So I'm trying to make this texture. I need to be able to make a perfect slice around any part of the sphere for it to look good (Imagine taking a sphere, and cutting a part off either left or right of the center with a katana). Anyone know how to do this?

Before anyone suggests it. I don't have access to any 3d modeling programs. Polar transformations don't make a perfectly correct slice. And using a 1:2 ratio also doesn't work.

To give an example of what I'm looking for look at the head templates. I just need to be able to make those sorts of lines anywhere I need to (Preferably without trial and error).

As an aside. For those of you who are familiar with spherical coordinates. If I wanted make a slice from a sphere... I think all that needs to be done is set: ρcos(θ)sin(φ) or ρsin(θ)sin(φ) equal to some constant less than 'ρ' and greater than zero? Dunno about that for sure though, or how I could use that to help out in this situation >_>

Showing the texture might help, a lot of people in this community would have one universal idea but many for the texture alone

Just something like this, but in texture form and rotated (As in I'm trying to make a cut on the sides, not the top).

Notice the concentric circles on the left and right?

That should show you how to do it ;)

Yes I'm wondering how to I make those circles. Without using trial and error.