Surveyor's azimuthal projection of ocean currents provides highly detailed Antarctic coastline.

Earlier, I cut a map of Antarctica out of a piece of paper, sliced it into 8 sections and then flipped them around 180 degrees so that the outside perimeter became the inside perimeter. It worked okay for a conceptual result but my original map's coastline was not very detailed. Nor was my flip very accurate since I was doing it with paper and scissors. Rick Potvin's Virtual Circumnavigation of Antarctica to Decide if Earth is Global or Flat: Geometry of inversion of Antarctica from island to ice plain

Lo and behold-- this morning after waking up too early and not being able to sleep, I did some surfing on "bubble level" and "flat earth" (working on another idea) and found a surveyor's map that seems to be a highly detailed and accurate version of my previous concept. They used tools more sophisticated than I did and came up with an interesting looking result-- along with the addition of ocean currents to boot. 

I paste their results here only as an initial effort but I now intend to update my updated 1898 Gleason azimuthal projection with the research stations as before  Rick Potvin's Virtual Circumnavigation of Antarctica to Decide if Earth is Global or Flat: Gleason Map Update-- only now with the more accurate coastline of the Antarctic rim. This will have never been done before. I will have been the first to integrate the surveyor's ocean current azimuthal projection WITH the Gleason map AND with the research stations of our modern era. For now, here is the projection with my source links to get started. I'll index this map under "surveyor's projection" for readers' future reference.

Is a flat earth circular?
https://forum.tfes.org/index.php?topic=2349.0

"surveyors" "flat earth" - Google Search
http://www.google.com/search?client=safari&rls=en&q=%22surveyors%22+%22flat+earth%22&ie=UTF-8&oe=UTF-8

Earth Ocean Currents | world maps with constant-scale natural boundaries
http://rightbasicbuilding.com/earth-ocean-currents-polar-views/

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UPDATE: I've erased the inner map using a paint program leaving only the the shoreline of the Antarctica Rim of Flat Earth.

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UPDATE: Here's a poor quality but conceptually interesting overlay of the 1895 Gleason map with my updated station locations combined with the surveyor's map.

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Here's an earlier non-labelled rim map I found somewhere-- sorry about not sourcing it exactly-- it's commonly popping up on flat earth searches. It compares favorably with my new find of the surveyor's map above although the new one does seem to have much more detail.