I am a GIS beginner using QGIS 1.8.0
I am trying to transform a world map from the standard WGS84 Coordinate Projection System to a set of rectangular polyconic gores, with a gore count of 12.
Please follow this link to see what a set of rectangular polyconic gores looks like: http://www.mapthematics.com/ProjectionsList.php?Projection=130#rectangular
Rectangular polyconic gores do not seem to be on the standard menu of Coordinate Projection Systems in QGIS.
I have found the Custom Coordinate Reference System dialog box in QGIS. I need to type in a definition of 'rectangular polyconic gores, with a gore count of 12' in the proj4 format into the dialog box to make it work.
- Does anyone know exactly what it is I need to type?
The reason I am trying to make a world map in the ‘Rectangular Polyconic Gores’ (called RPG from now on) projection so that it can be cut out and pasted onto a sphere to make a world globe. There is a free Photoshop plugin called Flaming Pear available which performs this task, but if vector data such as coastlines are saved as a raster in QGIS and then imported into Photoshop and transformed from WGS84 to RPG, the lines will get progressively narrower towards the poles. Therefore I need to do the projection transformation in QGIS where the data is still in vector format. If QGIS is not a suitable tool, and I need to be using a different GIS program, please let me know. I know that Mapthematics’ Geocart program will perform this task, but it costs a lot of money.
As suggested in the QGIS manual, I have started reading 'Cartographic Projection Procedures for the UNIX
Environment—A User’s Manual' by Gerald I. Evenden (available here: pubs.usgs.gov/of/1990/0284/report.pdf )
and 'Map projections - a working manual'by J.P. Snyder (available here: http://pubs.er.usgs.gov/publication/pp1395 ) in an effort to come up with the answer myself. However, I do not have proper mathematical or computer language training, so I find them virtually impossible to understand.
Below I have included links to all the related information I have found so far:
- Here is a well illustrated page with writing and equations, describing the RPG projection: http://members.shaw.ca/quadibloc/maps/mpo0502.htm
I found this quote at http://www.maxneupert.de/luc/ It apparently describes the mathematical formula behind the RPG:
‘’Bugayavevskiy and Snyder reference a third Book, by Ginzburg and Salmanova from 1964, pages 171 ff, as the source of the following formula, quote:
x = p sin δ, y = s + p(1 - cos δ)
p = kR cot φ, δ = λ(sin φ)/k
where k is a constant parameter, usually equal to 2 and s is the meridian distance of φ from the equator. If φ = 0, x = kRλ. To allow for the deformation from the curvature of the ball while maps are beeing pasted onto it, projection coordinates are multiplied by a constant coefficient determined from experience. End quote.’
- Here is an assembly language program describing RPG
along with some explanatory photos:
These pages are both in German.
- Max Neupert also says that a mathematical description of the RPG
Projection also turns up on:
page 222 of Map Projections - A Reference Manual by Lev M. Bugayavevskiy and John P. Snyder, 1995 ISBN 0-7484-0304-3
and page 155 of Kartographische Netzentwürfe by Karlheinz Wagner, 1949 (and 1962) ASIN B0000BP33E However, both these books cost money.
- Here ias an illustrated article from 1909 , which includes, amongst
other things, a discussion on how to create a set of RPGs
Here is the proj4 command line for the ‘SAD69 Brazil Polyconic, ESPG:29101’ projection, which I cut and pasted from QGIS CRS dialog box. Apparantly this projection is a close relative of the RPG projection, even though they visually appear to be completely different:
+proj=poly +lat_0=0 +lon_0=-54 +x_0=5000000 +y_0=10000000 +ellps=aust_SA +towgs84=-57,1,-41,0,0,0,0 +units=m +no_defs
If I find anything more Ill post it here. Id really love to get this one solved.