Moebius Strip using TikZ

I'm wondering whether is possible to draw a Moebius Strip using TikZ. The closest thing I've seen is in Texamples' page, but no luck so far!

Do you have any ideas? I don't even have a MWE (sorry)

• I suggest you to use inkscape to draw it. – Sigur Jun 10 '13 at 23:25

With PGFPlots:

\documentclass{standalone}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
hide axis,
view={40}{40}
]
point meta=x,
colormap/greenyellow,
samples=40,
samples y=5,
z buffer=sort,
domain=0:360,
y domain=-0.5:0.5
] (
{(1+0.5*y*cos(x/2)))*cos(x)},
{(1+0.5*y*cos(x/2)))*sin(x)},
{0.5*y*sin(x/2)});

samples=50,
domain=-145:180, % The domain needs to be adjusted manually, depending on the camera angle, unfortunately
samples y=0,
thick
] (
{cos(x)},
{sin(x)},
{0});
\end{axis}
\end{tikzpicture}

\end{document}

• Thank you for the marvellous answer! Is it possible to superpose the Moebius strip with the middle circle?, I'd like to highlight that the Moebius strip is based on a circle! :-P Thank you very much. – Dox Jun 11 '13 at 13:20
• @Dox: Yes, you can add a second plot for that. Unfortunately, PGFPlots can't do the z buffering for separate plots, so you'll have to set the domain for the circle manually to make sure the hidden parts aren't drawn. – Jake Jun 11 '13 at 13:47
• Magnificent! I tried, but got a much less nice than your. Cheers. – Dox Jun 11 '13 at 14:00
• @Jake: Why I get a triangular mesh instead of a rectangular mesh as you when I run this code (with pdflatex)? It's all about pgfplots package update or another trick? – rafaeldf Jun 13 '13 at 16:30
• @rafaeldf: That could be a viewer issue with the interpolated shading. Does using shader=faceted instead of shade=faceted interp help? – Jake Jun 13 '13 at 16:49

As a quotient space:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\begin{document}

\begin{tikzpicture}[
decoration={
markings,
mark=at position 0.5 with {\arrow{>}}}
]
\draw[postaction=decorate] (0,0) -- (2,0);
\draw (2,0) -- (2,-2);
\draw[postaction=decorate] (2,-2) -- (0,-2);
\draw (0,0) -- (0,-2);
\end{tikzpicture}

\end{document}


And now, taken from MoebiusStrip.tex:

% Title: Moebius Strip
% Tags: Clipping, Node positioning, Shadings, Macros
% Authors: Jacques Duma & Gerard Tisseau
% Site: http://math.et.info.free.fr/TikZ/index.html

\documentclass{article}

\usepackage{tikz}
\usepackage{verbatim}

\begin{comment}
:Title: Moebius Strip
:Tags: Clipping, Node positioning, Shadings, Macros
:Authors: Jacques Duma & Gerard Tisseau
:Site: http://math.et.info.free.fr/TikZ/index.html

To build this Moebius Strip, take a normal strip of paper, write "TikZ for LaTeX" on one side, give it 3 half-twists and join the ends.

The resulting strip has only one face and one boundary.
\end{comment}

% one third of the Moebius Strip
%: \strip{<angle>}
\newcommand{\strip}[1]{%
(0:2.8453) ++ (-30:1.5359) arc (60:0:2)
-- ++  (90:5) arc (0:60:2) -- ++ (150:3) arc (60:120:2)
-- ++ (210:5) arc (120:60:2) -- cycle;}

%: \MoebiusStrip{<text1>}{<text2>}{<text3>}
\newcommand{\MoebiusStrip}[3]{%
\begin{scope} [transform shape]
\strip{0}
\strip{120}
\strip{-120}
\draw (-60:3.5) node[scale=6,rotate=30] {#1};
\draw (180:3.5) node[scale=4,rotate=-90]{#3};
% redraw the first strip after clipping
\clip (-1.4,2.4)--(-.3,6.1)--(1.3,6.1)--(5.3,3.7)--(5.3,-2.7)--cycle;
\strip{0}
\draw (60:3.5) node [gray,xscale=-4,yscale=4,rotate=30]{#2};
\end{scope}}

\begin{document}

\pagestyle{empty}

\begin{center}
\begin{tikzpicture} [rotate=22]
\MoebiusStrip{Ti{\color{orange}\textit{k}}Z}{for}{\LaTeX}
\end{tikzpicture}
\end{center}

\end{document}


As a parametric surface with the Asymptote:

\documentclass{article}
\usepackage[inline]{asymptote}
\begin{document}
\begin{figure}
\centering
\begin{asy}
import graph3;
size(200,IgnoreAspect);
size3(200,IgnoreAspect);
currentprojection=orthographic(camera=(1.5,0.3,2),up=Z,target=(0.5,0,0),zoom=0.8);
real r=2, w=1;
real x(real u, real v){return (r+v/2*cos(3pi*u))*cos(2pi*u);};
real y(real u, real v){return (r+v/2*cos(3pi*u))*sin(2pi*u);};
real z(real u, real v){return (v/2*sin(3pi*u));};
triple f(pair p){return (x(p.x,p.y),y(p.x,p.y),z(p.x,p.y));};
draw(surface(f,(0,-w),(1,w),nu=9,Spline),orange);
\end{asy}
\caption{M\"obius strip.}
\end{figure}
\end{document}


With PSTricks. Stolen from Herbert's answer.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-3dplot}

\begin{document}
\psset{Beta=20}
\begin{pspicture}(-6,-3)(6,4)
\parametricplotThreeD[xPlotpoints=100,yPlotpoints=10](0,360)(-1,1){
t 2 div sin u mul }
\pstThreeDCoor[xMin=-1,yMin=-1,zMin=-1]
\parametricplotThreeD[xPlotpoints=100,yPlotpoints=1,
linecolor=red,linewidth=2pt,arrows=|->](180,-180){
t 2 div sin }
\end{pspicture}

\end{document}


Another PsTricks solution, using pst-solide3d, adapted from a code from Manuel Luque:

    \listfiles
\documentclass[pdf,dvipsnames,svgnames, x11names]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pst-solides3d}
\begin{document}
\pagestyle{empty}

\begin{pspicture}(-4.2,-1.7)(5.1,3)
\psset{unit=1.5}
\psframe*[linecolor=DarkSeaGreen4!80](-4.2,-1.7)(5.1,3)
\psset[pst-solides3d]{viewpoint=20 10 5, Decran=40, lightsrc=20 10 10}
\psPoint(3.5,0,0){X}
\psPoint(0,2.8,0){Y}
\psPoint(0,0,1.5){Z}
\psPoint(0,0,0){O}\uput[d](O){$O$}
\psline{->}(O)(X)\uput[-160](X){$x$}
\defFunction{mobius}(u,v)
{2 u v Cos mul add 2 v mul Cos mul}
{2 u v Cos mul add 2 v mul Sin mul}
{u v Sin mul}
\psSolid[object=surfaceparametree,linewidth=0.75\pslinewidth,
base=0.2 0.25 0 pi,linewidth=0.1,
function=mobius,
ngrid=.025]%
\psSolid[object=surfaceparametree,linewidth=0.75\pslinewidth,
base=-0.25 -0.2 0 pi,linewidth=0.1,
function=mobius,
ngrid=.025]%
\psSolid[object=surfaceparametree,linewidth=0.5\pslinewidth,
base=-0.25 0.25 0 pi,fillcolor=yellow!50,incolor=yellow!50,
function=mobius,
ngrid=.05]%
\psline{->}(O)(Y)\uput[-15](Y){$y$}
\psline{->}(O)(Z)\uput[u](Z){$z$}
\end{pspicture}

\end{document}