Get height of the current box

Question

I'm curious how does \vrule determine the height of the current box?

\documentclass{article}
\usepackage{amsmath}

\[
\Big(
    ~
    \vrule width.7pt
    ~
\Big)
\]

this image was created by stitching together different ones after compiling with each of \Bigg, \Big and \big delimiters.

How can I retentive the height of the current box as a dimension to use for my needs?

In sake of simplicity, lets consider the following: make the same rule with \rule[]{}{} command that has height as a mandatory argument. And I want it to produce the same rule as \vrule width.7pt by setting some kind of arguments that contain dimension of the current box

\rule[<current depth>]{.7pt}{<current height>}

---

But the actual need for that is to draw a curved line using tikz that would have a height of the current box.

this one has been created simply by eyeballing

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\[
\Big(
    \,
    \tikz[overlay]\draw (0,-9pt) to[in=10] (5pt, 16.5pt);
    \hspace{2ex}
\Big)
\]

---

Note:

The main requirement is to avoid saving a chunk of code with the box beforehand. The goal -- make it inline as \vrule does.

Answer 1

It's built in TeX. The command \vrule is a primitive that accepts dimensions specified via keywords

\vrule width <len> height <len> depth <len>

The keywords can appear in any order and even multiple times, the last specification wins.

The command \vrule has another property: it's a horizontal command, meaning that as soon as TeX scans it, it will switch to horizontal mode (making a paragraph) if it was in vertical mode; used in math mode it doesn't switch, but just typesets a rule.

In either case (horizontal or math mode) the \vrule will end up inside a horizontal box (maybe a line of a paragraph) and this is important to answer your question. If the dimensions of a \vrule are underspecified, some defaults are applied:

• the default for width is 0.4pt
• the default for height is the height of the enclosing \hbox
• the default for depth is the depth of the enclosing \hbox

This explains why

$\Bigl(\vrule\Bigr)$

will typeset a rule 0.4pt wide (thick, if you prefer) and as high and deep (above and below the baseline) as the formula, in this case the parentheses. You'd get the same dimensions with

$\Big|\vrule$

These default values are not available, because they're determined at typesetting time, when the user has lost any control on the process.

For your problem, you can measure a box:

\sbox0{Some text you want to measure height and depth of}

will provide the height as \ht0 and the depth as \dp0.

You can also allocate your own box register (it's better if the usage is not occasional): in the preamble you state

\newsavebox{\mybox}

(or whatever unused name you deem fit) and after doing

\sbox\mybox{Some text you want to measure height and depth of}

you can use \ht\mybox and \dp\mybox in any context where lengths are expected, for instance a \dimexpr.

Answer 2

egreg gave excellent explanations regarding \vrule; I won't attempt to duplicate this effort.

With the technique showed here, it is possible to obtain the depth, height and therefore also total height of the part of the formula you are interested in without any additional boxing, but this requires two compilation runs. I propose to do this using the tikzmark TikZ library. (Actually, I don't know how this library is implementated; maybe there is some boxing in this approach, but if so, it is completely automated.)

Beware however that the \tikzmarknode appears as a \mathchoice item in the math list; therefore, the spacing with respect to surrounding math items may be affected. However, you could wrap it inside \mathopen{...} and make it followed by \mathclose{} for instance, in order to adjust the spacing behavior according to the node contents.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc, tikzmark}

\begin{document}

\[
  \tikzmarknode{paren}{\Bigl( \mkern 18mu \Bigr)}
  %
  \begin{tikzpicture}[remember picture, overlay]
    \fill[red] (paren.north) circle[radius=1pt];
    \fill[blue] (paren.south) circle[radius=1pt];

    \draw (paren.south) to[in=10] (paren.north);

    \path let \p{north} = (paren.north),
              \p{base} = (paren.base),
              \p{south} = (paren.south),
              \n{totalheight} = {\y{north} - \y{south}},
              \n{depth} = {\y{base} - \y{south}} in
      \pgfextra{%
        \xdef\parenTotalHeight{\n{totalheight}}%
        \xdef\parenDepth{\n{depth}}%
      };
  \end{tikzpicture}
  %
  \typeout{The total height of the parenthesis is \parenTotalHeight.}% 18.40015pt
  \typeout{The depth of the parenthesis is \parenDepth.}             % 6.70009pt
  %
  \textcolor{green}{%
    \raisebox{-\parenDepth}{%
      \rule{0.4pt}{\parenTotalHeight}%
    }%
  }
\]

\end{document}

Note: since the coordinates are read from the .aux file, it is quite possible to draw the green rule before the parentheses—even use the coordinates immediately after \begin{document}.