[OSRS-PROJ] VanDerGrinten

Gerald I. Evenden gevenden at capecod.net
Fri Nov 17 11:56:22 EST 2000

Van Der Grinten is a spherical only projection.  If PROJ is used and no
specs are given for radius then a is used (e2 is ignored).  I suspect that
the problems arise due to errors (or/of omission) of specifing radius.
GCTP only has it in spherical form also.  I have never seen an ellipsoidal
development for it and rather doubt that one exists.

In PROJ, R_A specs radius of sphere of equivalent area of selected
ellipsoid.  The formula for Ra given below is used by PROJ for R_A.

Regarding "spherical approximations for some of these projections" I can
only add that many projections formulas are *only* derived for the spherical
earth.  Because of the nature of usage (usually in small scale maps) there
no point in ellipsoidal developments.  Ellipsoidal usage is *only* of
interest in large scale mapping,  grid systems and geodesic work.

Going back to Van Der Grinten, its main claim to fame is being used
for the Nat'l. Geographic Society seal and occasionally for a global
map.  Personally, I think there are a lot better global representations
(mainly pseudocylindricals).

Interesting, in the OSSIM specs below it only mentions some datum
but never mentions radius.  Projections *do not* care about datums.
*Only* ellipsoid specs or radii.

Jerry Evenden and the Low Riders, Katie and  Daisy May
gevenden at capecod.net  http://www.capecod.net/~gevenden
----- Original Message -----
From: Frank Warmerdam <warmerdam at pobox.com>
To: <osrs-proj at remotesensing.org>
Cc: OSSIM <ossim at remotesensing.org>; GeoTIFF Mailing List
<geotiff at remotesensing.org>
Sent: Friday, November 17, 2000 10:43 AM
Subject: [OSRS-PROJ] VanDerGrinten

> 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
> 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
> 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
>    equivelent results if force PROJ.4 to use a spherical earth model with
>    same value as generated above?
>  o Is there an easy way of finding which GCTP and Geotrans projection
>    from this approximation?
>  o Is there a reason why NIMA (and the USGS for GCTP) consider it
>    to use spherical approximations for some of these projections?
>  o How are those of us (like myself) trying to achieve data
>    between different systems supposed to handle these problems?
>  o Are there good venues (I mean online, not conferences) for discussion
>    issues like this?
>  o Are GCTP and/or Geotrans like to change the way they handle this (and
>    spherical projections)?   Is there someone we can contact to encourage
> 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
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