For working with raster images, get a piece of GIS software that supports reprojection of images (The GDAL package has good ones, but it's no GUI: QGIS has a GUI). This piece of software will get you into and out of your stereographic projection. Then find a package that will invert your image with respect to a circle ( https://github.com/synesthesiam/invert claims to be able to do this sort of thing, but I have not used it ) and use that on your intermediate image.
Vector data would be somewhat more complex because changing the points in this manner would most likely require a high-density data set and/or interpolation along the segments to avoid significant visual distortion.
GUI is definitely preferable (I love the concept of command line, but find the execution irksome). I'll check into QGIS (and of course GDAL out of curiosity, even though I probably won't go with that) and Synesthesiam's Invert (or an equivalent, if that goes pear-shaped on me). Thank you!!!
I won't worry about vectored, then. :-)
What doesn't kill me just p*sses me off... 😉
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