Drawing the Möbius band and the Klein bottle

Question

I have this:

\begin{tikzpicture}
\begin{axis}[hide axis, unit vector ratio=1 1 1, view={-30}{45}]
\addplot3 [surf, domain=0:360, y domain=-1:1] (    {(10+y*cos(3*x/2)))*cos(x)}, {(10+y*cos(3*x/2)))*sin(x)}, {y*sin(3*x/2)});
\end{axis}
\end{tikzpicture}

But it doesn´t works. I don´t know the reason. I would like to obtain exactly one of these:

Additionally, I´d like to draw a simple Klein bottle (without grid or shadows), but in this case I´ve nothing... :(

Thanks for the support!!

Welcome to TeX.SE! Please ask only one question in your question! Did you saw question https://tex.stackexchange.com/a/364134/16550 ? — Mensch, Mar 07 '19 at 19:17

score 3 · Answer 1 · answered Mar 07 '19 at 20:01

A colored Moebius band (run with xelatex):

\documentclass[pstricks]{standalone}
\usepackage{pst-3dplot}

\makeatletter
\define@key[psset]{pst-3dplot}{HueBegin}{% Between 0 and 1
 \def\PstHSB@HueBegin{#1}}
\define@key[psset]{pst-3dplot}{HueEnd}{% Between 0 and 1
 \def\PstHSB@HueEnd{#1}}
\define@boolkey[psset]{pst-3dplot}[Pst@]{HSB}[true]{}
% Default values
\psset[pst-3dplot]{HueBegin=0,HueEnd=1,HSB=false}
\psset{dimen=outer}

\def\parametricPlotThreeD@iii{%   without arrows (quickplot)
 \addto@pscode{%
   \psk@ThreeDplot@yPlotpoints {
     /Counter 0 def
     /t tMin def
     xyz \@nameuse{beginqp@\psplotstyle}
     /t t dt add def
     \psk@ThreeDplot@xPlotpoints\space 1 sub {
       xyz
       /Counter Counter 1 add def
       1 Counter eq { moveto currentpoint /OldY ED /OldX ED }
       {\ifPst@HSB % Other points than the first one
        /PointY exch def
        /PointX exch def
        Counter \psk@ThreeDplot@xPlotpoints\space div
        \PstHSB@HueEnd\space
        \PstHSB@HueBegin\space sub mul
        \PstHSB@HueBegin\space add
        1 1 sethsbcolor
        OldX OldY PointX PointY lineto lineto
        stroke
        PointX PointY moveto
    /OldX PointX def /OldY PointY def
      \else lineto \fi } ifelse
       /t t dt add def
     } repeat
     /t t dt sub def
     /u u du add def
   } repeat
 }%
 \@nameuse{endqp@\psplotstyle}%
}
\makeatother

\begin{document}
\psset{Beta=20}
\begin{pspicture}(-6,-3)(6,3)
\def\Radius{5 }
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,
 yPlotpoints=100,drawStyle=xyLines,HSB](0,365)(-1,1){
 t 2 div cos u mul \Radius add t cos mul
 t 2 div cos u mul \Radius add t sin mul
 t 2 div sin u mul }
%\pstThreeDCoor[xMin=-1,yMin=-1,zMin=-1]
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,yPlotpoints=1,
  linecolor=black,linewidth=1.5pt](488,-60){
 t 2 div cos \Radius add t cos mul
 t 2 div cos \Radius add t sin mul
 t 2 div sin }
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,yPlotpoints=1,
  linecolor=black,linewidth=1.5pt](631,513){
 t 2 div cos \Radius add t cos mul
 t 2 div cos \Radius add t sin mul
 t 2 div sin }
\end{pspicture}
\end{document}

score 3 · Answer 2 · answered Mar 07 '19 at 20:18

Your code works (IMHO).

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={moeb=3;phase=120;}]
\begin{axis}[hide axis, unit vector ratio=1 1 1, view={-30}{45}]
\addplot3 [surf, domain=0:360, y domain=-2:2,point
meta=rawy,shader=interp,samples=51,samples y=2] (   
 {(10+y*cos(moeb*x/2+phase)))*cos(x)}, {(10+y*cos(moeb*x/2+phase)))*sin(x)}, {y*sin(moeb*x/2+phase)});
\end{axis}
\end{tikzpicture}
\end{document}

You may change the plot by playing with moeb, phase and point meta.

score 2 · Answer 3 · 2019-03-07T21:39:17.747

I am not trying to give an exact answer but point out that your comment that gridded and grey is not desirable so taking your code example as found on this site with a few adjustments putting back we get this which I guess is a reasonable rendering That does help many people to understand the nature of a mobeius

But if you try to remove the grid and the color as you have done you will at best get a dot.

Equally there are many answers for bottles on this site that you can adapt by removing the features you don't want, but removing the grids make them less understandable.

Thus you could remove the lables from this one https://tex.stackexchange.com/a/77643/170109

Making a labeled Klein bottle using TikZ or pgfplots? pgfplots in combination with gnuplot requires additional semicolon pgfplots exp(-pow(deg(x),2) on domain 0:2*pi

Note for those wondering where to get their hands on a party piece for serving wine look at the manufacturer of the largest in the world

(http://www.kleinbottle.com/wine_bottle_klein_bottle.html)

Drawing the Möbius band and the Klein bottle

3 Answers3