I am trying to produce a figure of a wireframe torus, similar to the image produced by the following code which generates a wireframe sphere at a general "viewing angle":

%% helper macros

\newcommand\LongitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
\newcommand\LatitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % latitude
  \tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
  \tikzset{current plane/.prefix style={scale=#1}}
   % angle of "visibility"
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
  \draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
  \tikzset{current plane/.prefix style={scale=#1}}
  % angle of "visibility"
  \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
  \draw[current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);

%% document-wide tikz options and styles

  >=latex, % option for nice arrows
  inner sep=0pt,%
  outer sep=2pt,%
  mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,


\begin{tikzpicture} % "THE GLOBE" showcase

\def\R{2.5} % sphere radius
\def\angEl{35} % elevation angle
\filldraw[ball color=blue!40!white!80!green!40!] (0,0) circle (\R);
\foreach \t in {-80,-60,...,80} { \DrawLatitudeCircle[\R]{\t} }
\foreach \t in {-5,-35,...,-175} { \DrawLongitudeCircle[\R]{\t} }



enter image description here

This code fragment was taken from part of this texample.net page. I'm really quite unsure as to how to approach this problem. Seemingly I would want to parameterize the surface of the torus to draw the "Latitude" and "Longitude" lines, but I am not sure how to do so... Any insight into this problem would be greatly appreciated!

Note that any solution using any packages outsize TikZ/pgf are welcome.

  • Does How to draw a torus solves your problem?
    – Bobyandbob
    Nov 11 '17 at 16:39
  • Ideally I would have a "translucent" torus, where you can see the whole wireframe of the surface. I just edited the question with an image of the generated sphere.
    – pateryan
    Nov 11 '17 at 16:41
  • Specifically in a form that is as close to the above as possible. However in the worst case I will use one of those solutions.
    – pateryan
    Nov 11 '17 at 16:42
  • More like this=: How can I visualize a Torus with three paths?
    – Bobyandbob
    Nov 11 '17 at 16:42
  • @Bobyandbob, Yes that is much closer to what I had in mind! I'm pretty surprised at the volume of code required for the task in that thread. There must be a better way, no?
    – pateryan
    Nov 11 '17 at 16:44

I could not resist and stole my code almost entirely from this elegant answer. It is based on asymptote and reads

  import graph3;

  pen xarcPen=deepblue+0.7bp;
  pen yarcPen=deepred+0.7bp;


  int m=20;
  int n=10;
  real arcFactor=1;
  real R=2;
  real a=1;

  triple fs(pair t) {
    return ((R+a*Cos(t.y))*Cos(t.x),(R+a*Cos(t.y))*Sin(t.x),a*Sin(t.y));

  pair p,q,v;

  for(int i=1;i<=n;++i){
    for(int j=0;j<m;++j){

  surface s=surface(fs,(0,0),(360,360),8,8,Spline);
  draw(s,surfacepen=material(blue+opacity(0.6), emissivepen=0.2*white),render(compression=Low,merge=true));

Suppose you call the TeX file lattice.tex, then invoke

pdflatex lattice
asy -f pdf -noprc -render=4 lattice-1.asy
pdflatex lattice

in order to obtain

enter image description here

  • Excellent! Thank you so much :). If I could bother you a little more, how would I go about removing the dots at intersection points?
    – pateryan
    Nov 12 '17 at 1:30
  • @pateryan just remove (or comment out) the line dot(fs(p));
    – user121799
    Nov 12 '17 at 2:05

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