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I have used the sample code from latexdraw that draws a torus. I am trying to draw a filled circle and a dashed circle where they should be wrap around the torus instead of being drawn uniformly at z=0. I am looking for a TikZ solution. The closest I have seen is this solution but it is too difficult for me to decipher. Any help would be appreciated!

current output

\documentclass[margin=4pt]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{tikz-3dplot}
\usepgfplotslibrary{colormaps}

\pgfplotsset{
  compat=newest,
  colormap={manifoldmap}{color=(lightgray) color=(white) color=(lightgray)}
}

\begin{document}
\begin{tikzpicture}
  \def\R{2.75}     % Major radius (distance from torus centre to tube centre)
  \def\offset{0.5} % Radial displacement from the torus centre circle
  \def\thetaB{2.5} % Angular position (in radians) for highlighted point

  \begin{axis}[
    width=12cm,      
    axis equal image,
    hide axis,       
    z buffer=sort,   
    view={125}{35},  
    clip=false       
  ]
    % Parametric torus equations:
      % x = (R + cos(x)) cos(y)
      % y = (R + cos(x)) sin(y)
      % z = sin(x)
    \addplot3[
      surf,
      shader = faceted interp,
      samples = 30,
      samples y = 40,
      domain = 0:2*pi,
      domain y = 0:2*pi,
      colormap name = manifoldmap,
      thin,
      opacity=0.75
    ]
    (
      {(\R + cos(deg(x))) * cos(deg(y))},
      {(\R + cos(deg(x))) * sin(deg(y))},
      {sin(deg(x))}
    );
    \begin{scope}[canvas is xy plane at z=0, transform shape]
      \coordinate (p) at
        ({(\R + \offset) * cos(deg(\thetaB))},
         {(\R + \offset) * sin(deg(\thetaB))});
      \draw[fill=red, draw=none] (p) circle (4pt);
      \draw[blue, dashed, thick] (p) circle (16pt);
    \end{scope}
  \end{axis}
\end{tikzpicture}
\end{document}
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1 Answer 1

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Maybe this? For 3D, I'd personally use a specialized 3D package, not plain TikZ. Just had this old concept lying around.

\documentclass[tikz, border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\pgfmathdeclarefunction{sphereX}{2}{%
    % #1  - longitude
    % #2  - latitude
    \pgfmathparse{cos((#2) r)*cos((#1) r)}%
}
\pgfmathdeclarefunction{sphereY}{2}{%
    % #1  - longitude
    % #2  - latitude
    \pgfmathparse{cos((#2) r)*sin((#1) r)}%
}
\pgfmathdeclarefunction{sphereZ}{2}{%
    % #1  - longitude
    % #2  - latitude
    \pgfmathparse{sin((#2) r)}%
}
\begin{document}
    \tdplotsetmaincoords{60}{80}
    \begin{tikzpicture}[tdplot_main_coords]
        \foreach \ANGLE in {0,...,36} {
            \pgfmathsetmacro{\ANGLE}{\ANGLE*pi/18}
            \draw[domain=0:2*pi] plot (   
                {2*cos(\x r)+0.5*sphereX(\x,\ANGLE)},
                {2*sin(\x r)+0.5*sphereY(\x,\ANGLE)},
                {0.5*sphereZ(\x,\ANGLE)}
            );
            \draw[domain=0:2*pi] plot (   
                {2*cos(\ANGLE r)+0.5*sphereX(\ANGLE,\x)},
                {2*sin(\ANGLE r)+0.5*sphereY(\ANGLE,\x)},
                {0.5*sphereZ(\ANGLE,\x)}
            );
        }
        \pgfmathsetmacro{\ANGLE}{3*pi/2}
        \draw[domain=0:2*pi,red,ultra thick] plot (   
            {2*cos(\ANGLE r)+0.5*sphereX(\ANGLE,\x)},
            {2*sin(\ANGLE r)+0.5*sphereY(\ANGLE,\x)},
            {0.5*sphereZ(\ANGLE,\x)}
        );
    \end{tikzpicture}
\end{document}
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2
  • 1
    maybe add line cap=round could tweak the ellipse better🤔 Commented 2 hours ago
  • @Explorer I completely agree, and would normally do that for a polished illustration - I wasn't making this for aesthetic purposes, I just wanted to share the trigonometric-linear algebraic approach which I am so fond of. Commented 2 hours ago

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