Drawing a perspective ellipse with TikZ

up vote
3
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

asked 6 hours ago

Dinesh Shankar

1675

add a comment |

up vote
3
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

asked 6 hours ago

Dinesh Shankar

1675

add a comment |

up vote
3
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

asked 6 hours ago

Dinesh Shankar

1675

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

asked 6 hours ago

Dinesh Shankar

1675

asked 6 hours ago

Dinesh Shankar

1675

asked 6 hours ago

Dinesh Shankar

1675

asked 6 hours ago

Dinesh Shankar

1675

asked 6 hours ago

Dinesh Shankar

1675

add a comment |

2 Answers
2

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up vote
4
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

answered 6 hours ago

javadr

1,428313

add a comment |

up vote
3
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}.

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

add a comment |

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2 Answers
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up vote
4
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

answered 6 hours ago

javadr

1,428313

add a comment |

up vote
4
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

answered 6 hours ago

javadr

1,428313

add a comment |

up vote
4
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

answered 6 hours ago

javadr

1,428313

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

answered 6 hours ago

javadr

1,428313

answered 6 hours ago

javadr

1,428313

answered 6 hours ago

javadr

1,428313

answered 6 hours ago

javadr

1,428313

add a comment |

up vote
3
down vote

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}.

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

add a comment |

up vote
3
down vote

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}.

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

add a comment |

up vote
3
down vote

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}.

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

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}.

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

edited 4 hours ago

answered 5 hours ago

marmot

82.6k493176

answered 5 hours ago

marmot

82.6k493176

answered 5 hours ago

marmot

82.6k493176

add a comment |

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