[Tex/LaTex] Small text near arrow tips

arrowsdecorationspgf-decorationstikz-arrowstikz-pgf

How can I add some tiny text near arrow tips?

Details

I have an automaton like

Now I want each edge to have the usual arrow tip, and close to the tip additionally a tiny text $\tau$. How can I do that?

A nice and efficient solution would be great: Automatic positioning in a consistent manner, such that it becomes immediately visibly obvious that all arrows are of the type \underset{\scriptstyle \tau}{\Longrightarrow}. These criteria are more important than the exact positioning, but here's an example (with \tau^*, what I actually need) nevertheless:

enter image description here

Better yet: with some text smaller than \tiny, to set it apart from the other text:

enter image description here

I tried

(s0) edge[bend left] node[pos=0.3] {$a$} node[pos=0.9,swap] {$\tau^*$} (s1)

but nice positioning is very difficult that way.

Minimal example:

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

\begin{document}
\begin{tikzpicture}
\node[state,inner sep=0pt,minimum size=.7cm] at (0,0) (s0) {$s_0$};
\node[state,inner sep=0pt,minimum size=.7cm] at (-1,-1) (s1) {$s_1$};

\path[->] 
 (s0)+(-.5cm,.5cm) edge[bend right,double] (s0)
 (s0) edge[bend left,double] node[pos=0.3, auto] {$a$} (s1)
 (s1) edge[bend left,double] node [auto] {$\epsilon,a$} (s0)
 (s0) edge[loop above,double] node {$\epsilon,a$} (s0)
 (s1) edge[loop below,double] node {$\epsilon,a$} (s1)
 ;
\end{tikzpicture}
\end{document}

Best Answer

Automatic placement is not that easy to do because text is for TikZ simply a rectangular black box. We don’t know where in the text white space is that can be occupied by a line or an arrow tip and we also don’t know where the actual text is. This means that for the same placement options but for different angles (at that point on the path where the node shall be placed) we get very differently appealing results.

One work around is to rotate the nodes along the path so that they are placed the same relatively to the path itself. This is done in example 1 with the transform shape option (which may have disadvantages combined with other options like scale).

Admittedly, this may or may not be hard to read and understand. Example 2 shows nearly the same picture but without transform shape. The most upper-right node has to be raised so that it doesn’t overlap with the arrow tip.

A rather different approach is used in example 3 where the arrow text* key is used that calculates an angle the local coordinate system is rotated. The anchor of the placed node is then set in such a way that this anchor is nearest to the path, meaning that orthogonal to the path all node contents are farther away than this anchor. The circle shape is used to garuantee this (the corners of the un-transformed rectangular shape may protrude into the path again). This doesn’t help though against a big arrow tip.

Of course, if another path or another node is in the way TikZ and the decoration can’t prevent any overlapping.

This is by far not an idea solution but it could be made easier to adjust in certain instances by using arrow text=<optional additional distance>;<optional additional raise>:<optional alternative text> or something in that way.

Code

\documentclass[tikz,convert]{standalone}
\usetikzlibrary{automata,decorations.markings}
\makeatletter
\tikzset{
  arrow text/.style={
    decoration={
      name=markings,
      mark=at position -\pgfkeysvalueof{/tikz/arrow text distance} with {%
        \node[every arrow text node/.try] {$ #1 $};
      }
    },
    postaction=decorate
  },
  arrow text*/.style={
    decoration={
      name=markings,
      mark=at position -\pgfkeysvalueof{/tikz/arrow text distance} with {%
        \pgfinterruptboundingbox
          \pgfnode{coordinate}{center}{}{qrr@arrowtext@origin}{}%
          \pgftransformshift{\pgfpointxy{0}{1}}%
          \pgfnode{coordinate}{center}{}{qrr@arrowtext@down}{}%
        \endpgfinterruptboundingbox
        \begingroup
          \pgftransformreset
          \tikz@scan@one@point\pgfutil@firstofone(qrr@arrowtext@origin)\relax
          \pgf@xa\pgf@x\pgf@ya\pgf@y
          \tikz@scan@one@point\pgfutil@firstofone(qrr@arrowtext@down)\relax
          \advance\pgf@xa-\pgf@x\relax
          \advance\pgf@ya-\pgf@y\relax
          \csname pgfmathatan2\endcsname{+\pgf@xa}{+\pgf@ya}%
          \pgfmath@smuggleone\pgfmathresult
        \endgroup
        \let\qrr@arrowtext@anchor\pgfmathresult
        \node[every arrow text node/.try, anchor/.expanded=\qrr@arrowtext@anchor] {$ #1 $};
      }
    },
    postaction=decorate
  },
  arrow text*/.default={\tau\mkern-2mu^*},
  arrow text/.default={\tau\mkern-2mu^*},
  arrow text distance/.initial=3pt,
  arrow text raise/.style={/pgf/decoration/raise={#1}},
  every arrow text node/.style={font=\scriptsize,inner sep=+0pt,anchor=center},
  arrow text raise=5pt
}
\makeatother
\begin{document}
\begin{tikzpicture}[every arrow text node/.append style={transform shape}]
\node[state,inner sep=0pt,minimum size=.7cm] at (0,0) (s0) {$s_0$};
\node[state,inner sep=0pt,minimum size=.7cm] at (-1,-1) (s1) {$s_1$};

\path[->, every edge/.append style={double, arrow text}] 
                               (s0)+(-.5cm,.5cm) edge[bend right, arrow text distance=10pt]                                  (s0)
                                            (s0) edge[bend left, ]                        node[pos=0.3, auto] {$a$}          (s1)
                                                 edge[loop above,]                        node                {$\epsilon,a$} (s0)
                                            (s1) edge[bend left, arrow text distance=6pt] node[auto]          {$\epsilon,a$} (s0)
                                                 edge[loop below,]                        node                {$\epsilon,a$} (s1)
;
\end{tikzpicture}

\begin{tikzpicture}
\node[state,inner sep=0pt,minimum size=.7cm] at (0,0) (s0) {$s_0$};
\node[state,inner sep=0pt,minimum size=.7cm] at (-1,-1) (s1) {$s_1$};

\path[->, every edge/.append style={double, arrow text}] 
                               (s0)+(-.5cm,.5cm) edge[bend right, arrow text distance=10pt]                                    (s0)
                                            (s0) edge[bend left, ]                          node[pos=0.3, auto] {$a$}          (s1)
                                                 edge[loop above, arrow text raise=10pt]    node                {$\epsilon,a$} (s0)
                                            (s1) edge[bend left,  arrow text distance=6pt]  node[auto]          {$\epsilon,a$} (s0)
                                                 edge[loop below,]                          node                {$\epsilon,a$} (s1)
;
\end{tikzpicture}

\begin{tikzpicture}[
  every arrow text node/.append style={shape=circle},
  arrow text raise=1pt
  ]
\node[state,inner sep=0pt,minimum size=.7cm] at (0,0) (s0) {$s_0$};
\node[state,inner sep=0pt,minimum size=.7cm] at (-1,-1) (s1) {$s_1$};

\path[->, every edge/.append style={double, arrow text*}] 
                               (s0)+(-.5cm,.5cm) edge[bend right, arrow text distance=10pt]                                    (s0)
                                            (s0) edge[bend left, ]                          node[pos=0.3, auto] {$a$}          (s1)
                                                 edge[loop above,]                          node                {$\epsilon,a$} (s0)
                                            (s1) edge[bend left, arrow text distance=6pt]   node[auto]          {$\epsilon,a$} (s0)
                                                 edge[loop below,]                          node                {$\epsilon,a$} (s1)
;
\end{tikzpicture}
\end{document}

Output

Example 1 Example 2 Example 3

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