Can anyone tell me what is the intersection between the following two surfaces?
The portion of a radius-1 spherical surface defined by four points: (r1, θ1, φ1), (r2, θ2, φ2), (r3, θ1, φ3), (r4, θ4, φ4)
The portion of a radius-1 spherical surface defined by four points: (r1, θ1, φ1+x), (r2, θ2, φ2+x), (r3, θ1, φ3+x), (r4, θ4, φ4+x)
So basically I'm taking a "rectangular" (in quotes because it's really a spherical surface that has four corners like a rectangle) surface, rotating it x degrees in the direction of φ, and trying to figure out how to define the intersection between the original and final surface. I'm thinking it will either be nothing (if it rotates too far and there's no overlap), or a polygon defined by up to five points.