CNC
Overview
We used a DXF of an Austria map derived from the Austria location map SVG on Wikimedia Commons (by Lencer, CC BY-SA 3.0). The map below is the source image; below it is our cutting DXF rendered inline.
Source: Austria location map by Lencer, via Wikimedia Commons, CC BY-SA 3.0.
Our cutting DXF (austria_location_map.dxf) rendered inline.
CNC
We CNC-cut the Austria outline from the DXF. The slideshow below walks through the cut.
Slideshow
CNC-cutting the Austria outline.
Vacuum Forming
We then vacuum-formed the CNC-cut shape. The first try didn't work, because the heat was too low and the plastic never softened enough to take the shape of the mold. A second, hotter pull worked.
First attempt: too-low heat, the plastic didn't soften enough to conform to the mold.
Second attempt: plastic fully drawn over the CNC-cut Austria outline.
The finished vacuum form together with the CNC-cut piece, in front of some actual Austrian mountains.