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在 TikZ 中生成所有 16 种可能的 2 变量阴影维恩图？

tag-icon • tag-icon tikz-pgf diagrams tikzscale venn-diagrams
在 TikZ 中生成所有 16 种可能的 2 变量阴影维恩图？

设P和Q为两个陈述，每个陈述都有两个可能的真值：真（T）或假（F）。这些组成陈述P和Q可以通过 16 种可能的二元连接词连接起来，形成16 个独特的简单复合语句，每一个都可以用维恩图来说明（参见前面的链接）。

我已经看到了几种解决方案在这个问题中生成维恩图，但这些似乎都不容易调整，无法得到 16 个案例中的其他 15 个。实际上，我的问题本质上是 2 变量版本的这个问题。

我正在寻找的解决方案：

理想情况下，你可以通过输入以下内容来获得所需的 TikZ 图形

  • TTTT遮蔽所有 4 个区域
  • FFFF不遮蔽任何区域
  • FTTT遮蔽除交叉路口以外的所有区域
  • TFFF只遮蔽交叉路口
  • TTFF只遮蔽左边的圆圈
  • FFTT遮蔽左圆的补数
  • ETC...

是否有一个 TikZ 算法，可以通过对代码进行简单的调整来生成 16 种可能的维恩图中的任意一种？谢谢您的帮助！

答案1

无需剪辑或奇偶规则：

\documentclass[tikz,border=5]{standalone} 
\tikzset{%
  v 0/.style={fill=white}, v 1/.style={fill=blue!30},
  pics/venn/.style args={#1#2#3#4}{code={%
    \fill [v #1/.try] (-2,-1.5) rectangle (2,1.5);
    \fill [v #2/.try] (90:sin 60) arc (120:-120:1) arc (-60:60:1);
    \fill [v #3/.try] (90:sin 60) arc (60:300:1)   arc (240:120:1);
    \fill [v #4/.try] (90:sin 60) arc (120:240:1)  arc (-60:60:1);
    \draw (-2,-1.5) rectangle (2,1.5)
      (90:sin 60) arc (120:-120:1) arc (-60:60:1)
      arc (60:300:1) arc (240:120:1) -- cycle;
}}}
\pgfmathsetbasenumberlength{4}% <- Very important!
\begin{document} 
\begin{tikzpicture}[x=1em,y=1em]
\foreach \i in {0,...,15}{
  \pgfmathdectobase\n{\i}{2}
  \pic at ({mod(\i, 4)*6}, {-floor(\i/4)*4}) {venn/.expanded=\n};
}
\end{tikzpicture}
\end{document}

在此处输入图片描述

可以按如下方式应用：

\documentclass[border=5]{standalone} 
\usepackage{tikz,array,centernot,amsmath,mathrsfs}
\setlength{\extrarowheight}{2em}
\tikzset{%
  v 0/.style={fill=white}, v 1/.style={fill=blue!30},
  pics/venn/.style args={#1#2#3#4}{code={%
    \fill [v #4/.try] (-2,-1.5) rectangle (2,1.5);
    \fill [v #3/.try] (90:sin 60) arc (120:-120:1) arc (-60:60:1);
    \fill [v #2/.try] (90:sin 60) arc (60:300:1)   arc (240:120:1);
    \fill [v #1/.try] (90:sin 60) arc (120:240:1)  arc (-60:60:1);
    \draw (-2,-1.5) rectangle (2,1.5)
      (90:sin 60) arc (120:-120:1) arc (-60:60:1)
      arc (60:300:1) arc (240:120:1) -- cycle;
}}}
\newcommand\venn[2][]{{\tikz[every venn/.try, #1]\pic{venn/.expanded=#2};}}
\tikzset{every venn/.style={x=1em, y=1em, baseline=-.666ex, 
  v 1/.style={fill=gray}}}
\begin{document} 
$\displaystyle
\begin{array}{|c|c|c|c|}
\hline
\textrm{Truth Table} & \textrm{Venn Diagram} & \textrm{Connective} & \textrm{Connective Name} \\
\hline
FFFF & \venn{0000} & \mathscr{P} \perp \mathscr{Q} & \textrm{Contradiction} \\
FFFT & \venn{0001} & \mathscr{P} \overline{\lor} \mathscr{Q} & \textrm{Nondisjunction (Nor)} \\
FFTF & \venn{0010} & \mathscr{P} \centernot\impliedby \mathscr{Q} & \textrm{Converse Nonimplication} \\[2em]
\hline
\end{array}
$
\end{document}

在此处输入图片描述

以下是 3 变量版本：

\documentclass[tikz,border=5]{standalone} 
\tikzset{v 0/.style={fill=white}, v 1/.style={fill=blue!30},
   venn path 1/.style={insert path={ 
     (90:1/sqrt 3) arc (60:120:1) arc (180:0:1) arc (60:120:1) -- cycle }},
   venn path 2/.style={insert path={ 
     (90:1/sqrt 3) arc (120:180:1) arc (240:180:1) arc (120:60:1) -- cycle }},
   venn path 3/.style={insert path={ 
     (90:1/sqrt 3) arc (120:180:1) arc (240:300:1) arc (0:60:1) -- cycle }},
   pics/venn 3/.style args={#1#2#3#4#5#6#7#8}{code={%
     \fill [v #1] (-2,-2) rectangle (2,2);
     \fill [v #2, rotate=240, venn path 1]; 
     \fill [v #3, rotate=120, venn path 1];  
     \fill [v #4, venn path 1];  
     \fill [v #5, rotate=240, venn path 2];  
     \fill [v #6, rotate=120, venn path 2];  
     \fill [v #7, venn path 2];  
     \fill [v #8, venn path 3];
     \draw (90:1/sqrt 3) circle [radius=1] (210:1/sqrt 3) circle [radius=1]
       (330:1/sqrt 3) circle [radius=1] (-2, -2) rectangle (2,2);
}}}
\pgfmathsetbasenumberlength{8}% Still very important!
\begin{document} 
\begin{tikzpicture}[x=1em,y=1em]
\foreach \i in {0,...,255}{
  \pgfmathdectobase\n{\i}{2}
  \pic at ({mod(\i, 16)*4}, {-floor(\i/16)*4}) {venn 3/.expanded=\n};
}
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

那么你可以删除它(C)，你就完成了

\documentclass{article}
\usepackage{tikz}
\makeatletter
\def\venn@strip#1#2\venn@STOP{\def\venn@next{#1}\gdef\venn@rest{#2}}

\newcommand{\venn}[1]{%
\begin{tikzpicture}[scale=0.2]
\coordinate (A) at (0,0);
\coordinate (B) at (2,0);
\coordinate (S-SE) at (5,-3);
\coordinate (S-NW) at (-3,{sqrt(3)+3});
  \edef\venn@rest{#10000}%
  \foreach \i in {0,...,3} {
  \begin{scope}[even odd rule]
    \expandafter\venn@strip\venn@rest\venn@STOP
    \ifnum\venn@next=1\relax
    \pgfmathparse{Mod(\i,2) == 1 ? "(S-SE) rectangle (S-NW)" : ""}
    \path[clip] \pgfmathresult (A) circle[radius=2];
    \pgfmathparse{Mod(floor(\i/2),2) == 1 ? "(S-SE) rectangle (S-NW)" : ""}
    \path[clip] \pgfmathresult (B) circle[radius=2];
    \pgfmathparse{Mod(floor(\i/4),2) == 1 ? "(S-SE) rectangle (S-NW)" : ""}
    \fill[rounded corners,red] (S-SE) rectangle (S-NW);
    \fi
  \end{scope}
  }
    \draw[ultra thick] (A) circle[radius=2];
    \draw[ultra thick] (B) circle[radius=2];
    \draw[ultra thick,rounded corners] (S-SE) rectangle (S-NW);
\end{tikzpicture}
}

\makeatother

\newcommand{\allvendiagrams}{%
\foreach \j in {0,...,15} {%
  \def\venncode{}%
  \foreach \k in {0,...,3} {%
    \pgfmathparse{Mod(floor(\j/2^\k),2) == 1 ? "\venncode1" : "\venncode0"}%
    \global\let\venncode=\pgfmathresult%
  }
  \venn{\venncode}%
}\par%
}


\begin{document}
\venn{1000}
\venn{0100}
\venn{1100}
\allvendiagrams
\end{document}

在此处输入图片描述

答案3

图中的区域是使用裁剪和填充命令的组合绘制的。每个位位置编码了图中四个无交叉区域之一。这些区域是独立绘制的。

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \def\w{1.35}
  \def\h{1}
  \pgfmathsetmacro\rad{\h*.35}
  \def\sep{.2}
  \pgfmathsetmacro\Ax{\h/2}
  \pgfmathsetmacro\Bx{\w - \h/2}
  \pgfmathsetmacro\My{\h/2}
  \def\vennfill 1#1#2#3#4{%
    \begin{scope}[radius=\rad, even odd rule]
      \ifnum#1=1 %
        \begin{scope}
          \clip
            (0, 0) rectangle (\w, \h)
            (\Ax, \My) circle[]
          ;
          \clip
            (0, 0) rectangle (\w, \h)
            (\Bx, \My) circle[]
          ;
          \fill
            (0, 0) rectangle (\w, \h)
          ;
        \end{scope}
      \fi
      \ifnum#2=1 %
        \begin{scope}
          \clip
            (\Bx, \My) circle[]
          ;
          \fill[even odd rule]
            (\Ax, \My) circle[]
            (\Bx, \My) circle[]
          ;
        \end{scope}
      \fi
      \ifnum#3=1 %
        \begin{scope}
          \clip (\Ax, \My) circle[];
          \fill[even odd rule]
            (\Ax, \My) circle[]
            (\Bx, \My) circle[]
          ;
        \end{scope}
      \fi
      \ifnum#4=1 %
        \clip (\Ax, \My) circle[];
        \clip (\Bx, \My) circle[];
        \fill (\Ax, \My) circle[];
      \fi
    \end{scope}
  }%
  \path[
    venn/.pic={
      \expandafter\expandafter\expandafter\vennfill\tikzpictext
      \draw[radius=\rad]
        (0, 0) rectangle (\w, \h)
        (\h/2, \h/2) circle[]
        (\w-\h/2, \h/2) circle[]
      ;
    }
  ]
    \foreach \r in {0, ..., 3} {
      \foreach \c [evaluate=\c as \bin using bin(\r*4+\c+16)] in {0, ..., 3} {
        (\c*\w + \c*\sep, -\r*\h - \r*\sep)
        pic[fill=red, pic text=\bin] {venn}
      }
    }
  ;
\end{tikzpicture}
\end{document}

结果

答案4

以下是元帖子进行比较。这利用了两条圆形路径的特征buildcycle，我在回答这个问题。

prologues := 3;
outputtemplate := "%j%c.eps";

color venn_color; venn_color = 0.8[blue,white];
vardef venn(expr p, q, r, s) =
  save a, b, c, d, f, u; path a,b,c,d, f[]; u = 1cm;
  f1 = fullcircle scaled 1u shifted -(1/4u,0);
  f2 = fullcircle scaled 1u shifted +(1/4u,0);
  a = buildcycle(reverse f1, f2);
  b = buildcycle(f1 rotatedabout(center f1, 180), f2);
  c = a rotated 180;
  d = unitsquare shifted -(1/2,1/2) xscaled 2u yscaled 1.414u;
  image(unfill d; if p=1: fill d withcolor venn_color;
  unfill a; unfill b; unfill c; fi
  if q=1: fill a withcolor venn_color; fi
  if r=1: fill b withcolor venn_color; fi
  if s=1: fill c withcolor venn_color; fi
  draw a; draw c; draw d;)
enddef;

beginfig(1);
  for i=0 upto 1: for j=0 upto 1: for k=0 upto 1: for l=0 upto 1:
    x0 := 180i+90j; y0 := 120k+60l;
    draw venn(i,j,k,l) shifted z0;
    label(decimal i & decimal j & decimal k & decimal l, z0 shifted 27 down);
  endfor; endfor; endfor; endfor;
endfig;


end.

在此处输入图片描述

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