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I have a shapefile of the world continents in EPSG 4326.

To what reference system do I have to reproject my file to get a projecting like this globe below?enter image description here

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up vote 12 down vote accepted

This family of projection is called azimuthal orthographic (all rays from globe to flat map are parallel). You can define the Lat/long coordinates of the center of the projection to choose the visible hemisphere.

There is no EPSG code from what I know, but here is the PROJ.4 definition.

+proj=ortho +lat_0=Latitude at projection center 
            +lon_0=Longitude at projection center
            +x_0=False Easting
            +y_0=False Northing

example with lat = 0 and long = -41

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If you use a shapefile, you might have to clip it to the visible half of the globe, as I explained here:… – AndreJ Apr 25 '14 at 10:01

A variation (on the already suggested azimuthal orthographic projection) would be to use an azimuthal perspective projection, similar to what's used in Google Earth. This mimics what you'd see looking at a real globe via the lens of the eyes or camera, but covering a little less than a "full" hemisphere. I don't know the parameters to use, but you'd need to experiment with different altitudes and scales to get close to your given sketch map.

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