Using Photos of a Sphere to Create a 2D Equirectangular Map?

[Redrobes]

The way you need to go about doing this is to map coords on the real sphere so that you can get your equivalent pixels on the image located in the mapping.

Looking at the reflection of a polished ball bearing is quite similar to taking a panorama. I think its different but less so than you might think. If you have a pretty calibrated setup then you can use maths to map the photos to 2D but its a lot easier to let the computer do it.

There used to be some programs in a suite called Panotools - apparently still available (https://panotools.org/dersch/) where you can take panoramas and stitch them. I have seen that used on ball bearing reflections too.

The way to do if you can only do it approximately without calibration is to take multiple photos and try and set up the UV coords in blender and let it texture map a sphere. Once you have the UV maps all lined up then it can unwrap that texture back to a 2D with a projection.

The other way to do it would be to take zoomed up photos of the sphere rotating it about and using a paint package to stitch the bits together with a bit of warp to get it back to 2D. But thats a bit laborious.

A lot of this depends on how big the original ball is. Is it a globe sized or something much larger or smaller than that.

Edit: I think Waldronate is correct. The bit your missing in understanding is that once you can create a virtual 3D ball textured in blender from photos taken from a real ball such that the virtual ball matches the real ball, then blender knows enough about the texture mapping to unwrap them back to a 2D Mercator style map.