Okay that made me actually look at the code in OL (I made a patch for
dateline crossing polygons quite a while ago, but never really looked
further). getGeodesicArea is approximation on sphere based on
http://trs-new.jpl.nasa.gov/dspace/handle/2014/40409
Needs closely spaced vertices to have a hope I would say. Doing a proper
ellipsoid calculation isnt trivial. Looking it over, I think think I
would be very tempted to pass the geometry to the server and calculate
it properly there rather than try to implement the code in JS. However,
you could possibly get a reasonable approximation from equal area. ie
you take the geometry and work out parallels and centre Longitude for an
albers equal area conic projection. Project the geometry into that with
ProjJS. Get the area of the projected geometry with getArea. For very
large, very simple geometries this is still probably missing some
precision but I would suspect you would still get within a km2 or so.
Obvious ways
to improve it however require densifying by calculation of extra points
between vertices calculated on a great circle. I've got this stuff in
our corporate java libraries so I would go to the server to do it.
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