Occasionally, I see a question on TeX StackExchange where my first idea is "this can't be possible". Yet there always seems to be a way to do exactly what was asked for in TeX.

Can TeX, in principle, solve any typesetting task, i.e. is it "typeset complete" in the sense that any vector image (potentially with special rendering rules for different sizes (hinting)) can be reproduced in TeX?

P.S.: I know from many posts on this site that TeX is Turing complete, but "typeset completeness" doesn't necessarily follow because screen rendering has nothing to do with computation.

closed as too broad by Werner, Peter Jansson, jubobs, David Carlisle, moewe Feb 28 '14 at 16:34

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    there is an open problem list somewhere on the site for missing things. There are many issues that TeX can't (currently L3 team is attacking most of them) and won't (conscious design decisions or archaic technological limitations) handle. But more importantly if PDF or PS don't allow it you can't typeset it. – percusse Feb 28 '14 at 15:06
  • "But more importantly if PDF or PS don't allow it you can't typeset it." But PDF does support arbitrary vector images, right? – user24664 Feb 28 '14 at 15:12
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    related: Are there any open research problems in the world of TeX?; also see Franks talks »The stony road to complex layout« (2013) and »E-TeX: Guidelines to future TeX extensions --- revisited « (2012, PDF, mp4) – clemens Feb 28 '14 at 15:21
  • This question seems to be too broad, since it depends on what you wish to typeset. If you boil it down to putting a pixel anywhere on the page, then yes, TeX can do it. It may not always be easy to automate, but still doable. So, my short and long answer is "Maybe." – Werner Feb 28 '14 at 15:32