我如何用倾斜的平行线填充此区域

Question

我已取得以下成果：

使用以下代码：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (8,0);
  \coordinate (C) at ($(A)!.5!(B)$);
  \coordinate (D) at ($(A)!.5!(C)$);
  \coordinate (E) at ($(B)!.5!(C)$);

  \draw[dashed] (A) -- (B);
  \begin{scope}
  \clip (A) rectangle (8,-8);
  \draw (D) let \p1 = ($(C) - (D)$) in circle ({veclen(\x1,\y1)});
  \end{scope}

  \begin{scope}
  \clip (A) rectangle (8,8);
  \draw (C) let \p1 = ($(B) - (C)$) in circle ({veclen(\x1,\y1)});
  \end{scope}  

  \begin{scope}
  \clip (A) rectangle (8,8);
  \draw (E) let \p1 = ($(B) - (E)$) in circle ({veclen(\x1,\y1)});
  \end{scope}   
\end{tikzpicture}
\end{document} 

现在我要像这样填充区域：

Answer 1

像这样？

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,patterns}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (8,0);
  \draw[pattern=north east lines] let \p1 = ($(B) - (A)$) in (A) arc(180:360:{veclen(\x1,\y1)/4})
  arc(180:0:{veclen(\x1,\y1)/4}) arc(0:180:{veclen(\x1,\y1)/2});
  \draw[dashed] (A) -- (B);
\end{tikzpicture}
\end{document} 

或者

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (8,0);
  \draw[pattern=north east lines] (A) 
  arc(180:360:2)  arc(180:0:2) arc(0:180:4);
  \draw[dashed] (A) -- (B);
\end{tikzpicture}
\end{document}