[OSRS-PROJ] VanDerGrinten

[Frank Warmerdam]

OSSIM, PROJ.4 and Geotiff folks,

I am having a problem getting results of the VanDerGrinten projection in
PROJ.4 to match the results from OSSIM (with projections code derived from
Geotrans from NIMA).

Projection definition (in OSSIM terms):

ossim_image.meters_per_line:  60.000000000000000
ossim_image.meters_per_sample:  60.000000000000000
ossim_image.projection.projection.central_meridian:  -117.474542889
ossim_image.projection.projection.datum:  NAS-C
ossim_image.projection.projection.false_easting:  0.000
ossim_image.projection.projection.false_northing:  0.000
ossim_image.projection.projection.type:  GrintenProjection
ossim_image.tie_point_x:  -17789.435662079999020
ossim_image.tie_point_y:  3914051.301389410160482

OSSIM's GrintenProjection results:

Upper Left:  lat: 33 54.22N lon: 117 38.47W
Lower Right:  lat: 33 37.51N lon: 117 18.48W

Results using PROJ.4:

Corner Coordinates:
Upper Left  (  -17819.436, 3914081.301) (117d38'27.48"W, 33d52'5.27"N)
Lower Left  (  -17819.436, 3879401.301) (117d38'27.06"W, 33d35'23.38"N)
Upper Right (   17820.564, 3914081.301) (117d18'29.19"W, 33d52'5.27"N)
Lower Right (   17820.564, 3879401.301) (117d18'29.61"W, 33d35'23.38"N)
Center      (       0.564, 3896741.301) (117d28'28.34"W, 33d43'44.59"N)

The PROJ.4 and OSSIM results for the top left corner are different by
roughly 2 minutes in latitude ... far exceeding what might be expected
from simple numerical errors.  Interestingly the OSSIM results very closely
match results from EASI/PACE which uses code derived from the FORTRAN GCTP
package. 

Looking into the OSSIM/Geotrans code, I see a "spherical radius" is computed
from the major and minor ellipsoid axes, and is used later, using this
formula:

    Ra = a * (1.0 - es2 / 6.0 - 17.0 * es4 / 360.0 - 67.0 * es6 /3024.0);

My supposition is that this projection is being done based on a spherical
approximation for the earth, whereas I gather PROJ.4 actually does the 
calculation based on an ellipsoidal model.  Does people believe this to be
true? 

A few questions:
 o Is the approach to computing "Ra" above a standard method?  Should I get
   equivelent results if force PROJ.4 to use a spherical earth model with the
   same value as generated above? 

 o Is there an easy way of finding which GCTP and Geotrans projection suffer
   from this approximation? 

 o Is there a reason why NIMA (and the USGS for GCTP) consider it acceptable
   to use spherical approximations for some of these projections?

 o How are those of us (like myself) trying to achieve data interoperability
   between different systems supposed to handle these problems?  

 o Are there good venues (I mean online, not conferences) for discussion of 
   issues like this?  

 o Are GCTP and/or Geotrans like to change the way they handle this (and other
   spherical projections)?   Is there someone we can contact to encourage them?

I have directed replies to osrs-proj, as it seems like the best venue for
followup discussions. 
 
Best regards,

---------------------------------------+--------------------------------------
I set the clouds in motion - turn up   | Frank Warmerdam, warmerdam at pobox.com
light and sound - activate the windows | http://pobox.com/~warmerda
and watch the world go round - Rush    | Geospatial Programmer for Rent
----------------------------------------
PROJ.4 Discussion List
See http://www.remotesensing.org/proj for subscription, unsubscription
and other information.