[PROJ] projection Gall-Bomford (Gall Modified)

[Oscar van Vlijmen]

My two cents:

Gall-Bomford projection
===============

Gall's stereographic cylindrical:
y = R(1 + (1/2)sqrt(2)) tan ((1/2)phi).
For the Oxford version, devised by Guy Bomford about 1950 and called a modified Gall, the meridians are fairly straight at lower latitudes and curve slightly to decrease scale exaggeration near the poles, While the Gall cylindrical spacing is x = R.lambda/sqrt(2), Oxford's modification appears to fit approximately the formula
x = (1 - O.04.phi^4) R.lambda/sqrt(2).

Source: A Comparison of Pseudocylindrical Map Projections
John P. Snyder
The American Cartographer, Vol. 4 No. 1, 59-81 (1977), page 75


The formulas used by most map drawing programs for both Guy Bomford's Modified Gall projection and the Denoyer Semi-Elliptical projection were due to John P. Snyder. In his book Flattening the Earth, he mentions that projection in passing, noting that the scale of longitude is "about 1 - 0.4 * phi^4" where phi represents the latitude, compared to that of the equator, so he may merely have been attempting to sketch out roughly what the projection was like, not to seriously propose a method of drawing it. I haven't tried for an exact match myself; as noted above, I added a small term proportional to the square of the latitude to correct the visibly obvious deficiency of implementations of this formula. Scaled to a latitude in radians, my formula becomes 1 - .01857755 * phi^2 - .030077 * phi^4. I calculated it based on matching two of my measurements that seemed most representative, then checking that the overall result had roughly the same appearance as the real map.

Source: Pseudocylindrical and Pseudoconic Projections
Part of "Map Projections", by John J. G. Savard
http://quadibloc.com/maps/mpse04.htm


See also:
proj_cyl_stere.c, Cylindrical Stereographic projection code by Gerald I. Evenden, 2003, 2006, part of the package libproj - library of cartographic projections.


Yours,
Oscar van Vlijmen





> Op 27 april 2020 om 12:38 schreef David Gispert <davidgispert at gmail.com>:
> 
>     Hi everybody.
> 
>     I need help to aggregate the Gall-Bombford projection to Qgis.
> 
>     I don't have the characteristics of this projection.
> 
>     Only this:
> 
>     https://map-projections.net/compare.php?p1=gall-bomford&p2=gall-stereographic&w=1&sm=1&d=1
> 
>     Thank you very much for your help
> 
>     Salutacions,
> 
>     David Gispert
>     davidgispert at gmail.com mailto:davidgispert at gmail.com
>     _______________________________________________
>     PROJ mailing list
>     PROJ at lists.osgeo.org
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