[Proj] Geocentric vs. Geodetic latitude

[Frank Warmerdam]

Folks,

Thanks for the help everyone! I am reassured that my clients understanding
is correct, not withstanding the fact that from George's satellite perspective
the geocentric angles are more meaningful.

I implemented the conversion by converting the geocentric latitude (and a
nominal longitude of 0) to geocentric x/y/z coordinates, and then using the
existing geocentric x/y/z to geodetic code from Geotrans.  This seems to
work fine, and matches the results with proj.

For my dataset I was getting the following Geocentric values:
Upper Left  (  85.0000000,  32.9833333) ( 85d 0'0.00"E, 32d59'0.00"N)
Lower Left  (  85.0000000,  32.2491667) ( 85d 0'0.00"E, 32d14'57.00"N)
Upper Right (  85.9675000,  32.9833333) ( 85d58'3.00"E, 32d59'0.00"N)
Lower Right (  85.9675000,  32.2491667) ( 85d58'3.00"E, 32d14'57.00"N)
Center      (  85.4837500,  32.6162500) ( 85d29'1.50"E, 32d36'58.50"N)

After converting to geodetic I get:
Upper Left  (  85.0000000,  33.1593160) ( 85d 0'0.00"E, 33d 9'33.54"N)
Lower Left  (  85.0000000,  32.4230943) ( 85d 0'0.00"E, 32d25'23.14"N)
Upper Right (  85.9675000,  33.1593160) ( 85d58'3.00"E, 33d 9'33.54"N)
Lower Right (  85.9675000,  32.4230943) ( 85d58'3.00"E, 32d25'23.14"N)
Center      (  85.4837500,  32.7912051) ( 85d29'1.50"E, 32d47'28.34"N)

To test in PROJ.4 I dummied up a projected value at the top left latitude
in projected coordinates (on the central meridian) and test converted it
to lat/long using the default geodetic and then using the geocentric option
(+geoc). The results matched well:

warmerda at gdal2200[284]% proj +proj=utm +zone=11 +datum=WGS84 +geoc
-117 32.9833333
500000.00       3668948.95
warmerda at gdal2200[285]% proj -I +proj=utm +zone=11 +datum=WGS84 +geoc
500000.00       3668948.95
117dW   32d59'N
warmerda at gdal2200[286]% proj -I +proj=utm +zone=11 +datum=WGS84
500000.00       3668948.95
117dW   33d9'33.537"N

So, I think I am in the clear.  I didn't find the actual geocentric code
in PROJ.4, and had never used this +geoc option before.

By the way, I don't think I mentioned it in my original post but the
geocentric lat/long values are coming from NITF files.  The NITF 2.0
specification had an option to give corner coordinates in geocentric
lat/long in addition to the more common geodetic lat/long.  In my code
I just want to convert to geocentric.  I am not convinced that there is
much actual data distributed in this form, but a client wants it supported
so I am doing it.

Best regards,
-- 
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I set the clouds in motion - turn up   | Frank Warmerdam, warmerdam at pobox.com
light and sound - activate the windows | http://pobox.com/~warmerdam
and watch the world go round - Rush    | Geospatial Programmer for Rent