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I recently came across this new map projection, the Authagraph. It seems pretty interesting and I'd like to play around with it, but I can't seem to find the math for projecting it, short of deriving it from scratch.

Is the math behind the Authagraph documented anywhere online?

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The original implementation by Hajime Narukawa is closed source, so we're not exactly sure how it is drawn.

Here is an open source implementation of a "pseudo-Authagraph" by Marcin Ciura, which is approximate to the original: enter image description here

See C source code for implementation with PROJ.4. (NB. The original link is broken, an archived version is available here.)

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In addition to the one mentioned by Mike T, There is another open source approximation (which I believe is closer to the original) by Justin Haruaki Kunimune described and made available on his blog with code available on github.

Comparison between Kunimune's version (black line) and the original (green)

Comparison between Kunimune's version (black line) and the original (green)

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