At 12:18 PM 10/16/01 -0700, Bill Thoen wrote:
>Mark Neuhaus also pointed out that projected coordinate systems
>do not align to north anywhere except along their central
>meridian

Any cylindrical projection in its equatorial (natural) aspect will maintain 
true north along every meridian, so another option when computing azimuths 
is to use a cylindrical projection (such as Mercator, Peters, etc.).  A 
bigger issue is conformality: if the projection is not at least locally 
conformal, azimuths can be in error by a lot.  The maximum deviation 
(between the calculated and actual angles between any two azimuths) can be 
computed and is often showed along with Tissot indicatrices in books on map 
projections.  (For conformal projections, this maximum deviation is zero, 
by definition.)  One can also compute map divergence, which is the angle 
between apparent north and true north.  This varies from point to point and 
can be shown on a map by lines of constant divergence.  (Last summer I 
picked up a nice hiker's map in Banff showing these lines for UTM.  At that 
location the divergences are several degrees.)  You can then adjust every 
computed azimuth by the divergence if you like.  Pictures illustrating some 
of these ideas appear at http://www.quantdec.com/tissot/ .  Of course all 
these considerations are local and break down when computing azimuths over 
large distances (typically more than a degree of arc), for which either 
specialized projections or spherical trigonometry are the best options when 
accuracy is needed.

--Bill Huber



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