Fitting Shapes Around Irregular Nodes In TikZ

Question

I have the following Hasse diagram

which uses the following code:

\documentclass[a4paper, 12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{fit}    

\begin{document}

    \begin{figure}[h]
    \centering
    \begin{tikzpicture}
      \node (abc) at (0,4) {$\{a,b,c\}$};
      \node (ab) at (-2,2) {$\{a,b\}$};
      \node (ac) at (0,2) {$\{a,c\}$};
      \node (bc) at (2,2) {$\{b,c\}$};
      \node (a) at (-2,0) {$\{a\}$};
      \node (b) at (0,0) {$\{b\}$};
      \node (c) at (2,0) {$\{c\}$};
      \node (empty) at (0,-2) {$\{\}$};
      \draw (abc) -- (ab) -- (a) -- (empty) -- (c) -- (bc) -- (abc) -- (ac) -- (a)
      (ac) -- (c)
      (b) -- (empty);
      \draw[preaction={draw=white, -,line width=6pt}] (ab) -- (b) -- (bc);
    \end{tikzpicture}
    \label{fig:hasse}
\end{figure}

\end{document}

I am attempting to draw a box around some of the nodes like so:

\documentclass[a4paper, 12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{fit}    

\begin{document}

    \begin{figure}[h]
    \centering
    \begin{tikzpicture}
      \node (abc) at (0,4) {$\{a,b,c\}$};
      \node (ab) at (-2,2) {$\{a,b\}$};
      \node (ac) at (0,2) {$\{a,c\}$};
      \node (bc) at (2,2) {$\{b,c\}$};
      \node (a) at (-2,0) {$\{a\}$};
      \node (b) at (0,0) {$\{b\}$};
      \node (c) at (2,0) {$\{c\}$};
      \node (empty) at (0,-2) {$\{\}$};
      \draw (abc) -- (ab) -- (a) -- (empty) -- (c) -- (bc) -- (abc) -- (ac) -- (a)
      (ac) -- (c)
      (b) -- (empty);
      \draw[preaction={draw=white, -,line width=6pt}] (ab) -- (b) -- (bc);
    \node[draw,dotted,fit=(ab) (a) (b)] {};
    \end{tikzpicture}
    \label{fig:hasse}
\end{figure}

\end{document}

which (unsurprisingly) ends up looking like this:

What I would like (ideally) is to make some round corner triangle that covers the nodes (ab), (a) and (b) such that (ac) remains uncovered. I'm quite new to tikz (though I use tikz-cd a fair amount) so I'm unsure which library would help without overly convoluting the code (several answers I've read I wouldn't be able to adapt for my purposes without explanation).

Any help appreciated, thanks!

Answer 1

You can do it also with tikz-cd.

With execute at end picture={...} you can add any TikZ command you need to execute after drawing you tikzcd.

The crossing over idea is by Sebastiano's deleted answer.

If you don't want to name the matrix you can use \tikzcdmatrixname directly (see this answer by marmot, for example).

To set some options for all the tikzcd of your document, you could use \tikzcdset{...}, see Section 2 Controlling the appearance of diagrams of the package documentation.

The matrix syntax is analogous to any other LaTeX table: & to separate the cells and \\ to separate the rows.

The command \ar is an abbreviation for \arrow. Its options u, d, l and r mean up, down, left and right (the direction of the arrow).

The option execute at end picture={...} allows you to add some TikZ commands to be executed after the drawing of the diagram.

mymatr-n-m is the element at row n and column m of matrix mymatr.

\coordinate (comodo) at (mymatr-2-1.north west |- mymatr-3-1.south west); create the point comodo with coordinate x = the one of mymatr-2-1.north west and coordinate y = the mymatr-3-1.south west.

\draw (A) -- (B); draws a line from A to B.

dashed and rounded corners are options with obviuos meaning.

yshift=... shifts the coordinate vertically, xshift=... horizontally.

cycle at the end tells that the path has to go from here to the starting point.

\documentclass[a4paper,12pt]{article}
\usepackage{tikz-cd}
\tikzcdset{
    every arrow/.append style={dash},
    every diagram/.style={
        row sep=50pt,
        column sep=30pt
        }, 
    }

\begin{document}
\begin{tikzcd}[
    every matrix/.style={name=mymatr},
    execute at end picture={
        \coordinate (comodo) at (mymatr-2-1.north west |- mymatr-3-1.south west); 
        \draw[dashed, rounded corners] ([yshift=3pt]mymatr-2-1.north west) --  ([yshift=-3pt]comodo) -- ([yshift=-3pt, xshift=2pt]mymatr-3-2.south east) -- ([yshift=4pt, xshift=2pt]mymatr-3-2.north east) -- ([yshift=3pt]mymatr-2-1.north east) -- cycle;
        }
    ]
 & \{a,b,c\} \ar[ld] \ar[d] \ar[rd]\\
\{a,b\} \ar[d] & \{a,c\} \ar[ld] \ar[rd] & \{b,c\} \ar[d, crossing over] \ar[ld, crossing over] \\
\{a\} \ar[rd] & \{b\} \ar[lu, crossing over] \ar[d, crossing over] & \{c\} \ar[ld] \\
 & \{\}  
\end{tikzcd}
\end{document}

Answer 2

To be more flexible you can manually draw the path around your desired nodes:

\documentclass[a4paper, 12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{fit}    

\begin{document}

    \begin{figure}[h]
    \centering
    \begin{tikzpicture}
      \node (abc) at (0,4) {$\{a,b,c\}$};
      \node (ab) at (-2,2) {$\{a,b\}$};
      \node (ac) at (0,2) {$\{a,c\}$};
      \node (bc) at (2,2) {$\{b,c\}$};
      \node (a) at (-2,0) {$\{a\}$};
      \node (b) at (0,0) {$\{b\}$};
      \node (c) at (2,0) {$\{c\}$};
      \node (empty) at (0,-2) {$\{\}$};
      \draw (abc) -- (ab) -- (a) -- (empty) -- (c) -- (bc) -- (abc) -- (ac) -- (a)
      (ac) -- (c)
      (b) -- (empty);
      \draw[preaction={draw=white, -,line width=6pt}] (ab) -- (b) -- (bc);
\draw[dotted,rounded corners=20pt] ([yshift=0.9cm]ab.north west) -- ([xshift=-0.15cm,yshift=-0.1cm]a.south west) -- ([xshift=0.7cm,yshift=-0.1cm]b.south east) -- cycle;
    \end{tikzpicture}
    \label{fig:hasse}
\end{figure}

\end{document}