# Shear transform a “box”

Using the graphicx package, I can make any arbitrary box rotated using the \rotatebox{...}{...} command. Is there a comparable command in any package that lets me shear a box, i.e., producing a kind of general slanting?

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With a slightly more recent pdfTeX than in David's answer, you can more directly do affine transforms using \pdfsetmatrix. I don't claim to know anything about this, but here is roughly what graphicx does under the hood in \rotatebox (with a different matrix, of course).

\documentclass{article}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][.5]
{%
\mbox
{%
\sbox{\foobox}{#2}%
\hskip\wd\foobox
\pdfsave
\pdfsetmatrix{1 0 #1 1}%
\llap{\usebox{\foobox}}%
\pdfrestore
}%
}
\begin{document}
\slantbox{Hello, world!}

\slantbox[-2]{Hello, world!}
\slantbox[-1]{Hello, world!}
\slantbox[-.8]{Hello, world!}
\slantbox[-.6]{Hello, world!}
\slantbox[-.4]{Hello, world!}
\slantbox[-.2]{Hello, world!}

\slantbox[.2]{Hello, world!}
\slantbox[.4]{Hello, world!}
\slantbox[.6]{Hello, world!}
\slantbox[.8]{Hello, world!}
\slantbox[1]{Hello, world!}
\slantbox[2]{Hello, world!}

\end{document}


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Do we want this for LaTeX3? It should be pretty easy to code as I've already got the basics sorted. –  Joseph Wright Jul 13 '12 at 17:10
I'm still a bit confused. How do those four numbers correspond to a transformation matrix? Is it just a list of elements of the matrix left to right, row by row? Would \slantbox[0]{} amount to the identity transformation? –  Seamus Jul 13 '12 at 17:15
@Seamus: yes, the four numbers 1, 0, #1, and 1 are the entries in the 2×2 matrix defining the linear transformation. David's answer with \pdfliteral allows arbitrary affine transformation (so the 4 coefficients for the linear part, and 2 coefficients for the offset, I think). –  Bruno Le Floch Jul 13 '12 at 17:47
@Joseph: I was thinking of it (I didn't upvote your comment, so at least one other person would like that), but I'm not sure whether we should give \box_linear_transform:Nnnnn for arbitrary parameters, or \box_vertical_shear:Nn and \box_horizontal_shear:Nn, or... –  Bruno Le Floch Jul 13 '12 at 17:59
@BrunoLeFloch If we provide a mechanism here, we should have the 'general case' shear, something like \box_shear:Nnn or even as you say a totally-general transformation (\box_affine:Nnnnn?). One for LaTeX-L –  Joseph Wright Jul 13 '12 at 18:40

You can mess with the coordinate matrix, but at your own risk...

\documentclass{article}

\begin{document}

ABC\pdfliteral{ q 2 0.1 0.6 .4 0 0 cm}\rlap{XYZ}\pdfliteral{ Q}

\end{document}

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q (\pdfsave) and Q (\pdfrestore) should be used at the same place. Otherwise the coordinate system of TeX and its output device get indeed messed up. –  Heiko Oberdiek Jun 19 '14 at 15:36
@HeikoOberdiek ah yes I wrote some driver graphics back end files once, clearly I forgot everything, I'll add an rlap.... –  David Carlisle Jun 19 '14 at 15:49

Shear transforms can be decomposed into scalings and rotations.

% \hshearbox{vertical_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial vertical downscale is often necessary for a 3d projection
\newcommand{\hshearbox}[3]{\scalebox{0.866025}[#2]{\rotatebox{210}%
{\scalebox{1.73205}[-0.57735]{\rotatebox{60}{\scalebox{-1.1547}[#1]{#3}}}}}}
% \vshearbox{horizontal_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial horizontal downscale is often necessary for a 3d projection
\newcommand{\vshearbox}[3]{\scalebox{#2}[0.866025]{\rotatebox{210}%
{\scalebox{-0.57735}[1.73205]{\rotatebox{60}{\scalebox{#1}[-1.1547]{#3}}}}}}

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Aha, TikZability opportunity!

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[cm={1,0,1,1,(0,0)}] % Sets the coordinate trafo matrix entries.
\node[transform shape] at (0,0) {ABC};
\end{scope}
\begin{scope}[cm={1,0,-1,1,(0,0)}]
\node[transform shape] at (3,0) {Hello};
\end{scope}
\begin{scope}[cm={1,0,-1,-1,(0,0)}]
\node[transform shape] at (2,2) {World};
\end{scope}
\begin{scope}[cm={1,0,1,-1,(0,0)}]
\node[transform shape] at (1,2) {FOObar?};
\end{scope}
\end{tikzpicture}
\end{document}


You can put into nodes instead of boxes (with less risk :P).

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