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Re: spherical geometry



RAUBER, JOEL wrote:
As a side note, the airlines and mariners have long been interested
in the solution to this problem. And certain map projections have
been designed to facilitate the solution.

Those are two different statements.

Yes, aviators and mariners are interested in great-circle
directions ... but they are also interested in other things
such as shapes and distances. There is no projection that
can accurately portray angles *and* distances over large
areas.

Yes, projections exist that more-or-less instantly solve
David's large-distance great-circle problem
http://mac.usgs.gov/mac/isb/pubs/MapProjections/projections.html
... but to the best of my knowledge, you cannot go down
to the airport or the marina and buy such a thing.


For small areas, there are any number of conformal projections.
US Sectional Aeronautical Charts, for instance, use Lambert
conformal conic projections. These have acceptable accuracy
within their coverage area (a few hundred miles on a side).
But if somebody tries to stitch such things together to make
a large flat map with global coverage, they're going to get an
unsubtle object lesson in geometry.