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
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You can mess with the coordinate matrix, but at your own risk...
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Aha, TikZability opportunity!
You can put into nodes instead of boxes (with less risk :P).
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