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Start by downloading a high-res copy of the Rand McNally 1940 map. Follow the image link to the detail view:


Vector Data and QGIS

This downloads a file called 5969008.jpg.

Download vector data from Natural Earth, selecting a few layers that match the content of the 1940 map:

The projection of the 1940 map looks a bit like Mollweide centered on 59°W, so we start by reprojecting the vector data into the right PROJ.4 projection string:

ogr2ogr -t_srs '+proj=moll +lon_0=-59' ne_50m_admin_0_countries-moll.shp ne_50m_admin_0_countries.shp
ogr2ogr -t_srs '+proj=moll +lon_0=-59' ne_50m_populated_places-moll.shp ne_50m_populated_places.shp
ogr2ogr -t_srs '+proj=moll +lon_0=-59' ne_50m_graticules_5-moll.shp ne_50m_graticules_5.shp

In QGIS, the location can be read from the coordinates display:


Warping The Map

Back in the 1940 map, corresponding pixel coordinates can be read from Adobe Photoshop’s info panel:


Using GDAL, define a series of ground control points (GCP) centered on cities in the Natural Earth data and the 1940 map. Use gdal_translate to describe the downloaded map and then gdalwarp to bend it into shape:

gdal_translate -a_srs '+proj=moll +lon_0=-59' \
    -gcp 1233 1249 -1655000 775000 \
    -gcp 4893 2183 2040000 -459000 \
    -gcp 2925 5242 52000 -4176000 \
    -gcp 1170 3053 -1788000 -1483000 \
    -gcp 2256 6916 -767000 -6044000 \
    -of VRT 5969008.jpg 5969008-moll.vrt

gdalwarp -co COMPRESS=JPEG -co JPEG_QUALITY=50 \
    -tps -r cubic 5969008-moll.vrt 5969008-moll.tif

Opening the result in QGIS and comparing it to the 5° graticules shows that the Mollweide guess was probably wrong:


The exactly horizontal lines of latitude in the original map suggest a pseudocylindrical projection, and a look at a list of examples shows that Sinusoidal might be better. Try it all again with a different PROJ.4 string:

ogr2ogr -t_srs '+proj=sinu +lon_0=-59' ne_50m_admin_0_countries-sinu.shp ne_50m_admin_0_countries.shp
ogr2ogr -t_srs '+proj=sinu +lon_0=-59' ne_50m_populated_places-sinu.shp ne_50m_populated_places.shp
ogr2ogr -t_srs '+proj=sinu +lon_0=-59' ne_50m_graticules_5-sinu.shp ne_50m_graticules_5.shp

The pixel coordinates will be identical, but the locations will be slightly different and must be read from QGIS again:

gdal_translate -a_srs '+proj=sinu +lon_0=-59' \
    -gcp 1233 1249 -1838000 696000 \
    -gcp 4893 2183 2266000 -414000 \
    -gcp 2925 5242 52000 -3826000 \
    -gcp 1170 3053 -1970000 -1329000 \
    -gcp 2256 6916 -711000 -5719000 \
    -of VRT 5969008.jpg 5969008-sinu.vrt

gdalwarp -co COMPRESS=JPEG -co JPEG_QUALITY=50 \
    -tps -r cubic 5969008-sinu.vrt 5969008-sinu.tif

The results looks pretty good:


Cutting Tiles

For web map display, convert the warped map to map tiles using starting at map zoom level 6: -w openlayers -z 0-6 \
    -c 'Rand McNally 1940' -t 'Map of South and Central America' \
    5969008-sinu.tif tiles

Convert all generated PNG tiles to smaller JPEG images using Python and convert: