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使用 TikZ 的 Moebius Strip

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使用 TikZ 的 Moebius Strip

我想知道是否可以使用 来绘制莫比乌斯带TikZ。我见过的最接近的东西是Texamples 页面，但至今还没有运气！

你有什么想法吗？我甚至没有 MWE（抱歉）

答案1

使用 PGFPlots：

\documentclass{standalone}


\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
    hide axis,
    view={40}{40}
]
\addplot3 [
    surf, shader=faceted interp,
    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)});

\addplot3 [
    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}

答案2

作为商空间：

\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}

在此处输入图片描述

现在，摘自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]{%
\shadedraw[very thick,top color=white,bottom color=gray,rotate=#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}

在此处输入图片描述

答案3

在此处输入图片描述

作为具有以下特征的参数曲面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}

答案4

另一个 PsTricks 解决方案，使用pst-solide3d，改编自 Manuel Luque 的代码：

    \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}

在此处输入图片描述

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