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How to map a convex quadrilateral onto a square so that lines would transform into lines?

An illustration for this

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  • $\begingroup$ Do you want it to send the vertices to the vertices? That won't exist for a general convex quadrilateral. $\endgroup$ – user8268 Jan 26 '17 at 17:47
  • $\begingroup$ I used the wrong words for the search before I posted the question. See the answer $\endgroup$ – Alex Jan 26 '17 at 17:50
  • $\begingroup$ I see - if you can't edit the title then at least change the body of your question (that you want a projective, not a conformal map) $\endgroup$ – user8268 Jan 26 '17 at 18:13
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The answer is Patapom's $(u, v) \rightarrow (x, y)$ transform here:
Mapping Irregular Quadrilateral to a Rectangle

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