集合论 - 应用奇偶规则

Question

有人能帮我为这些图像创建 tikz 图片吗？非常感谢。

我尝试过这个：

\documentclass[tikz,border=3mm]{standalone}

\begin{document}

\def\A{(0.5, 1) .. controls ++(180:-1) and ++(280: 2) .. (2.5, 3) .. controls ++(280:-1) and ++(170: -.5) .. (.5, 3) .. controls ++(170: 1) and ++(180: 1) .. (0.5, 1);}
\def\B{(1.5, 2) .. controls ++(150:-2) and ++(280: 1) .. ( 4.5, 2.5) .. controls ++(280:-1) and ++(180:-1) .. ( 3, 4) .. controls ++(180: 1) and ++(175:-1) .. (1, 4.5) .. controls ++(175: 1) and ++(150: 1) .. (1.5,2);}
\def\R{(-1,0) rectangle (5,5);}
\begin{tikzpicture}
    \draw[very thick] \R; 
    \begin{scope} \clip \A; 
    \fill[gray] \B; 
    \end{scope} 
    \draw \A; \draw \B; 
\end{tikzpicture}

\end{document}

Answer 1

以下是您可以做的四个例子（您可能会从该起点找到实现其他所有目标的方法）。您已经做得很好了。

\documentclass[tikz,border=3.14mm]{standalone}

\begin{document}
    \def\a{(1,3.5)(2,4.5)(3,3.5)(3.5,4)(4,3.5)(3.5,2.5)(4.5,1.5)(4.5,1)(3.5,1)(3.5,2)(1.5,2.5)}
    \def\b{(.5,.5)(1,2)(2.5,3)(2,1)}
    \def\A{plot[smooth cycle,tension=.75] coordinates {\a}}
    \def\B{plot[smooth cycle,tension=1] coordinates {\b}}
        
    \begin{tikzpicture}
        \fill[orange,even odd rule] \A \B;
        \draw[orange!50!black] \A \B;
    \end{tikzpicture}
    
    \begin{tikzpicture}
        \begin{scope}
            \clip \A;
            \fill[orange] \B;
        \end{scope}
        \draw[orange!50!black] \A \B;
    \end{tikzpicture}
    
    \begin{tikzpicture}
        \begin{scope}[even odd rule]
            \clip \A;
            \fill[orange,even odd rule] \A \B;
        \end{scope}
        \draw[orange!50!black] \A \B;
    \end{tikzpicture}

    \begin{tikzpicture}
        \begin{scope}[even odd rule]
            \clip \B;
            \fill[orange,even odd rule] \A \B;
        \end{scope}
        \draw[orange!50!black] \A \B;
    \end{tikzpicture}
    
\end{document}