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 _______________________________________________________________________ List hosting provided by Directions Magazine | www.directionsmag.com | To unsubscribe, send e-mail to [EMAIL PROTECTED] and put "unsubscribe MapInfo-L" in the message body.
