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?
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?
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

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.
My web-based Globus Map Projector can also do that for you. Go here: https://www.winski.net/?page_id=12, and choose the full version of the projector. From there you can simply select your project to to ortographic.