怎样画出辫子中的“输入-输出”形式？

Question

如何绘制这样的图表？我找不到任何有关包装中的闭合环或杯子和盖子的文档braids。

参考：结和物理，第 4 版，作者：Louis Kauffman。

Answer 1

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture}[ultra thick, xscale=0.5]
\foreach \myy in {3,6,...,12}{
\draw[dashed] (-1,\myy) -- (6,\myy);
}
\draw
(0,6)
arc[radius=1, start angle=180, delta angle=-180]
arc[radius=1, start angle=180, delta angle=180]
-- (4,12)
to[out=90, in=90+50, looseness=1.2] (6,12)
to[out=-90+50, in=90-50, looseness=0.8] (6,3)
to[out=-90-50, in=-90, looseness=1.2] (4,3)
arc[radius=1, start angle=0, delta angle=180]
to[out=-90, in=-90-50, looseness=0.8] (6,2.5)
to[out=90-50, in=-90+50, looseness=1] (6,12.5)
to[out=90+50, in=90, looseness=0.8] (2,12)
arc[radius=1, start angle=0, delta angle=-180]
to[out=90, in=90+50, looseness=0.8] (6,13)
to[out=-90+50, in=90-50, looseness=1.2] (6,2)
to[out=-90-50, in=-90, looseness=0.8] (0,3)
-- cycle;
\draw (1,9) circle[radius=1];
\end{tikzpicture}
\end{document}