Reading the contents of a box

Question

Is it possible to take a box and retrieve the following information from it:

• A list of all "top level" internal boxes;
• All intervening space (kerns and glue: did I forget another type of space?)?

You might wonder why I want this. The reason is that I would like to be able to write, in a natural manner, a piece of text, but then to place each character inside a TikZ node without changing the spacing. The reason for that is so that I can refer to individual terms in a formula (say, for the purpose of putting arrows between them).

Currently I achieve this by doing the following:

\documentclass{article}
\usepackage{tikz}
\usetikzpackage{chains}
\begin{document}

\tikzstyle{node text}=
 [start chain,
  every node/.append style = {
   on chain, inner sep = 0pt, outer sep = 0pt,
   execute at begin node = \strut}, 
  node distance = 0pt]

\newcommand{\NodeTextCell}[2][]{
 \node [inner sep = 0pt, outer sep = 0pt, #1] (my node)
 \tikz[node text]{
  \foreach \letter [count = \n] in {#2}
   \node (my node*\n) {\letter};
 }
}

\begin{tikzpicture}
 \NodeTextCell{A, {}\otimes{}, B, {}\otimes{}, C}
 \draw (my node*1.north) to[bend left=30] (my node*3.north);
\end{tikzpicture}
\end{document}

That's a little clunky, but I can live with it if necessary. If you can think of a better way to do just this with TikZ, that would also serve as an answer. Thanks!

Answer 1

There are \unhbox and \unvbox to unpack the contents of a box into the current list. Then you would have to go through the list with \lastskip and \lastbox. This is not for the faint of heart, but there are examples of this in Victor Eijkhout's TeX by Topic as well as in the TeXbook.

Answer 2

Luatex has what looks to me like nice support for this, having primitives for traversing over the contents of boxes (which it represents internally using the more general concept of typed nodes).

If you have a smattering of Lua and read the first three chapters and section 4.10 of the Luatex manual, you will know as much as I do about how to use this. Hopefully one of our actual Luatex experts here will be able to say something more substantial. But it looks to me that in Luatex, the answers are:

1. \hboxes are nodes of type hlist, which contain their top-level boxes as their list of contents, with the boxes being the nodes in the list with a box type. Luatex provides an iterator primitive, node.traverse, for this, which has to be a huge improvement over \lastbox;
2. I'm not really clear on how glue is handled in Luatex, but I guess that the intervening space you want is the items of the same list with the glue or kern type (and I am also not sure whether other nodes might have space value). Then node.dimension gives the dimensions of the space.