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Ellipse as superposition of noncoplanar equal amplitude circles

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.

[ conics | GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella
by Eckhard Hitzer (Fukui).