Replacing length registers in expressions

Question

I have some understanding on how to use length registers for calculations. However, I always end up requiring way too many length registers for tasks which could probably be solved better by expressions. How can avoid the use of so many registers?

To make things more precise: I have a MWE, which does what I want:

\documentclass{article}
\usepackage{calc}

\def\cone{CONTENT ONE}
\def\ctwo{CONTENT TWO}

\begin{document}

\newdimen\coneheight
\newdimen\conewidth
\newdimen\ctwoheight
\settoheight{\coneheight}{\cone}
\settowidth{\conewidth}{\cone}
\settoheight{\ctwoheight}{\ctwo}
\newdimen\scaled
\setlength{\scaled}{\dimexpr \numexpr \ctwoheight * \conewidth / \coneheight  \relax sp\relax}
Result: \the\scaled

\end{document}

What I am think of is something like this:

\usepackage{calc}

\def\cone{CONTENT ONE}
\def\ctwo{CONTENT TWO}

\begin{document}

\newdimen\better
\setlength{\better}{\dimexpr \numexpr \heightof{\ctwo} * \widthof{\cone} / \heightof{\cone} \relax sp\relax}
Better: \the\better

\end{document}

but unfortunately this code barks at me in all possible kinds...which I do not understand, since I am actually only replacing length registers by length expressions. Or not?

What am I doing wrong and how can I end up in a more compact expression style which avoids placing all lengths into registers?

Answer 1

\documentclass{article}
\usepackage{calc}

\newcommand\cone{CONTENT ONE}
\newcommand\ctwo{CONTENT TWO}
\newlength\scaled

\begin{document}

\setlength{\scaled}{\widthof{\cone}*\ratio{\heightof{\ctwo}}{\heightof{\cone}}}

\the\scaled

\end{document}

The output is

76.66681pt

Answer 2

Use temporary box registers to capture the dimensions needed.

In the MWE, I show for comparison both the original approach "Result" of the OP, as well as the revised "Better" approach using box registers.

\documentclass{article}
\usepackage{calc}

\def\cone{CONTENT ONE}
\def\ctwo{CONTENT TWO}

\begin{document}

\newdimen\coneheight
\newdimen\conewidth
\newdimen\ctwoheight
\settoheight{\coneheight}{\cone}
\settowidth{\conewidth}{\cone}
\settoheight{\ctwoheight}{\ctwo}
\newdimen\scaled
\setlength{\scaled}{\dimexpr \numexpr \ctwoheight * \conewidth / \coneheight  \relax sp\relax}
Result: \the\scaled

\sbox0\cone
\sbox2\ctwo
\newdimen\better
\setlength{\better}{\dimexpr \numexpr \ht2 * \wd0 / \ht0 \relax sp\relax}
Better: \the\better

\end{document}

If one wishes to avoid scrogging the temporary box registers, one can create new saveboxes:

\documentclass{article}
\usepackage{calc}

\def\cone{CONTENT ONE}
\def\ctwo{CONTENT TWO}

\begin{document}

\newsavebox\boxone
\newsavebox\boxtwo
\sbox\boxone\cone
\sbox\boxtwo\ctwo
\newdimen\better
\setlength{\better}{\dimexpr \numexpr \ht\boxtwo * \wd\boxone / \ht\boxone \relax sp\relax}
Better: \the\better

\end{document}