使用 TikZ 实现维恩图中集合之间的交集

Question

我希望集合 P 和 Q 的交集为白色，如附图所示。

我的命令如下：

\documentclass[10pt, a4paper, serif, xcolor = {divpsnames, svgnames}]{beamer}
\usepackage{amsmath, mathtools, mathrsfs, amstext, xfrac}
\usepackage[utf8]{inputenc}
\usepackage[brazil]{babel}
\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}
    \begin{frame}
        \frametitle{}{}
           \begin{figure}
               \centering
                   \begin{tikzpicture}
                       \begin{scope}[fill opacity = .5, text opacity = 1]
            \draw[fill = Green!70!white, even odd rule] (5, -2) rectangle (-3.5, 2) (0:2cm) circle [radius = 1];
            \draw[fill = Green!70!white, draw = black, even odd rule] (0, 0) circle [radius = 1.5];
            \draw[fill = white, draw = black, even odd rule] (0:2cm) circle [radius = 1];
    
                \node at (2, 1.3) (Q) {$Q$};
                \node at (0, 1.7) (P) {$P$};
                \node at (4.7, 1.7) (E) {$E$};
                       \end{scope}
                   \end{tikzpicture}
                       \caption{Representação de $P - Q$.}
                           \label{fig9}
        \end{figure}

    \end{frame}
\end{document}

提前致谢！

Answer 1

简单的方法没有任何魔法，用比背景更深的绿色填充左侧圆圈（集合）的非减法部分，正如您所希望的那样：

\documentclass{standalone}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\fill[Green!35!white, even odd rule]
  (5,-2) rectangle (-3.5,2)
  (0:2cm) circle[radius = 1];
\fill[Green!60!white] (0,0) circle[radius=1.5];
\filldraw[fill=white, draw=black] (0:2cm) circle [radius=1];
\draw[black] (0, 0) circle [radius=1.5];

\node at (2, 1.3) (Q) {$Q$};
\node at (0, 1.7) (P) {$P$};
\node at (4.7, 1.7) (E) {$E$};
\end{tikzpicture}

\end{document}

以下是使用剪切将交叉点填充为白色的另一种方法：

\documentclass{standalone}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\fill[Green!35!white, even odd rule]
  (5,-2) rectangle (-3.5,2)
  (0:2cm) circle [radius=1];
\filldraw[fill=Green!60!white, draw=black] (0,0) circle[radius=1.5];

\begin{scope}
  \clip (0:2cm) circle[radius=1];
  \filldraw[fill=white, draw=black] (0,0) circle[radius=1.5];
\end{scope}

\draw[black] (0:2cm) circle [radius=1];
\node at (2, 1.3) (Q) {$Q$};
\node at (0, 1.7) (P) {$P$};
\node at (4.7, 1.7) (E) {$E$};
\end{tikzpicture}

\end{document}

有了这个，您可以简单地编辑fill=white以用您选择的颜色填充两个集合的交集。

Answer 2

这只是为了好玩，并为您提供一些从各种帖子（当然还有链接）收集的标准技巧。有可能有一个even odd clip和重用路径。不幸的是，通过实现的“官方”版本use path并不总是能满足我们的要求，因此还有reuse path，它允许我们回收之前通过存储在宏中的路径save path。一般来说，这个工具箱可以相当方便地用于绘制任何维恩图，这些工具也收集在实验钛钾Z 库venn，但我在这里没有使用它。使用even odd clip我们可以填充除Q圆圈之外的所有内容。

\documentclass[10pt, a4paper, serif, xcolor = {divpsnames, svgnames}]{beamer}
\usepackage{tikz}
% based on
% https://tex.stackexchange.com/a/38995/121799
% https://tex.stackexchange.com/a/76216
% https://tex.stackexchange.com/a/59168/194703
% https://tex.stackexchange.com/q/448920/194703
\makeatletter 
\tikzset{
  reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}},
  even odd clip/.code={\pgfseteorule}}
\makeatother
\usepackage{amssymb}
\begin{document}
\begin{frame}[t]
\frametitle{Another Venn diagram}
\begin{figure}
 \centering
 \begin{tikzpicture}
  \begin{scope}[fill opacity = .5]
   \draw[save path=\pathE]  (-3.5, -2) rectangle (5, 2);
   \draw[save path=\pathQ]  (0, 0) circle [radius = 1.5];
   \draw[save path=\pathP] (0:2cm) circle [radius = 1];
   \clip[even odd clip,reuse path=\pathP]  (-3.5, -2) -|(5, 2) -| cycle;
   \fill[Green!70!white,use path=\pathE]; 
   \fill[Green!70!white,use path=\pathQ];
  \end{scope}
  \node at (2, 1.3) (Q) {$Q$};
  \node at (0, 1.7) (P) {$P$};
  \path (5, 2)  node[below left](E) {$E$};
 \end{tikzpicture}
 \caption{Representa\c{c}\~ao de $P - Q$.}
 \label{fig9}
\end{figure}
\end{frame}
\end{document}