使用 tqft 绘制共边

Question

我想要绘制如下的共边图：

但可能更复杂。为此，我使用了tqft。但是传入和传出的边界组件应该等距且对齐。我真正想要的是以下内容：

假设有传入边界分量1,2,...,n和传出边界分量1',2', ...,n'（等距且对齐），这些分量的位置是预先固定的；绘制连接边界分量的共边线{1,4}, {2,3,4',5'}, {1',3',6'}等。任何提示都将不胜感激。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{tqft}

\begin{document}
\begin{tikzpicture}
\pic[
  tqft,
  incoming boundary components=2,
  outgoing boundary components=2,
  draw,
  at={(1,0)},
  name=a,
  every outgoing lower boundary component/.style={draw},
  offset=1,
  cobordism height=3cm,
];
\pic[tqft,
     incoming boundary components=2,
     outgoing boundary components=0,
     draw,
     name=b,
         ];
 \pic[tqft,
     incoming boundary components=2,
     outgoing boundary components=0,
     draw,
     at={(4.5,0)},
     name=c,
         ];
\pic[tqft,
     incoming boundary components=0,
     outgoing boundary components=3,
     draw,
     name=d,
     every outgoing lower boundary component/.style={draw},
     at={(0,-1)},
         ];
\pic[tqft,
    incoming boundary components=0,
    outgoing boundary components=1,
    draw,
    name=e,
    every outgoing lower boundary component/.style={draw},
    at={(6.5,-1)},
        ];
 \end{tikzpicture}
\end{document} 

Answer 1

这看起来是 tqft 库的一个非常有用的功能。我已经尝试实现它了，我想知道在将它推送到 CTAN 之前它是否“在野外”有效。您可以从以下位置获取该软件包github，下载文件tqft.dtx并运行tex tqft.dtx以生成包文件。将它们放在 TeX 可以找到的地方，然后尝试以下代码。

\documentclass{standalone}
%\url{https://tex.stackexchange.com/q/312405/86}
\usepackage{tikz}
\usetikzlibrary{tqft}

\begin{document}
\begin{tikzpicture}[
  tqft,
  every outgoing boundary component/.style={fill=blue!50},
  outgoing boundary component 3/.style={fill=none,draw=red},
  every incoming boundary component/.style={fill=green!50},
  every lower boundary component/.style={draw,ultra thick, dashed},
  every upper boundary component/.style={draw,purple},
  cobordism/.style={fill=red!50},
  cobordism edge/.style={draw},
  genus=3,
  hole 2/.style={ultra thick, blue},
  view from=incoming,
  anchor=between incoming 1 and 2
]
\pic[name=a,tqft,
    incoming boundary components=5,
    skip incoming boundary components={2,4},
    outgoing boundary components=7,
    skip outgoing boundary components={2,3,5},
    offset=-.5];

\begin{scope}[every pin edge/.style={<-}]
\foreach \anchor/\ang in {
  hole 1/-90,
  hole 2/90,
  hole 3/-90,
  incoming boundary 3/90,
  outgoing boundary 4/-90,
  between last incoming and last outgoing/0,
  between first incoming and first outgoing/180,
  between incoming 1 and 3/90,
  between outgoing 1 and 4/-90,
  between outgoing 4 and 6/-90
} {
  \node[pin=\ang:\anchor,at=(a-\anchor),inner sep=0pt] {};
}
\draw[<-] (0,0) -- ++(0,3);
\end{scope}
\end{tikzpicture}
\end{document}

上面演示了两个新的键：

• skip incoming boundary components={2,4}
• skip outgoing boundary components={2,3,5}

对于这两组边界组件，组件数量（由incoming boundary components=5和设定outgoing boundary components=7）决定了可用的边界槽总数。然后，新键会指定要忽略哪些槽。因此，在上述共边系统中，实际上只有 3 个传入边界组件，因为第 2 个和第 4 个被忽略了。请注意，锚点是根据间隙定义的，因此边界组件被标记为1、3和5。

上述代码生成了下图。

欢迎评论、提出错误和功能请求 - 可以在这里或在 github 上。

---

为了完整起见，这里是我对您的原始图片的渲染，其中所有边界组件均已对齐。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,tqft}
\usepackage{tqft}

\tikzset{
  tqft/use nodes=false,
}

\begin{document}

\begin{tikzpicture}[
  tqft,
  every outgoing boundary component/.style={fill=blue!50},
  outgoing boundary component 3/.style={fill=none,draw=red},
  every incoming boundary component/.style={fill=green!50},
  every lower boundary component/.style={draw,ultra thick, dashed},
  every upper boundary component/.style={draw,purple},
  cobordism/.style={fill=red!50},
  cobordism edge/.style={draw},
  view from=incoming,
  cobordism height=4cm,
]
\begin{scope}[every node/.style={rotate=90}]
\pic[name=a,
  tqft,
  incoming boundary components=3,
  skip incoming boundary components=2,
  outgoing boundary components=0
  ];
\pic[name=b,
  tqft,
  incoming boundary components=3,
  skip incoming boundary components=2,
  outgoing boundary components=3,
  skip outgoing boundary components=2,
  offset=1,
  anchor=incoming boundary 1,
  at=(a-incoming boundary 2)
];
\pic[name=c,
  tqft,
  incoming boundary components=2,
  outgoing boundary components=0,
  anchor={(0,0)},
  at=(b-incoming boundary 3)
];
\pic[name=d,
  tqft,
  incoming boundary components=0,
  outgoing boundary components=4,
  skip outgoing boundary components=3,
  at=(a-incoming boundary 1)
];
\pic[name=e,
  tqft,
  incoming boundary components=0,
  outgoing boundary components=1,
  at=(c-incoming boundary 2)
];
\end{scope}
\end{tikzpicture}

\end{document}