I still don't know the logic that is used when placing seams. I usually place them in a circle shape around parts of an object to separate them.
Placing seams in particular places can affect the flow of textures on objects, and also impacts the resolution of the texture depending on how well you are able to unpack your UV islands.
Regarding the flow of textures, if youre using a tilable texture, such as fabric, the texture is going to warp with the direction of the UV as the 3d space is translated to 2d. It also means that those boundaries will become start and stop points that will be visible.
As for the resolution, if you unwrap things as circles, there will be a lot of negative space in your texture space that isn't being used. So if you had a 2048x2048 texture image, and a giant circle in the center, you would only be getting maybe 75% of that resolution from the texture. Because of this its easier to optimize your use of texture space with shapes that interlock.
But if you mean the logic of making seams to unwrap to specific shapes, it's a bit hard to explain. The best analogy I have, is to think of how a cardboard box is constructed. You want to mark seams in a way that those pieces can be folded up into their 3d shape as naturally as possible without stretching the pieces. There is an overlay in the UV editor that will color your unwrap to show how much stretching is occurring.
Hope that helps!
It all makes a lot more sense now. Your post is very in depth, I wasn't thinking about how circles would take up space in the UV editor
Thank you!