I would like to resolve pixel X,Y positions, on a Robinson projected map, to lat longs.

I have a found a JavaScript function that can resolve lat longs to pixels - https://github.com/afar/robinson_projection - but I cannot work out (or find an implementation of) pixels to lat longs.

I have found various articles about how Robinson projection works, such as https://simplemaps.com/flash/robinson-projection-in-as3-gpl/

I'm basically stuck at this point - the maths required to work out lat long from pixel X,Y is well beyond my terrible maths ability - and despite reading these things quite a few times, the logic isn't clear to me either.

I assumed the logic is in the d3-geo or d3-geo-projection source code somewhere, but couldn't find anything when searching through it.

Looking at Wikipedia, there is this:

Coordinates of points on a map are computed as follows:

..but I don't really understand how to put it into Javascript, or work out "the central meridian chosen for the map", and even then are these "coordinates" the same as pixel values?

Background info:

I'm trying to make a very lightweight, simple javascript function, that can do lat long to pixel X,Y and vice versa, for both Mercator and Robinson projections - without using d3 etc.. I want it to be less then 2kb minified and gzipped, no deps.

I've got Mercator working OK - there's lot of examples. But still struggling with Robinson projection.

The full code, if it helps, is here: https://github.com/sc0ttj/component/pull/53

(Side note, which may affect the solution I need:

For some reason I had to change latSign = getSign(lat) to latSign = 0-getSign(lat) to get the map to show the right way up, vertically - see https://github.com/sc0ttj/component/pull/53/files#diff-dc34d0b1b3b6f92f7c3e71af717cf56a5f98923980b859c128d793991690ebdcR64.)

I'm shamelessly standing on the shoulders of these two projects:

• https://github.com/nunobaldaia/mercatormap
• https://github.com/afar/robinson_projection