🚀 go-pugleaf

Hello,

I need to compute the distance between two points on the surface of an
ellipsoid.  I'm looking for the distance *on* the surface.  In short,
I'm after the length of the shortest geodesic curve joining the
points.

Since the Earth is roughly ellipsoidal, I suspect this is a well-known
problem in geographical sciences.  Unfortunately, I don't know the
geography literature, so any pointers in this direction would be
appreciated.

Searching the web mostly turned up discussion on spherical geometry,
with a nod to the fact that the earth is actually ellipsoidal.  It
also turned up some code in netlib,

    http://www.netlib.org/ode/geodesic/

written by William L. Anderson of Elements Research.  As far as I can
make out, this code computes an approximation of the geodesic on a
discretized ellipsoid, using gradient-descent optimization.

I was -- perhaps naively -- hoping for a closed-form solution, such as
that of the "great circles" on the sphere.  

I need more than a program or set of formulae.  I need to understand
the underlying equations enough to implement the computation myself.
Differential geometry and calculus of variations don't frighten me; I
spent the weekend reading differential geometry texts.  ;-)  I could
probably work out the geodesic equations myself, but if you can spare
me the trouble, I'd be ever so glad.

Thanks,

Steve

P.S.  I'd be grateful if you could CC me on any posted replies.