I'm hoping this is the right place to find help with this. Here's a brief description of what I have so far and the context for what I need.
I'm creating a star map within Unity 2D, consisting of one rectangular map, with an equirectangular projection, showing the stars from declination -45 to +60. To make this I've used the HYG star database found here, filtered out the stars I don't need then converted the RA value to longitude (-RA * 15), and used the Dec value as latitude. This is then pulled into unity, scaling the long/lat by (a/360) * 24 where l is long/lat to give X co-ordinates between 0 & 24.
The trouble is replicating this for the polar map. I need the stars above declination 45.
I've tried using QGIS to project the stars as polar, but this is not working, I'm not sure why. I've found a different dataset that I can get projected properly for both maps, but exporting the co-ordinate data to a CSV gives me massive numbers and I'm not sure how to go about scaling it correctly.
Ideally, I'm looking for a way of converting RA and Dec to coordinates for a polar projection with a given radius (12), OR a way of scaling the co-ordinates from QGIS.
EDIT: I've found this page with a formula, which looks like what I might need, I just don't understand it.
EDIT: Images for reference.
EDIT: My (I think correct) makeshift solution.
Each star is pulled into unity, at
(0,D) units away from the centre point of the map. Where
D = declination/360 * 24 (to scale it correctly). The star is then rotated around the centre point by
Rdegrees, where R is
-right ascension * 15 (right ascension goes between 0 and 24, so * 15 to scale to 0-360. Negative to flip the image to be correct).