Invisible text (\phantom) with kerning?

Question

In my answer to another question, I've used an upside-down A as a V-with-strikethrough character. After playing with it a bit, I've realized that this doesn't give appropriate kerning if the character is followed by a subscript, presumably because the A is placed in a rotatebox.

It seems that the best way to get around this is to place the upside-down A in a zero-width box using llap/rlap and then insert an invisible V, so that the same kerning as would be used for a regular V is applied. Unfortunately, if I use \phantom{V}, it seems that result is a box (no kerning).

Is there a \phantom-like function which makes the character invisible/non-selectable but maintains the same kerning?

Edit: I came up with a hack which checks to see whether the following text is subscript, then applies kerning if it is. The key component is

\@ifnextchar_{\kern-0.17em}{} 
     % if the next char is "_", add negative kerning 
     % otherwise, do nothing

And the full \Vol command is then

\makeatletter
\newcommand{\Vol}{\rotatebox[origin=c]{180}{\ensuremath{A}}\@ifnextchar_{\kern-0.17em}{}}
\makeatother

Nonetheless, if there is a more elegant way of keeping the exact kerning from the original V, I'd be interested to hear about it.

Answer 1

You can use an ordinary math-mode V and \put a horizontal line where you need it. It won't scale, but it's easily adjustable.

\newcommand{\Vol}{\rotatebox[origin=c]{180}{\ensuremath{A}}}
\newcommand{\volume}{\put(2,4){\line(1,0){3}}V}

However, the desired symbol is not really an upside-down A, but rather a V with a horizontal strike-through as seen here:

So instead of using \ooalign as in the original solution without subscripts, you can use \rlap as in the macro:

\newcommand{\volsym}{\rlap{\kern.08em--}V}

Then $\volsym_n$ will produce the output

This has the additional advantage of providing the correct spacing to the left of the volume element in the Reynolds transport theorem:

Using \ooalign:

Using \rlap:

The \rlap version will scale with size (\tiny, \large, \Huge, etc.), but a separate macro is needed if the volume symbol appears in a subscript. Even \mathchoice won't work since it separates the choices from the subscript and results in the same bad kerning.

\newcommand{\volsubsym}{\rlap{\scriptsize\kern.08em--}V}

will produce the correct scripted version. So $M_{\volsubsym_n}$ will produce

If (for reasons I cannot imagine) you needed a scriptscript size, you could use

\newcommand{\volsubsubsym}{\rlap{\tiny\kern.08em--}V}

Here is the complete code:

\documentclass{article}

\newcommand{\volume}{\mathop{\ooalign{\hfil$V$\hfil\cr\kern0.08em--\hfil\cr}}\nolimits}

\newcommand{\volsym}{\rlap{\kern.08em--}V}
\newcommand{\volsubsym}{\rlap{\scriptsize\kern.08em--}V}

\newcommand{\dd}{\mathrm{d}}

\begin{document}
\noindent Let $\volume_n$ represent system volume. (using \verb`\ooalign`---bad kerning)  
\newline Let $V_n$ represent system volume. (math V)
\newline Let $\volsym_n$ represent system volume. (using \verb`\rlap`---correct kerning)
\bigskip
\newline As a subscript, $M_{\volsubsym_n}$ renders correctly.

\[
\frac{\dd}{\dd t}\int_{\Omega(t)}\mathbf{f}\,\dd\volume\qquad
\frac{\dd}{\dd t}\int_{\Omega(t)}\mathbf{f}\,\dd\volsym
\]

\end{document}