{standalone}
          
usepackage{tikz-3dplot}
          
usetikzlibrary{intersections,backgrounds}
          
makeatletter
          
%from https://tex.stackexchange.com/a/375604/121799
          
%along x axis
          
define@key{x sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{x sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{x sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
          
    setkeys{x sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along y axis
          
define@key{y sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{y sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{y sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
          
    setkeys{y sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}
          

          
%along z axis
          
define@key{z sphericalkeys}{radius}{defmyradius{#1}}
          
define@key{z sphericalkeys}{theta}{defmytheta{#1}}
          
define@key{z sphericalkeys}{phi}{defmyphi{#1}}
          
tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
          
    setkeys{z sphericalkeys}{#1}%
          
    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}
          

          

          
makeatother % https://tex.stackexchange.com/a/438695/121799
          

          
% definitions to make your life easier
          
tikzset{rotate axes about y axis/.code={
          
path (y spherical cs:radius=1,theta=90,phi=0+#1) coordinate(xpp)
          
(y spherical cs:radius=1,theta=00,phi=90+#1) coordinate(ypp) 
          
(y spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},rotate axes about x axis/.code={
          
path (x spherical cs:radius=1,theta=00,phi=90+#1) coordinate(xpp)
          
(x spherical cs:radius=1,theta=90,phi=00+#1) coordinate(ypp) 
          
(x spherical cs:radius=1,theta=90,phi=90+#1) coordinate(zpp);
          
},
          
pitch/.style={rotate axes about y axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}},
          
roll/.style={rotate axes about x axis=#1,x={(xpp)},y={(ypp)},z={(zpp)}}
          
}
          
begin{document}
          
tdplotsetmaincoords{60}{130}
          
begin{tikzpicture}[scale=3.2,tdplot_main_coords,>=latex,line join=bevel]
          
    coordinate (O) at (0,0,0);
          
    draw[thick,->] (O) -- (1.2,0,0) node[anchor=north east]{$x$};
          
    draw[thick,->] (O) -- (0,1.2,0) node[anchor=north west]{$y$};
          
    draw[thick,->] (O) -- (0,0,1.2) node[anchor=south]{$z$};
          
    draw[dashed] (O) -- (-1.2,0,0);
          
    pgfmathsetmacro{mya}{0.4}
          
    pgfmathsetmacro{myb}{0.8}
          
    % lines in the background
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=-70:-250,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray,dashed] plot[variable=x,domain=tdplotmainphi:tdplotmainphi+180,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);   
          
    % fill
          
    tdplotsetrotatedcoords{0}{0}{tdplotmainphi}   
          
    begin{scope}[tdplot_rotated_coords]
          
    begin{scope}[roll=-5]
          
    fill[gray!40,opacity=0.6] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    end{scope}
          
    % lines in the foreground
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({mya*cos(x)},{0},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=-70:110,smooth,samples=51]({0},{mya*cos(x)},{myb*sin(x)});
          
    draw[gray] plot[variable=x,domain=tdplotmainphi-180:tdplotmainphi,smooth,samples=51]({mya*cos(x)},{mya*sin(x)},0);  
          
    % redraw "visible" part of the axes
          
    draw[thick,->] (mya,0,0) -- (1.2,0,0);
          
    draw[thick,->] (0,mya,0) -- (0,1.2,0);
          
    draw[thick,->] (0,0,myb) -- (0,0,1.2);   
          
    pgfmathsetmacro{rvec}{1.5}
          
    pgfmathsetmacro{thetavec}{40}
          
    pgfmathsetmacro{phivec}{60}
          
    tdplotsetrotatedcoords{0}{0}{phivec}  
          
    begin{scope}[tdplot_rotated_coords]
          
    path[name path=elli] plot[variable=x,domain=0:360,smooth,samples=51]({mya*cos(x)},{0},{{myb*sin(x)}});
          
    end{scope}
          
    tdplotsetcoord{P}{rvec}{thetavec}{phivec}
          
    node[anchor=south west,color=red] at (P) {P};
          
    begin{scope}[on background layer]
          
    draw[-stealth,color=red,very thick,name path global=P] (O) -- (P);
          
    end{scope}
          
    draw[-stealth,color=red,very thick,name intersections={of=P and elli}] 
          
    (intersection-1) -- (P);
          
end{tikzpicture}
          
end{document}


          enter image description here



          This is an ellipsoid in perspective, see e.g.



          enter image description here



          to note that you view on the ellipsoid from the top, as dictated by the angle theta=60 in tdplotsetmaincoords{60}{130}.







          share|improve this answer














          share|improve this answer



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          edited Dec 12 at 21:11

























          answered Dec 12 at 20:16









          marmot

          84.4k495179




          84.4k495179












          • This is wonderful! I really appreciate your answer. Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:31


















          • This is wonderful! I really appreciate your answer. Thank you a lot.
            – Dinesh Shankar
            Dec 13 at 2:31
















          This is wonderful! I really appreciate your answer. Thank you a lot.
          – Dinesh Shankar
          Dec 13 at 2:31




          This is wonderful! I really appreciate your answer. Thank you a lot.
          – Dinesh Shankar
          Dec 13 at 2:31


















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