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    $\begingroup$ You can use this: mathematica.stackexchange.com/q/59463/5478 $\endgroup$
    – Kuba ♦
    Commented Jul 15, 2018 at 7:48
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    $\begingroup$ Show us the code you have already tried, your definitions for maps and shapes and so on. This site is not about algorithms, but about Wolfram Mathematica programming so please edit your question to make it explicitly about programming in Mathematica/Wolfram Language . Include a formatted minimum example of the code you are working on. $\endgroup$
    – rhermans
    Commented Jul 15, 2018 at 9:32
  • $\begingroup$ @Kuba That is interesting, but it is not appropriate for a map transformation because the points move proportionately to the length of the perimeter which results in distortion. For example, in the case of the United States, the area around the great lakes would become gigantic in the projected map due to the longer coastline in that area. $\endgroup$
    – Tyler Durden
    Commented Jul 15, 2018 at 12:42
  • $\begingroup$ @TylerDurden it is hard to avoid distortions here, isn't it? And you only mentioned your preferences somewhere in comments below answers. But yes, I agree it is only a quick start tip rather than full solution. $\endgroup$
    – Kuba ♦
    Commented Jul 16, 2018 at 7:19