[gdal-dev] Geodetic Problem

[Frank Warmerdam]

David Baker (Geoscience) wrote:
> Frank and the List,
> 
>  
> 
> I have a geodetic problem I hope GDAL/OGR can solve.
> 
>  
> 
> The setup:
> 
>  
> 
> I have two radio towers each the same height and at the same elevation 
> being 10,000 meters apart.  I know the latitude and longitude of the 
> first tower and those coordinates reference WGS84 (though they could be 
> any geographic CRS, NAD27, NAD83, etc.).  I also now the baring to the 
> second from the first measured from true north at the first tower.
> 
>  
> 
> The problem:
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>  
> 
> Given the above information and using the prebuilt tools, GDAL/OGR 
> utilities, what workflow would one use to calculate the latitude and 
> longitude of the second tower?
> 
>  
> 
> The hints I have gotten so far say to use a conformal projection (UTM 
> maybe?) centered at the first point with a scale factor of 1, a local 
> projection.  Calculate the Cartesian offsets from the first point to the 
> second based on the azimuth of the given baring.  Using the baring 
> calculate the x and y offsets to the second point and use offsets to 
> find the x and y of the second point in the local coordinate system.  
> Then, reproject the x and y of the second point to the latitude and 
> longitude in the CRS of the first points latitude and longitude.  If 
> this is correct, I guess the question is, what would the proj4 
> parameters be for such a local projections.

David,

The above will give a pretty good approximation, degrading as the
distance increases.  However, the proper way to do this is using
great circle operations.  The PROJ.4 "geod" program can do this:

   http://trac.osgeo.org/proj/wiki/man_geod

There is more information on geodesic operations at:

   http://trac.osgeo.org/proj/wiki/GeodesicCalculations

Best regards,
-- 
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I set the clouds in motion - turn up   | Frank Warmerdam, warmerdam at pobox.com
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