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What is the formula for the Nicolosi Globular projection?

In other words, what is the function that maps the coordinate (φ, λ) on the sphere to the coordinate (x, y) on the plane?

Example of a Nicolosi Globular projection

You can assume that there are two such functions, one for each of the two hemispheres of the projection, such that the origin (x = 0, y = 0) in both cases is in the center of the given hemisphere.

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  • I was surprised I couldn't find an easy answer to this. Since proj4 recognizes it, the source code does include a conversion routine (github.com/route-me/route-me/blob/master/Proj4/PJ_nocol.c) but it'll require some work to extract a formula from that code. Note: this question crossposted to math.stackexchange.com/questions/1672580/…
    – user1462
    Commented Feb 26, 2016 at 16:32
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    It's in Voxland and Snyder's An Album of Map Projections, p234 (pdf). Because there are 7-8 equations plus references to two other Globular projections, I'm not reproducing here. There's no inverse listed.
    – mkennedy
    Commented Feb 26, 2016 at 18:18
  • There's an alternative version of the forward Nicolosi equations in Fenna's Cartographic Science (2007, ISBN 9780849381690). From that one can work out the inverse for getting the longitude from x and y, but getting the latitude apparently takes an iterative procedure.
    – rschmunk
    Commented Apr 23, 2018 at 3:25

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Not a proper answer, but may help to end up with mapping procedure

Formulas from the book mentioned above by @mkennedy were successfully executed by Torben Jansen on Observable in the article Nicolosi globular projection with the implementation of JavaScript and D3 library.

Moreover, it also includes Nicolosi hemispheres shown with an example.

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