*Sphere Projection* uses the [Spherical coordinate system][1]:
- *radial distance* $r$ (or $ρ$) is not used, because it’s a projection,
- *azimuth* $\varphi$ (also known as a [polar coordinate][2]) is translated to $x$ in the texture,
- *inclination* (*elevation*) $θ$ is translated to $y$ in the texture.

[![][3]][3]

There are some [aliasing][4] problems visible on the azimuth seam and from far away in the *Difference* blending, and even when zooming some differences can still be spotted – maybe the algorithm could be improved by e.g. changing the orders of calculations, so the float errors are reduced?

[![][5]][5]

In geometry nodes you don’t have the *Generated* coordinate system, but you don’t need it, and in fact, using the *Object* coordinate system is simpler, because you can remove the first *Vector Math*, which makes sure the center of sphere is in the origin:

[![][6]][6]

[![][7]][7]

[<img src="https://blend-exchange.com/embedImage.png?bid=XsL74JDD" />](https://blend-exchange.com/b/XsL74JDD/)

  [1]: https://en.wikipedia.org/wiki/Spherical_coordinate_system
  [2]: https://en.wikipedia.org/wiki/Polar_coordinate_system
  [3]: https://i.sstatic.net/2tqtF.png
  [4]: https://en.wikipedia.org/wiki/Aliasing
  [5]: https://i.sstatic.net/CAbIn.gif
  [6]: https://i.sstatic.net/hryXn.png
  [7]: https://i.sstatic.net/jgOHt.gif