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如何绘制这样的平面交点？

tag-icon • tag-icon tikz-pgf
如何绘制这样的平面交点？

在此处输入图片描述

我做了什么来生成第一个图形：

  \begin{tikzpicture}
    [3d view={60}{30}]
  
    % bottom plane
    \draw[plane,fill=blue!50] 
    (-1,-1,0) -- (1,-1,0) -- (1,1,0) -- (-1,1,0) -- cycle;
    \draw[plane,fill=green!50] 
    (0,-1,-1) -- (0,1,-1) -- (0,1,1) -- (0,-1,1) -- cycle;
    \draw[plane,fill=red!50] 
    (-1,0,-1) -- (1,0,-1) -- (1,0,1) -- (-1,0,1) -- cycle;
    \draw[line,thin] (-1,0,0)--(1,0,0) (0,-1,0)--(0,1,0) (0,0,1)--(0,0,-1);

但是这些代码效果不太好，没有显示交叉关系。 在此处输入图片描述 如何解决这个问题？

\结束{tikzpicture}

我尝试了 PGFplots 包，使用以下代码：

    \begin{tikzpicture}
    \begin{axis}[
      axis lines=center,
      plot box ratio={1}{1}{1},
      view={60}{45},
      samples=2,
      domain=-1:1,
      ]
    \addplot3[surf,opacity=0.5]{x+y};                
    \addplot3[surf,opacity=0.5]{y};   
    \addplot3[surf,opacity=0.5]{x};                 
    \end{axis}
    \end{tikzpicture}

画平面虽然比较容易，但是表达相交关系的能力还不够。

答案1

一种方法是将平面分成几部分，然后从后到前绘制它们（或使用图层）。像这样：

\documentclass[border=2mm]{standalone}
\usepackage    {tikz}
\usetikzlibrary{3d}


\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,x={(-0.8562cm,-0.3116cm)},y={(0.5166cm,-0.5166cm)},z={(0cm,0.7975cm)}]
  \def\op{1}
  \draw[fill=red!50,  fill opacity=\op] ( 0,-1,-1) -- ( 0,0,-1) -- (0,0,0) -- ( 0,-1,0) -- cycle; % It doesn't show
  \draw[fill=green!50,fill opacity=\op] (-1, 0,-1) -- ( 1,0,-1) -- (1,0,0) -- (-1, 0,0) -- cycle;
  \draw[fill=red!50,  fill opacity=\op] ( 0, 1,-1) -- ( 0,0,-1) -- (0,0,0) -- ( 0, 1,0) -- cycle;
  \draw[fill=blue!50, fill opacity=\op] (-1,-1, 0) -- (-1,1, 0) -- (1,1,0) -- ( 1,-1,0) -- cycle;
  \draw[fill=red!50,  fill opacity=\op] ( 0,-1, 0) -- ( 0,0, 0) -- (0,0,1) -- ( 0,-1,1) -- cycle; 
  \draw[fill=green!50,fill opacity=\op] (-1, 0, 0) -- ( 1,0, 0) -- (1,0,1) -- (-1, 0,1) -- cycle;  
  \draw[fill=red!50,  fill opacity=\op] ( 0, 1, 0) -- ( 0,0, 0) -- (0,0,1) -- ( 0, 1,1) -- cycle;  
\end{tikzpicture}

\begin{tikzpicture}[line cap=round,line join=round,x={(-0.8562cm,-0.3116cm)},y={(0.5166cm,-0.5166cm)},z={(0cm,0.7975cm)}]
  \def\op{0.8}
  \draw[fill=red!50,  fill opacity=\op] ( 0,-1,-1) -- ( 0,0,-1) -- (0,0,0) -- ( 0,-1,0) -- cycle;
  \draw[fill=green!50,fill opacity=\op] (-1, 0,-1) -- ( 1,0,-1) -- (1,0,0) -- (-1, 0,0) -- cycle;
  \draw[fill=red!50,  fill opacity=\op] ( 0, 1,-1) -- ( 0,0,-1) -- (0,0,0) -- ( 0, 1,0) -- cycle;
  \draw[fill=blue!50, fill opacity=\op] (-1,-1, 0) -- (-1,1, 0) -- (1,1,0) -- ( 1,-1,0) -- cycle;
  \draw[fill=red!50,  fill opacity=\op] ( 0,-1, 0) -- ( 0,0, 0) -- (0,0,1) -- ( 0,-1,1) -- cycle; 
  \draw[fill=green!50,fill opacity=\op] (-1, 0, 0) -- ( 1,0, 0) -- (1,0,1) -- (-1, 0,1) -- cycle;  
  \draw[fill=red!50,  fill opacity=\op] ( 0, 1, 0) -- ( 0,0, 0) -- (0,0,1) -- ( 0, 1,1) -- cycle;  
\end{tikzpicture}
\end{document}

该绘图有两个图形，具有不同的不透明度值： 在此处输入图片描述

答案2

pst-solide3d我粗略地解决了这个问题，使用提供名为的函数的包fusion可以解决交叉问题，但仍然留有一些奇怪的错误。


\documentclass{article}
\usepackage[dvipsnames]{pstricks}
\usepackage{pst-solides3d}
\pagestyle{empty}

\begin{document}

\newcommand\hjpunit{0.3cm}
\newcommand\hjpcoorsize{(-5,-5)(5,5)}
\newcommand\hjpplancolor{gray!70}
\newcommand\hjpplinecolor{white}
\newcommand\hjpplinewidth{0.1pt}
\newcommand\hjpngrid{8 8}
\psset{unit=\hjpunit}
.
    \begin{pspicture}(-5,-5)(5,5)%这个没法宏替换，会出问题
        \psset{Decran=10,viewpoint=40 55 40 rtp2xyz, lightsrc=viewpoint}
      \defFunction[algebraic]{Func}(x,y){}{}{(x^0.3)*(y^0.7)}
      \psSolid[object=surface,base=0 18 0 18,function=Func,ngrid=\hjpngrid,
               name=FUNC,action=none]
      % 只要去掉前面的注释,就可以完美运行,添加就运行不了,是一个奇怪的问题
      \psSolid[object=plan,definition=equation,
         args={[1 0 0 0]},% 0.5x+0.7y-10=0
         base=-15 15 -10 10 ,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
         name=PLANE0,action=none]
      \psSolid[object=plan,definition=equation,
         args={[0 1 0 0]},% 0.5x+0.7y-10=0
         base= -10 10 -15 15,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
         name=PLANE1,action=none]
      \psSolid[object=plan,definition=equation,
         args={[0 0 1 0]},% 0.5x+0.7y-10=0
         base=-10 10 -10 10,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
         name=PLANE2,action=none]
        %\psSolid[object=fusion,base=PLANE_s FUNC ]
        \psSolid[object=fusion,base=PLANE0_s PLANE1_s PLANE2_s,linewidth=\hjpplinewidth,linecolor=\hjpplinecolor,fillcolor=blue!20,
      ]
       %\gridIIID[Zmin=-4,Zmax=16](0,16)(0,16)
      \end{pspicture}
.
    \begin{pspicture}(-5,-5)(5,5)
        \psset{Decran=10,viewpoint=35 100 35 rtp2xyz, lightsrc=viewpoint}
        \defFunction[algebraic]{Func}(x,y){}{}{(x^0.3)*(y^0.7)}
        \psSolid[object=surface,base=0 18 0 18,function=Func,ngrid=\hjpngrid,
                 name=FUNC,action=none]
        % 只要去掉前面的注释,就可以完美运行,添加就运行不了,是一个奇怪的问题
        \psSolid[object=plan,definition=equation,
           args={[-1 0 1 -1]},% 0.5x+0.7y-10=0
           base=-15 15 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE0,action=none]
        \psSolid[object=plan,definition=equation,
           args={[1 0 1 -1]},% 0.5x+0.7y-10=0
           base=-15 15 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE1,action=none]
        \psSolid[object=plan,definition=equation,
           args={[0 0 1 -1]},% 0.5x+0.7y-10=0
           base=-15 15 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE2,action=none]
          %\psSolid[object=fusion,base=PLANE_s FUNC ]
          \psSolid[object=fusion,base=PLANE0_s PLANE1_s PLANE2_s,linewidth=\hjpplinewidth,linecolor=\hjpplinecolor,fillcolor=blue!20,
        ]
         %\gridIIID[Zmin=-4,Zmax=16](0,16)(0,16)
        \end{pspicture}
.
    \begin{pspicture}(-5,-5)(5,5)
        \psset{Decran=10,viewpoint=35 120 60 rtp2xyz, lightsrc=viewpoint}
        \defFunction[algebraic]{Func}(x,y){}{}{(x^0.3)*(y^0.7)}
        \psSolid[object=surface,base=0 18 0 18,function=Func,ngrid=\hjpngrid,
                 name=FUNC,action=none]
        % 只要去掉前面的注释,就可以完美运行,添加就运行不了,是一个奇怪的问题
        \psSolid[object=plan,definition=equation,
           args={[-4 0 1 -9]},% 0.5x+0.7y-10=0
           base=-15 15 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE0,action=none](-6,0,0)
        \psSolid[object=plan,definition=equation,
           args={[1.5 0 1 -8]},% 0.5x+0.7y-10=0
           base=-15 15  -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE1,action=none](4,0,0)
        \psSolid[object=plan,definition=equation,
           args={[0 0 1 -1]},% 0.5x+0.7y-10=0
           base=-15 15  -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE2,action=none]
          %\psSolid[object=fusion,base=PLANE_s FUNC ]
          \psSolid[object=fusion,base=PLANE0_s PLANE1_s PLANE2_s,linewidth=\hjpplinewidth,linecolor=\hjpplinecolor,fillcolor=blue!20,
        ]
         %\gridIIID[Zmin=-4,Zmax=16](0,16)(0,16)
        \end{pspicture}
.
    \begin{pspicture}(-5,-5)(5,5)
        \psset{Decran=10,viewpoint=30 65 30 rtp2xyz, lightsrc=viewpoint}
        \defFunction[algebraic]{Func}(x,y){}{}{(x^0.3)*(y^0.7)}
        \psSolid[object=surface,base=0 18 0 18,function=Func,ngrid=\hjpngrid,
                 name=FUNC,action=none]
        % 只要去掉前面的注释,就可以完美运行,添加就运行不了,是一个奇怪的问题
        \psSolid[object=plan,definition=equation,
           args={[1 0 0 6]},% 0.5x+0.7y-10=0
           base=-10 10 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE0,action=none]
        \psSolid[object=plan,definition=equation,
           args={[1 0 0 -6]},% 0.5x+0.7y-10=0
            base=-10 10 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE1,action=none]
        \psSolid[object=plan,definition=equation,
           args={[0 0 1 0]},% 0.5x+0.7y-10=0
           base=-15 15 -5 5,ngrid=\hjpngrid,fillcolor=\hjpplancolor,
           name=PLANE2,action=none]
          %\psSolid[object=fusion,base=PLANE_s FUNC ]
          \psSolid[object=fusion,base=PLANE0_s PLANE1_s PLANE2_s,linewidth=\hjpplinewidth,linecolor=\hjpplinecolor,fillcolor=blue!20,
        ]
         %\gridIIID[Zmin=-4,Zmax=16](0,16)(0,16)
        \end{pspicture}
\end{document}

在此处输入图片描述

在我的代码中，如果我删除这些行，编译器将返回一个错误Error: /undefined in PLANE0_s

        \defFunction[algebraic]{Func}(x,y){}{}{(x^0.3)*(y^0.7)}
        \psSolid[object=surface,base=0 18 0 18,function=Func,ngrid=\hjpngrid,
                 name=FUNC,action=none]

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