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    $\begingroup$ How is this implemented in Mathematica? $\endgroup$
    – Tyler Durden
    Commented Jul 15, 2018 at 14:06
  • $\begingroup$ @TylerDurden: I only know it has been implemented (perhaps not in Mathematica). I added a link. $\endgroup$
    – Joseph O'Rourke
    Commented Jul 15, 2018 at 14:15
  • $\begingroup$ The Stephenson suffers from the same problem mentioned in my comment to the original question in that it distorts the map in areas of complex perimeters. The "great lakes problem". Eg in the example shown you can see how the gray dot is distorted. In a map projection this point should be relatively close to the coastline, because it is close to the coastline in the geodesic data. You may want to read the question more closely and think about how maps are designed to answer better.. $\endgroup$
    – Tyler Durden
    Commented Jul 15, 2018 at 14:35
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    $\begingroup$ @Tyler Any such mapping would introduce distortion of distances. Conformal maps have the nice property that they still preserve angles. $\endgroup$
    – Henrik Schumacher
    Commented Jul 15, 2018 at 14:40
  • $\begingroup$ @HenrikSchumacher For my purposes, I care most that the distance to the nearest point on the coastline are close to their geodesic distance. The angle to a distant point is not important. $\endgroup$
    – Tyler Durden
    Commented Jul 15, 2018 at 14:43