Cfrgtkky

Using pgfplots, I plotted a torus, with a knot that lies on its surface:

begin{tikzpicture}

 begin{axis}[axis equal image]



 addplot3[domain=0:360, y domain=0:360, samples=20, surf, z buffer=sort]

 (

  {(2 + cos(x))*cos(y)},

  {(2 + cos(x))*sin(y)},

  {sin(x)}

 );



 addplot3[domain=0:360, samples=50]

 (

 {(2 + cos(2*x))*cos(3*x)},

 {(2 + cos(2*x))*sin(3*x)},

 {sin(2*x)}

 );

 end{axis}

end{tikzpicture} 

However, it turns out that the knot is not shown properly, because parts of it that should be hidden by the surface, aren't. It should look something like this:

One of the first things I tried is putting in a z buffer=sort key for the knot's graph, however, this just screws up the curve. I guess the issue is that the torus and the knot have to somehow know about each other, for z buffer=sort to work, but there is no good way to do so.

Are there other approaches? I am open to trying non-pgfplots solutions.

Here is a proposal but this is not really my proposal. It is a combination of this answer and this answer. Personally I like to use asypictureB by the author of the second answer. You can compile this e.g. with pdflatex -shell-escape.

documentclass[margin=3.14mm]{standalone}

usepackage{asypictureB}

begin{document} % based on https://tex.stackexchange.com/a/149759/121799 and

% https://tex.stackexchange.com/a/149784/121799

begin{asypicture}{name=torus}

import graph3;



size(200,0);

currentprojection=orthographic(4,0,2);



//inner radius

real R=2;

//outer radius

real a=0.75;



//surface:

triple f(pair t) {

  return ((R+a*cos(t.y))*cos(t.x),(R+a*cos(t.y))*sin(t.x),a*sin(t.y));

}



//path:

real x(real t) {return cos(t*3)*(R + a*cos(t));}

real y(real t) {return sin(t*3)*(R + a*cos(t));}

real z(real t) {return a*sin(t);}



pen p=blue+opacity(0.33);

// make surface and path

surface s=surface(f,(0,0),(2pi,2pi),8,8,Spline);

path3 q=graph(x,y,z,0,6*pi,operator ..);



// draw surface and path

draw(s,surfacepen=material(diffusepen=blue+opacity(0.33), emissivepen=blue));

real linewidth = 2pt;

draw(q, p=linewidth + orange);

end{asypicture}

end{document}

Of course, one can also color different stretches of the path differently. Please let me know if there are problems, or if I should remove this answer because it does not represent any real progress compared to what is already on the market.