I hereby retract my assertion that the great-circle navigation
problem is a good illustration of Clifford Algebra techniques.
Sorry. The problem is just too easy.
You *can* solve it that way. And there are related problems
where you really need the power of Clifford Algebra. But
if all you want are the headings along the great circle, it
turns out you can do it with
-- just scalars and ordinary grade=1 vectors (no bivectors,
or equivalently no quaternions), and
-- nothing more than a dot product (no wedge products).
I would like to emphasis a "style point" ... my approach is
essentially a non-trigonometric approach. You can keep track
of your position, updating your position as you move along
the great circle, *without* using trigonometric functions or
any other transcendental functions.
Or to say the same thing in more positive terms, this style
focusses attention on the vectors. Vectors are physical
things, geometric things, having a reality independent of
any coordinate system. Operations such as the dot product
are independent of the coordinate system. Most of what
makes the great-circle nav problem seem hard is just the
cruftiness of the polar coordinate system.