\documentclass{article}
\def\version{1.0}
\parskip 1em
\parindent 0em
\newcommand\rl{\rule{3em}{0in}}
\usepackage{scalerel}
\usepackage{verbatim}

\begin{document}
\begin{center}
\LARGE The \textsf{scalerel} Package\\
\rule{0em}{.7em}\small Routines for constrained scaling and stretching
of objects, either relative to a reference object or in absolute terms\\
\rule{0em}{2.7em}\large Steven B. Segletes\\
steven.b.segletes.civ@mail.mil\\
\rule{0em}{1.7em}\today\\
v\version
\end{center}

\section{Commands and Description}
The \textsf{scalerel} package is used to scale and vertically stretch
objects, either relative to other objects, or in absolute terms.  Its
commands may be invoked in either math mode or text mode (if there is no
math in the objects to manipulate); however, the objects it manipulates
will, by default, be processed in math mode.  Nonetheless, one may
process the objects in text mode (assuming they do not contain
math-specific characters or commands) by specifying arguments as
\verb|{$object$}|, instead of the usual \verb|{object}|.

There are four basic commands with the \textsf{scalerel} package, two
of which have star variants:
\begin{verbatim}
  \scalerel[*][max_width]{object}{reference}
  \stretchrel[*][min_aspect]{object}{reference}
  \scaleto[max_width]{object}{height}
  \stretchto[min_aspect]{object}{height}
\end{verbatim} 
In all cases, \verb|object| is the object to be scaled or vertically
stretched.  It can be as simple as a symbol, like a summation sign
($\sum$), or it can be an object of complex description.  Likewise, in
cases of \textit{relative} scaling and stretching, \verb|reference| is
the reference object in relation to which the manipulated
\verb|object| is scaled or vertically stretched.  The \verb|reference|
may likewise be of complex description (such as a mathematical
expression).  When an \verb|object| is scaled or stretched
\textit{relative} to a \verb|reference| object, it is also vertically
shifted, if necessary, so that its vertical extent conforms to that of
the \verb|reference| object.

In cases of scaling or stretching \textit{to} a specified size,
\verb|height| will the final vertical height of \verb|object| following
a scale or stretch manipulation.  Since scaling or stretching to an
absolute size provides no \verb|reference| object, the baseline of
manipulated \verb|object| remains unchanged.

In cases of scaling (relative or absolute), the constraint
\verb|max_width| is optionally specified as the maximum width allowable
for the manipulated object.  If the manipulated width would otherwise
exceed this limit, the
\verb|object| width is scaled back to this limit.  If the \verb|object|
width is scaled back, its aspect ratio will change with respect to its
original shape.

By definition, vertical stretching will change the aspect ratio of an
object.  In the case of stretching (relative or absolute), the
constraint \verb|min_aspect| is the minimum aspect ratio allowed by the
stretch.  Its value is given in \%, such that a parameter value of
\texttt{100} indicates 100\% or an aspect ratio of 1.  If the stretch
would otherwise cause the manipulated \verb|object|'s aspect ratio to
fall below this value, the width of the manipulated \verb|object| is
increased to meet this minimum threshold.  The value of
\verb|min_aspect| must be an integer.

Because \textit{relative} scaling or stretching is done
\textit{relative} to a reference object, the \verb|\scalerel| and
\verb|\stretchrel| commands will, by default, print out the
manipulated \verb|object| followed immediately by the \verb|reference|
object.  Because this may not always be desired, the star (*) version of
these commands suppresses the output of the \verb|reference| object, so
that only the \verb|object| that was manipulated is output.

\section{Examples}

Now for a few examples.  Let us define
\begin{verbatim}
    \def\preblob{\displaystyle\sum_{i=0}^3}
    \def\blob{\displaystyle\frac{\displaystyle\frac{x^3}{z+r^3}}%
              {\displaystyle\frac{y}{x^2}}%
    }
\end{verbatim}
    \def\preblob{\displaystyle\sum_{i=0}^3}
    \def\blob{\displaystyle\frac{\displaystyle\frac{x^3}{z+r^3}}%
              {\displaystyle\frac{y}{x^2}}%
    }
Here are the raw definitions of \verb|$\preblob\blob$|, unscaled:

    \rl$\preblob\blob$

\subsection{The $\backslash$\texttt{scalerel} Command}

Now we employ \verb|$\scalerel{\preblob}{\blob}$|

    \rl$\scalerel{\preblob}{\blob}$

If we wish constrain the width of the summation to 3ex, we employ\\
\verb|$\scalerel[3ex]{\preblob}{\blob}$|

    \rl$\scalerel[3ex]{\preblob}{\blob}$

Of course, if the manipulated object contains text symbols, a width
constraint will change their aspect ratio, which may not be desirable.

Now let's say you wanted to introduce notation to bound mathematical
expressions by triangles. After defining
\verb|\blob| as before, you could use\\
\verb|$\scalerel[3ex]{\triangleleft}{\blob}|\\
\verb|\scalerel*[3ex]{\triangleright}{\blob}$|

\rl%
$\scalerel[3ex]{\triangleleft}{\blob}\scalerel*[3ex]{\triangleright}{\blob}$

Here, the second call to \verb|\scalerel| was with the star (\verb|*|)
option, indicating that \verb|\blob| should not be printed out following
the right-hand delimiter.  A less-tall expression would appear in those
same delimiters as

\rl%
$\scalerel[3ex]{\triangleleft}{Q}\scalerel*[3ex]{\triangleright}{Q}$

Because the width limit had not been reached, no horizontal compression
of the object was required.

\subsection{The $\backslash$\texttt{stretchrel} Command}

In its most simple application \verb|\stretchrel| can be used in the
fashion of a \verb|\left\{| in math mode.  While there is no reason to
replace that more efficient usage supplied by \LaTeX{}, it is
nonetheless instructional to see a comparison of 
\verb|$\left\{\blob\right.$| and \verb|$\stretchrel[400]{\{}{\blob}$|, to
see how the aspect-ratio limiting option can be employed to avoid an
overly stretched manipulation:

\rl$\left\{\blob\right.$  ~~~~~ $\stretchrel[400]{\{}{\blob}$

The expression on the right uses a standard \{ character, which has been
vertically stretched, but limited to an aspect ratio of 4.  To use
symbols for which the \verb|\left| nomenclature will not work,
\verb|\stretchrel| provides a viable alternative, as shown in this
stick-figure example:\\
\verb|3m $\stretchrel[500]{\updownarrow\,}|\\
\verb|{\fbox{\rule[-1.8em]{0ex}{4em}Work Table}}$|

\rl3m $\stretchrel[500]{\updownarrow\,}
  {\fbox{\rule[-1.8em]{0ex}{4em}Work Table}}$

or in this use, \verb|$\stretchrel[225]{\int}{\blob} dx$|, of the
stretched integral sign (aspect limited to 2.25):

\rl$\stretchrel[225]{\int}{\blob} dx$


\subsection{Baseline Shifts of \textit{Relative} Scales and Shifts}

It was mentioned that when \verb|\scalerel| and \verb|\stretchrel| are
employed, the manipulated object gets vertically shifted to match the
extent of the reference object.  To see how this works, we provide the
following example, that employs some inline math. and scaling.  

\rl\underline{The baseline is the line that runs under this text}
\fbox{$\scalerel{i}{\blob}$}\underline{\scaleto{i}{43.32pt}}

The first case of the large letter ``i'' was generated with 
\verb|\scalerel|, and so the baseline of the ``i'', normally not a
descending letter, was dropped to conform to the descended reference
equation.  All of this was set in an \verb|\fbox| to show the extent of
the objects.  For comparison, an ``i'' of the samesize was then placed
using a \verb|\scaleto| command, which does not change the baseline of
the original object.

\subsection{The $\backslash$\texttt{scaleto} and
$\backslash$\texttt{stretchto} Commands}

The \verb|\scaleto| and \verb|\stretchto| commands are comparable to the
\verb|\scalerel| and \verb|\stretchrel| commands, except they do not
accept a reference object as their second mandatory argument.  Rather,
they take an absolute height (specified with units).  These commands use
the same optional arguments as \verb|\scalerel| and \verb|\stretchrel|
to constrain the width and/or the aspect ratio, respectively, of the
manipulated object.

As was mentioned in the prior section, a difference between these and
the \textit{relative} commands is that an object's baseline is not
altered with the use of \verb|\scaleto| and \verb|\stretchto|.  Because
there is no reference object employed with these commands, there is no
need for starred (\verb|*|) versions of these commands, which would
otherwise suppress the printing of the reference object.

Examples follow the established pattern established in prior sections.
First, we scale the equation blob used as an example in this
documentation to a vertical extent of 80pt, preserving the original
aspect ratio,

\rl\verb|$\scaleto{\blob}{80pt}$      | $\scaleto{\blob}{80pt}$

Then, we stretch the Greek letter, capital phi, to 60pt, but constrain
the aspect ratio to no less than 1.75.

\rl\verb|$\stretchto[175]{\Phi}{60pt}$      | $\stretchto[175]{\Phi}{80pt}$

\section{Future Development}

It would be relatively straightforward to extend this approach to
horizontal scaling problems.  However, it is not exactly clear to the
author what format is best suited for user needs.  If he gets feedback
in that regard, it will inform him how best to proceed.

\section{Code Listing}

\verbatiminput{scalerel.sty}

\end{document}
