How to Express a circle in Spherical Coordinates

The simple explanation is I’m trying to use an arbitrary plane to trim a NURBS unit sphere.
I’ve already got a system set up where I just sample a bunch of points and interpolate, but this problem has been itching at me for the past two days.

I don’t even know where to start. If anybody could give me that, or a plan of attack, I don’t mind doing the heavy lifting.


Sorry for the double post, but I couldn’t find where to edit my post.
I used the first formula from that page because my circles are going to be relatively large on the sphere.
I just plugged in y and x for the standpoint Latitude and Longitude, and solved for y

y = acos( (cos(a) - sin§sin(x)) / (cos§cos(x)) ) + L
Where a is the internal angle formed by the circle’s center, the center of the sphere, and any point on the circle.
p is the latitude of the center of the circle
L is the longitude of the center of the circle

The graph for this only shows half of the curve, but it’s trivial to mirror it