参数化绘图 3D、螺旋线和星形球体

Question

有人能帮我用 LaTeX 创建两个图——一个螺旋线和一个星体球体吗？所附图片是 Mathematica 的截图，显示了所需的结果。

Answer 1

运行xelatex（需要一些时间）或latex->dvips->ps2pdf：

\documentclass{article}
\usepackage{pst-solides3d}
\begin{document}

\psset{unit=0.75}
\begin{pspicture}(-3,-4)(3,6)
\psset{viewpoint=20 70 10 rtp2xyz,Decran=20,lightsrc=viewpoint}
% Parametric Surfaces
\defFunction[algebraic]{helix}(u,v)
 {(1.2+0.5*cos(v))*cos(u)}
 {(1.2+0.5*cos(v))*sin(u)}
 {0.5*sin(v)+u/Pi}
\psSolid[object=surfaceparametree,linewidth=0.5\pslinewidth,
 base=-7 6.5 0 TwoPi,hue=0 1,function=helix,ngrid=30 0.4]%
\gridIIID[Zmin=-3,Zmax=3](-2,2)(-2,2)
\end{pspicture}

\psset{unit=3cm}
\begin{pspicture}(-2,-2)(2,2)
\psset{viewpoint=20 70 10 rtp2xyz,Decran=20,lightsrc=viewpoint}
% Parametric Surfaces
\defFunction[algebraic]{helix}(u,v)
 {(cos(v)*cos(u))^3}
 {(cos(v)*sin(u))^3}
 {sin(v)^3}
\psSolid[object=surfaceparametree,linewidth=0.5\pslinewidth,
 base=0 Pi 0 TwoPi,fillcolor=red,function=helix,ngrid=20 40]%
\gridIIID[Zmin=-1,Zmax=1,showAxes=false](-1,1)(-1,1)
\end{pspicture}

\end{document}

Answer 2

这是我的版本：

\documentclass[border=10pt]{standalone}
\usepackage[pdftex]{graphicx}
\usepackage{pgfplots}
\usepgfplotslibrary{colormaps}


\begin{document}
\begin{tikzpicture}[yscale=2, xscale=1]
  \begin{axis}[axis line style={draw=none}, 
      view={170}{-20},
      grid=major,
      xmin=0,xmax=2,
      ymin=0,ymax=2,
      zmin=0,zmax=4,
      enlargelimits=upper,
      xtick=\empty,
      ytick=\empty,
      ztick=\empty,
      %colormap/bone,
      trig format plots=rad,
      clip=false
    ]
    \addplot3 [ surf, domain=0:12.566, domain y=0:6.28,
      samples=70, samples y=70,
      variable=\u, variable y=\v,
    point meta=u*v, opacity=0.4 ]
     ({(1.2+0.5*cos(v))*cos(u)},
     {(1.2+0.5*cos(v))*sin(u)},
     {0.5*sin(v)+u/(3.0)});


  \end{axis}
\end{tikzpicture}
\end{document}

这是图片