Tiny Planet Algorithm?

So I’ve recently been looking at the Tiny Planet images.

I’ve been googling a few things to try and find out how images are converted from normal to a tiny planet. Some phone apps, as well as photoshop do this.

I think Photoshop does it by converting Cartesian coordinates to Polar coordinates.
I found a good explanation of converting them here.

However, I am yet to find somewhere that describes an algorithm of the process.

Is there a set formula? or is it more complex than that?

I’m not sure if it’s as easy as moving pixels and converting coordinates because I think some form of stretching must be included… hence, looking for an algorithm and this exchange as a resource. Thanks.

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