From a brief search on Wikipedia on the meaning of fulldome graphics, I am guessing (and I will love that you show me where I am wrong, as I should be) that it is some kind of texture changes at the surface of a sphere.
For the unwrap problem you are facing, does it help if you used the primitive UV Sphere with its default UV Map, so you do not need to unwrap.
If my answer has no relationship to your question, I would appreciate that you leave an explanation or some link to one about what you mean by Fulldome graphics … Fulldome foootage
You shall use it on your uvmesh. It works there aswell. If I get you right then you have fisheye images at hand and want to align the uv mesh. The fisheyes border is completely spherical but your uv not. Thats why you select the verts/ edges at the outer edge of your almost circular uv mesh an make it circular like I wrote.
Ok if you checked the image then it shouldnt be that, fine.
What, the uv mesh? No. Its dependent on the algorithm used to unwrap. And the alignment is also rather very seldom right in the center. Typically you have more than one uv island. And what you show there arent blenders default uvs you unwrapped it to be like that.
But simply check to most left and most right uv values to see if its off.
Cant say much to that. It depends on so many things. Is eg your sphere really axial symmetrical on a mesh level, what its not if eg you chose an uneven vertcount, then it will already start to be slightly off. Just made a short test here and its off at the third decimal place. Should be fine to align with the typical texture resolution, the difference might be due to numerical floating point reasons.
What you use here is a generic unwrapping, not procedural uvs. So its not faulty. Its the result of an algorithm that tries to minimize the angular distortion over all faces.
If you see that the center is off, then use the uv mapping tools at hand to fix it.
Its as i said from the beginning. Do a To Sphere, center it and you’re done.
I doubt you’ll find an addon that will make you happy in this regard. You can do a projection mapping but that will leave you back with other problems. You can use Geometry Nodes and generate the UVs, or do a manual tweak of the mapping you have.
I fundamentally question whether it is possible to perfect this.
Because when we do uvunwrap, we put a little bit of space on the image outside of UV to solve this problem.
Well there is a point depending on the given the texture resolution and mesh density where a perfect circle is well enough approximated by the mesh to hit the right pixels along the circular border. But the distribution of the inside also has to fit to what the camera lens did with the fisheye. But to make it short LCSM and related algorithms arent built to deliver perfect spheres. Its just a speciial case. Doing it in a proecedural way would be the best fit.