如何在 pgf/tikz 中填充 3 个圆弧的重叠部分？

Question

我有一张如下图所示的图片：

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
  \draw(0,0) -- (4,0) -- (4,4) -- (0,4) -- (0,0);
  \draw(0,0) arc(-90:90:2);
  \draw[dashed](0,0) arc(-90:-270:2);  
  \draw(0,0) arc(180:90:4);
  \draw(0,0) arc(180:90:4);
  \draw[dashed](0,0) arc(-180:90:4);  
  \draw(4,0) arc(-90:-180:4);
  \draw[dashed](4,0) arc(-90:180:4);  
\end{tikzpicture}

\end{document}

现在我想在 3 个圆弧重叠的部分上画阴影，我该怎么做呢？就像这张图一样：

如果我想在 ABC 之间画线，该怎么办？非常感谢！

Answer 1

除了填充线的阴影之外，还有类似这样的填充。您可以在环境\clip内部借助一些帮助进行填充scope。要设置交叉点的坐标，请使用intersections库。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns,intersections}
\begin{document}

\begin{tikzpicture}
  \begin{scope}
    \clip(0,2) circle (2);
    \clip(4,0) circle (4);
    \fill[pattern=north west lines,pattern color=red](4,4) circle (4);
  \end{scope}
  %\draw(0,0) -- (4,0) -- (4,4) -- (0,4) -- (0,0);
  \draw (0,0) rectangle (4,4);
  \draw[name path=left](0,0) arc(-90:90:2);
  \draw[dashed](0,0) arc(-90:-270:2);  
  \draw[name path=lower](0,0) arc(180:90:4);
  %\draw(0,0) arc(180:90:4);
  \draw[dashed](0,0) arc(-180:90:4);  
  \draw[name path=upper](4,0) arc(-90:-180:4);
  \draw[dashed](4,0) arc(-90:180:4);  
  %%
  \path [name intersections={of=lower and upper}];
  \coordinate (A) at (intersection-1);
  \path [name intersections={of=left and upper}];
  \coordinate (B) at (intersection-1);
  \path [name intersections={of=left and lower}];
  \coordinate (C) at (intersection-2);
  %%
  \node[left,red] at (A) {A};
  \node[below,red] at (B) {B};
  \node[above,red] at (C) {C};
  %%
  \fill[blue,fill=blue,opacity=0.3] (A)--(B)--(C)--cycle;
  \draw[blue,thick] (A)--(B)--(C)--cycle;
\end{tikzpicture}

\end{document}