4

I would like to add "dots/points" to each grid intersection in the torus below.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{colormaps}
\pgfplotsset{
    compat=newest
}

\begin{document}   
\begin{tikzpicture}
    \begin{axis}[view={120}{30},
        axis equal image,
        hide axis,
        z buffer = sort,
        scale = 1.5
    ]
    \addplot3[
            surf,
            samples = 20,
            samples y = 40,
            domain = 0:2*pi,
            domain y = 0:2*pi,
        ](
            {(1+sin(deg(\x)))*cos(deg(\y))},
            {(1+sin(deg(\x)))*sin(deg(\y))},
            {cos(deg(\x))}
        );
    \end{axis}
\end{tikzpicture}
\end{document}

I tried to add something like this to my code above:

\addplot3 coordinates (
        {(1+sin(deg(\x)))*cos(deg(\y))},
        {(1+sin(deg(\x)))*sin(deg(\y))},
        {cos(deg(\x))}
    );

but this causes my code to freeze. What should I do?

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3
  • 1
    Welcome! Can you complete your code so people can compile it as-is? An image of your current output might also be helpful.
    – cfr
    Sep 21 at 0:03
  • (I am curious) in which context the dots at grid intersections make sense? for decorating only?
    – Black Mild
    Sep 21 at 14:53
  • 1
    @BlackMild It makes sense in the context of a toric code: at some of the vertices, I may want to put a vertex type operator (like a cross). I asked about the dots just to make my question clearer.
    – aprendiz
    Sep 21 at 15:14

2 Answers 2

Reset to default
5 
\documentclass[tikz, border=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[view={120}{30},
axis equal image,
hide axis,
z buffer=sort,
]
\addplot3[
surf, mark=*, mark size=0.2,
samples=20,
samples y=40,
domain=0:2*pi,
domain y=0:2*pi,
](
{(1+sin(deg(\x)))*cos(deg(\y))},
{(1+sin(deg(\x)))*sin(deg(\y))},
{cos(deg(\x))}
);
\end{axis}
\end{tikzpicture}
\end{document}

Torus with lines and marks

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2
  • Thanks a lot, it was already very helpful. I do need only the front points, so far was not able to.
    – aprendiz
    Sep 21 at 0:36
  • Markers and surfaces do not share the same depth information. They are drawn on top of each other. -a scatter plot does not have a z-buffer. The only way to do what you want in PGFPlots, is to make several \addplot3 or \draw in e.g. a \foreach (or \pgfplotsinvokeforeach) with manual adjusted domain to fit with the view . You can also describe what is in view with a function and use z filter/.expression. Start e.g. with z filter/.expression={y+x<cos(deg(\x)) ? nan : z}
    – hpekristiansen
    Sep 21 at 2:16
4

Is this what you want? I use Asymptote that is maths-oriented.

The code is adapted from one in Asymptote gallery. We can put dots or any decoration at grid intersections. The parameters m and n are the numbers for horizontal and vertical mesh-lines. Feel free to change them, also R and a as you wish.

The code can be run standalone online at asymptote.ualberta.ca or imbbed in a LaTeX document https://www.overleaf.com/read/pffryywkwxqy

enter image description here

// Run on http://asymptote.ualberta.ca/
// This code is adapted from 
// https://asymptote.sourceforge.io/gallery/3Dwebgl/parametricsurface.asy

import graph3;
size(200,0);
currentprojection=orthographic(4,0,2,zoom=.8);

real R=2;
real a=.8;

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)
);}

pen p=black+1pt;
int m=20;  // x-mesh
int n=12;   // y-mesh
surface s=surface(f,(0,0),(2pi,2pi),m,n,Spline);

// surface & mesh
draw(s,yellow,meshpen=p);

for (int i=0; i<m; ++i)
for (int j=0; j<n; ++j)
dot(f((i*2pi/m,j*2pi/n)),red);

PS: with opacity option, then we can see the hidden part

draw(s,yellow+opacity(.5),meshpen=p);

enter image description here

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