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My initial solution was to convert from spherical to cartesian, then calculate the vector from #1 to #2 and cross that with the vector from #1 to #3. Then a positive/negative z value would give me left/right.

However this doesn't see to work in the southern hemisphere, nor very well at the poles. Someone thought it would help to dot-product the resulting cross-product with the initial vector to point #1, but that hasn't seemed to produce a consistant result at various problem points on a sphere.

Any ideas, I'm I chasing the wrong concepts, should I be focusing more on a full 3d matrix solution instead of simple vectors?