Given a sphere radius of 1 and center at (0,0,0,), I have a list of xyz points in spherical coordinates of the form:
[-0.31828382 -0.6678262 0.67283251] # between -1 and 1
what would be the way to get their projected coordinates on a containing cube of same size?
You need to project this vector until one of the components first intercepts the cube boundary. Since your boundaries are -1 and +1, this is simple.
The component with the largest magnitude is the third one, 0.672... Divide each component by that magnitude, and you have your interception point:
[-0.31828382, -0.6678262, 0.67283251]
[-0.47305060, -0.9925594, 1.0]
Can you take it from there?