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I have Natural Earth shapefile (for example this file: link) covering whole globe in -180:180 range. I want to offset this file, so that it starts from Greenwich prime meridian instead -180.

How can I do this with gdal/ogr?

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This isn't possible with gdal/ogr tools. Some Python script can probably do it, thou.

Only case when this could be possible is if no geometries are present at meridian we wish to offset to, otherwise ugly things happen like showed here: How do you change the prime meridian of a map?

If that requirement is satisfied this command can be used to offset shapefile:

ogr2ogr out.shp in.shp --config CENTER_LONG 180

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