Is there such a thing as a `\mathrule`? (rounded endcaps)

Question

When I am creating hybrid math glyphs, I will find myself often times stacking \rules about the place. But if you look at a collection of CM math symbols (top row), and compare it to a \rule (2nd row)

\documentclass{article}
\begin{document}
\noindent$+ - = \subset \geq \ni$\\$\rule{2ex}{.3pt}$
\end{document}

you will find that strokes comprising the math glyphs exhibit rounded ends, whereas a rule has flattened ends. At typical size, the difference may be insignificant, but for scaled-up glyphs, it is noticeable.

Is there a version of a \rule, which I jokingly here called \mathrule, that will provide the functionality (even the syntax) of a \rule, but with rounded endcaps? (preferably not with tikz, but something more native).

I've considered stretching and squeezing, for example, a minus sign, but that will result in spherical end caps becoming elliptical, especially when the distortion is large.

---

I was going to put this attempt up to get the ball rolling, but Herbert beat me to it. I'll still leave it here as food for thought.

\documentclass{article}
\usepackage{scalerel}
\usepackage{verbatimbox}
\newsavebox\clippedbullet
\sbox{\clippedbullet}{\addvbuffer[.0pt -.55pt]{$\bullet$}}
\def\CB{\usebox{\clippedbullet}}
\newcommand\mathrule[3][0pt]{%
\raisebox{#1}{\scaleleftright{\kern-.8pt\CB\kern-2.5pt}%
  {\rule{#2-#3}{#3}}{\kern-2.4pt\CB\kern+.0pt}}%
}
\begin{document}
\noindent\mathrule[2pt]{2ex}{.5pt} \mathrule{3ex}{1pt} \mathrule[-1pt]{2ex}{2pt}\\
\rule[2pt]{2ex}{.5pt} \rule{3ex}{1pt} \rule[-1pt]{2ex}{2pt}
\end{document}

Answer 1

\pdfcompresslevel=0 %%% to see how it works in the pdf code
\pdfcompresslevel=0
\documentclass{article}
\parindent=0pt
\makeatletter
\def\mathrule#1#2{%
  \@tempdima=\dimexpr#1-0.5#2
  \@tempdimb=#2
  \@tempdimc=0.5#2
  \hbox to #1{%
    \pdfliteral{ 
      q []0 d 
      1 J %  set line cap to rounded ends
      \strip@pt\@tempdimb\space w \strip@pt\@tempdimc\space 0 m 
      \strip@pt\@tempdima\space 0 l S Q }}}
\makeatletter

\begin{document}
x\mathrule{60bp}{2bp}x

x$\rule{60bp}{2bp}$x
\end{document}

Answer 2

I am posting this as the final result of taking Herbert's solution where I wanted it, which is a drop in replacement for \rule that provides rounded line caps. Herbert deserves the credit and will get the points, but others (like me) might wish to see/use this more seamless drop-in for \rule.

Herbert's solution needed to be placed into an hbox, as he allowed, but it needed substantially more adjustments, as well. The horizontal and vertical kernings were offset relative to that box, the vertical alignment of the rounded rule differed from that of a \rule, just to name a few.

EDIT: I've also taken the initiative to force \mathrule to make a rule with the rounded endcaps on side/side or else the top/bottom, depending on which dimension is larger, such that

\mathrule{2ex}{2ex}
\mathrule{3ex}{2ex}
\mathrule{2ex}{3ex}

gives

In my MWE below, I put the final result through the paces of placing the \mathrule on a line by itself, placing it amongst text, stacking it, as well as \fboxing it, in all cases comparing to its equivalent \rule. The \mystery@factor in this MWE was later resolved by Dan in his comment. His correction is incorporated into the style file roundrule.sty that I present at the end of this answer.

\pdfcompresslevel=0 %%% to see how it works in the pdf code
\documentclass{article}
\usepackage{graphicx}
\usepackage{stackengine}% Used for testing; not needed for \math(v)rule's
\parindent=0pt
\makeatletter

\newcommand\mathrule[3][0pt]{%
  \ifdim#2>#3\math@hrule[#1]{#2}{#3}\else\math@vrule[#1]{#2}{#3}\fi}

\newcommand\math@hrule[3][0pt]{%
  \gdef\mystery@factor{0.07}%
 \@tempdima=#3%
  \rule[#1]{0pt}{#3}% Needed to account for .5\@tempdima vertical offset of rounded rule
  \raisebox{.5\@tempdima+#1}{%
    \makebox[#2][l]{\kern-.5\@tempdima\@@mathrule{#2}{#3}}}%
}

\newcommand\math@vrule[3][0pt]{%
  \gdef\mystery@factor{0.0}%
 \@tempdima=#2%
  \rule[#1]{0pt}{#3}% Needed to account for .5\@tempdima vertical offset of rounded rule
  \raisebox{-.0\@tempdima+#1}{%
    \kern0.5\@tempdima%
    \rotatebox{90}{\kern-0.5\@tempdima\makebox[#3][l]{\@@mathrule{#3}{#2}}}%
    \kern0.5\@tempdima}%
}

\def\@@mathrule#1#2{%
  \@tempdimb=#2%
  \@tempdima=\dimexpr#1-\mystery@factor\@tempdimb%Why 0.07 for \math@hrule?
  \pdfliteral{%
    q []0 d %
    1 J %  set line cap to rounded ends
    \strip@pt\@tempdimb\space w \strip@pt\@tempdimb\space 0 m %
    \strip@pt\@tempdima\space 0 l S Q }}
\makeatother
\begin{document}
\mathrule{60bp}{1bp}\par
\rule{60bp}{1bp}\par
x\mathrule[-1pt]{20bp}{1bp}x\mathrule{20bp}{1bp}x\par
x\rule[-1pt]{20bp}{1bp}x\rule{20bp}{1bp}x\par
\stackunder[2pt]{\rule{60bp}{3bp}}{\mathrule{60bp}{3bp}}\par
\fbox{\mathrule[-1ex]{4ex}{.5ex}}\fbox{\rule[-1ex]{4ex}{.5ex}}\par
\fbox{\mathrule[+1ex]{4ex}{.5ex}}\fbox{\rule[+1ex]{4ex}{.5ex}}\par
\clearpage
\mathrule{1bp}{60bp} \rule{1bp}{60bp}\par
x\mathrule[-1pt]{1bp}{20bp}x\mathrule{1bp}{20bp}x%
  \rule[-1pt]{1bp}{20bp}x\rule{1bp}{20bp}x\par
x\rule[-1pt]{1bp}{20bp}x\rule{1bp}{20bp}x\par
\stackunder[2pt]{\rule{3bp}{10bp}\mathrule{3bp}{10bp}}%
  {\mathrule{3bp}{10bp}\rule{3bp}{10bp}}\par
\fbox{\mathrule[-1ex]{.5ex}{4ex}}\fbox{\rule[-1ex]{.5ex}{4ex}}\par
\fbox{\mathrule[+1ex]{.5ex}{4ex}}\fbox{\rule[+1ex]{.5ex}{4ex}}\par
\end{document}

For those interested in an ad hoc package (and taking azetina's renaming suggestion since it functions outside of math mode), here is roundrule.sty, introducing the macro \roundrule[]{}{}. And thanks to Dan for resolving and eliminating the mystery factor. Of course, \roundrules can be used in text mode without the use of dollar delimiters. Feel free to \let\rrule\roundrule in your preamble, if you get tired of typing the long name.

EDITED to require package calc as well.

\ProvidesPackage{roundrule}
[2014/05/01 V1.01 Provides rules with rounded endcaps]
%
% THIS MATERIAL IS SUBJECT TO THE LaTeX Project Public License
%
% Special thanks to users Herbert and Prof. Dan Luecking at tex.stackexchange.com:
% http://tex.stackexchange.com/questions/161297/
%        is-there-such-a-thing-as-a-mathrule-rounded-endcaps
%
% V1.00 - initial release
% V1.01 - require package calc, which was omitted as an oversight.

\pdfcompresslevel=0 %%% to see how it works in the pdf code
\RequirePackage{graphicx}
\RequirePackage{calc}

\newcommand\roundrule[3][0pt]{%
  \ifdim#2>#3\round@hrule[#1]{#2}{#3}\else\round@vrule[#1]{#2}{#3}\fi}

\newcommand\round@hrule[3][0pt]{%
  \@tempdima=#3%
  \rule[#1]{0pt}{#3}% Needed to account for .5\@tempdima vertical offset of rounded rule
  \raisebox{.5\@tempdima+#1}{%
    \makebox[#2][l]{\kern-.5\@tempdima\@@roundrule{#2}{#3}}}%
}

\newcommand\round@vrule[3][0pt]{%
  \@tempdima=#2%
  \rule[#1]{0pt}{#3}% Needed to account for .5\@tempdima vertical offset of rounded rule
  \raisebox{-.0\@tempdima+#1}{%
    \kern0.5\@tempdima%
    \rotatebox{90}{\kern-0.5\@tempdima\makebox[#3][l]{\@@roundrule{#3}{#2}}}%
    \kern0.5\@tempdima}%
}

\def\@@roundrule#1#2{%
  \@tempdima=#1%
  \@tempdimb=#2%
  \@tempdima=0.996264\@tempdima% LaTeX to PDF point conversion (72/72.27)
  \@tempdimb=0.996264\@tempdimb% LaTeX to PDF point conversion (72/72.27)
  \pdfliteral{%
    q []0 d %
    1 J %  set line cap to rounded ends
    \strip@pt\@tempdimb\space w \strip@pt\@tempdimb\space 0 m %
    \strip@pt\@tempdima\space 0 l S Q }}

\endinput