Is it possible to crop glyphs?

Question

I want to crop \rightarrow so that the head remains but the tail is shorter. The reason I want a short-tailed rightarrow "\shortrightarrow" is because of my ultimate goal: to obtain a double headed arrow with the same width as the original.

In the source2e \rightarrow is defined as follows:

393 \DeclareMathSymbol{\rightarrow}{\mathrel}{symbols}{"21} 

RELATED: Arrow heads on \twoheadrightarrow

With a "\shortrightarrow" I can easily construct the desired double headed rightarrow with the same width as the original. (n.b. \twoheadrightarrow has too small arrow heads; the answer provided in the above RELATED link does not have the same width as the original \rightarrow)

I tried to investigate how \xrightarrow is defined in hopes of being able to modify the code so that I can obtain a short-tailed \rightarrow. Unfortunately I found that the code uses \cleaders to render multiple copies of \relbar, so my investigation ended.

Now I resort to asking the TeX community for advice. Is it possible to crop glyphs?

EDIT: I want to provide an example of how I managed to create a custom \hookrightarrow so that the width is the same as \rightarrow. My ultimate goal is motivated by my recent ability to define \inj. (inj is short for injection; the double headed arrow will be used for surjection 'surj')

\newcommand{\inj}{\mathrel{\mathpalette\inj@{}}}
\newcommand{\inj@}[2]{\sbox0{$\m@th#1\lhook$}\ooalign{%
  $\m@th#1\rightarrow$\cr
  \smash{\fboxrule=0pt\fboxsep=0pt\fcolorbox{red}{white}{$\m@th#1\lhook\kern-.333\wd0$}}}}

Answer 1

Use trimclip:

\documentclass{article}
\usepackage{amsmath,trimclip}

\makeatletter
\newcommand{\tworightarrow}{\mathrel{\text{\two@rightarrow}}}
\newcommand{\two@rightarrow}{%
  \sbox0{$\m@th\rightarrow$}%
  \smash{\rlap{\kern0.1\wd0 \clipbox{{.3\width} {-\height} 0pt {-\height}}{$\m@th\rightarrow$}}}%
  $\m@th\rightarrow$%
}

\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.1pt}% just for the example

\begin{document}

\fbox{$\rightarrow$}

\fbox{$\tworightarrow$}

$a\rightarrow b$

$a\tworightarrow b$

$\tworightarrow \quad \scriptstyle \tworightarrow \quad \scriptscriptstyle \tworightarrow$

\end{document}