PSTriks 3D 球体随机分布在圆环内

Question

我想在圆环内随机分布“n”个球体（或球体）。我用来生成圆环的代码如下：

\documentclass[12pt]{standalone}
\usepackage{pstricks}
\usepackage{pst-3dplot}
\pagestyle{empty}
\def\drawCircles{%
  \parametricplotThreeD[xPlotpoints=100](0,360)(0,360){%
    /k 2 def /k2 4 def
    t cos k mul 4 u sin k mul add mul
    t sin k mul 4 u sin k mul add mul
    u cos k2 mul
  }
  \parametricplotThreeD[yPlotpoints=100](0,360)(0,360){%
    /k 2 def /k2 4 def
    u cos k mul 4 t sin k mul add mul
    u sin k mul 4 t sin k mul add mul
    t cos k2 mul
  }
}
\begin{document}
\psset{unit=0.75}
\begin{pspicture}(-28,-8)(28,8)
    \psset{Beta=10,Alpha=0,linewidth=0.1pt,linecolor=blue}
    \drawCircles
\end{pspicture}
\end{document}

我该如何使用 PSTricks 来实现？谢谢！

Answer 1

这是一个平行视图中的 3d 对象，没有隐藏线，因此很难看到前后。使用包更有意义pst-solides3d。它可以处理带有隐藏线的透视图。

\documentclass[12pt,pstricks]{standalone}
\usepackage{pstricks}
\usepackage{pst-3dplot}
\pagestyle{empty}
\def\drawCircles{%
    \parametricplotThreeD[xPlotpoints=100](0,360)(0,360){%
        /k 2 def /k2 4 def
        t cos k mul 4 u sin k mul add mul
        t sin k mul 4 u sin k mul add mul
        u cos k2 mul
    }
    \parametricplotThreeD[yPlotpoints=100](0,360)(0,360){%
        /k 2 def /k2 4 def
        u cos k mul 4 t sin k mul add mul
        u sin k mul 4 t sin k mul add mul
        t cos k2 mul
    }
}
\begin{document}
    \psset{unit=0.75}
    \begin{pspicture}(-15,-10)(15,10)
    \psset{Beta=30,Alpha=0,linewidth=0.1pt,linecolor=blue}
    \pstThreeDCoor[xMax=6,yMax=6,zMax=6]
    \drawCircles
    \pstThreeDSphere(0,8,0){4}
    \pstThreeDSphere(8,0,0){4}
    \pstThreeDSphere(0,-8,0){4}
    \pstThreeDSphere(-8,0,0){4}
    \end{pspicture}

    \begin{pspicture}(-15,-10)(15,10)
    \psset{Beta=30,Alpha=0,linewidth=0.1pt,linecolor=blue}
    \pstThreeDCoor[xMax=6,yMax=6,zMax=6]
    \pstThreeDSphere(0,8,0){4}
    \pstThreeDSphere(8,0,0){4}
    \pstThreeDSphere(0,-8,0){4}
    \pstThreeDSphere(-8,0,0){4}
    \drawCircles
\end{pspicture}
\end{document}

对于随机值（这里只针对 +/- x：

\pstThreeDSphere( rrand rand 17 mod 8 sub, dup \pst@number\psunit\space div dup mul 64 exch sub sqrt,0){4}
\pstThreeDSphere( rand 17 mod 8 sub, dup \pst@number\psunit\space div dup mul 64 exch sub sqrt,0){4}
\pstThreeDSphere( rand 17 mod 8 sub, dup \pst@number\psunit\space div dup mul 64 exch sub sqrt,0){4}
\pstThreeDSphere( rand 17 mod 8 sub, dup \pst@number\psunit\space div dup mul 64 exch sub sqrt,0){4}