That might be one solution, but I am not keeping track of this. I am evaluating the cross product at arbitrary times. Mostly at t = 0 and t = 1. You can rotate around one of the edges and between these extreme frames the dot product between n(0) and n(1) might have flipped.

That might be one solution, but I am not keeping track of this. I am evaluating the cross product at arbitrary times. Mostly at t = 0 and t = 1. You can rotate around one each and between these extreme frames the dot product between n(0) and n(1) might have flipped.