Spherical Coordinates Stereographic Projection Inverse

stereographic_inverse.py

import maya.api.OpenMaya as om
from math import *

def T(z):
    return 0.5 * z

for i, p in enumerate(cmds.ls('unit.vtx[*]', fl=True)):
    x, y, z = cmds.xform(p, q=True, t=True)
    x = T(x)
    y = T(y)
    xprime = 2 * x / (1 + pow(x, 2) + pow(y, 2))
    yprime = 2 * y / (1 + pow(x, 2) + pow(y, 2))
    zprime = (-1 + pow(x, 2) + pow(y, 2)) / (1 + pow(x, 2) + pow(y, 2))
    proj = om.MVector(xprime, yprime, zprime)
    cmds.xform('unit.vtx[{0}]'.format(i), t=proj)