Scale a TikZ picture according to current font in math mode

Question

I want to define a simple shape and use it as a binary math operator. This implies that it should scale when used as a subscript (e.g., the same behavior as \bigcirc). My attempts so far led me here:

\documentclass{article}

\usepackage{tikz,amsmath}

\DeclareRobustCommand{\myop}{%
  \mathbin{\text{\tikz \node[circle,draw=black,scale=0.4] () {$r$};}}}

\begin{document}
$A \bigcirc B$ $_{A \bigcirc B}$

$A \myop B$ $_{A \myop B}$
\end{document}

As one can see, the TikZ variant doesn't behave well: in the first case, the shape is smaller than the operands, while it is pretty much of the same height in the second one. Removing the scale, adding some minimum size=0mm,inner sep=0mm, etc. did not change anything to the problem. Hence:

Question: How can I obtain a smooth scaling of the operator?

Answer 1

The problem is that the inner sep and line width do not change with the font. The solution is to define a length that does change proportionately with the font. I chose the height of \mathstrut, but almost anything will do. Also, by drawing the circle separately, you can adjust its size and the size of the contents ($r$) separately.

\documentclass{article}

\newlength{\tempdima}

\usepackage{tikz,amsmath}

\DeclareRobustCommand{\myop}{%
  \mathbin{\text{\settoheight{\tempdima}{\mathstrut}\raisebox{-.3\tempdima}{%
    \tikz{\draw[line width=0.05\tempdima] circle (0.6\tempdima);
    \node[scale=0.8] {$r$};}}}}}

\begin{document}
$A \bigcirc B$ $_{A \bigcirc B}$

$A \myop B$ $_{A \myop B}$
\end{document}