I'm trying to calculate the reflection of a point across another point, both of which are on the surface of a sphere. I believe I could do this by getting the formula for the great circle of the sphere that contains those two points, reflecting the central angle of the great circle to get the point I want, and then converting it back.
I know how to convert between 3D Cartesian and spherical coordinates and have both for the two points, but I have no idea where to begin to try to get a great circle from the two points, or if this is even the best approach.
I was initially just reflecting longitude and latitude as if they were on a plane until testing that revealed that doesn't work at all so I started looking up spherical geometry on Wikipedia. I found a formula to get the distance between my two points here (http://en.wikipedia.org/wiki/Great-circle_distance) but I don't know where to go from there.
Thanks to anyone that can provide any assistance!
EDIT: I just found this: http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula I believe this can be used to more simply solve my problem.