An ellipse (yellow) can be represented as superposition of two noncoplanar circular motions with
equal amplitude, frequency and phase.
r = 1/2 a (exp(phi i-) + exp(phi i+)),
with the two unit bivectors i- (green) and i+ (blue). The vector b (orange) is given by
b = 1/2 a (i- + i+) = 1/2 a . (i- + i+)
You can change the view interactively by dragging the three red points with the mouse pointer.
Compare the animated view.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).