I have a coordinate system where North has the angle value 1. East +0.707 and West -0.707. South has the angle 0. It's very annoying to calculate angle deltas in this angle system. Is there a nice way to convert it to a standard 0 to 360 degree coordinate system? Python solution preferred but I'm more interested in the operations instead of ready to use implementation.
That angle system is very weird. It seems like your "angle" is calculated as sin(radians(d/2)) where d is actual angle in degrees (with south being 0° and east 90°). You can invert this:
>>> from math import *
>>> ewns = [0.707, -0.707, 1.0, 0.0]
>>> [degrees(asin(x) * 2) for x in ewns]
[89.98269667432403, -89.98269667432403, 180.0, 0.0]
Optionally round and add % 360 to get 0..360 instead of -180..180:
>>> [round(degrees(asin(x) * 2)) % 360 for x in ewns]
[90, 270, 180, 0]