four_dimensional_rotation_an_script.py

"""
in p s
in q s
in t s
in verts v
out verts_out v
"""

import numpy as np
import math
from mathutils import Vector
from animation_nodes.data_structures import Vector3DList

cos_pt = math.cos(p*t)
sin_pt = math.sin(p*t)
cos_qt = math.cos(q*t)
sin_qt = math.sin(q*t)

verts_out = Vector3DList()
for v in verts:
    x, y, z = v[0], v[1], v[2]
    
    # reverse stereographically project to Riemann hypersphere
    xb = 2 * x / (1 + x * x + y * y + z * z)
    yb = 2 * y / (1 + x * x + y * y + z * z)
    zb = 2 * z / (1 + x * x + y * y + z * z)
    wb = (-1 + x * x + y * y + z * z) / (1 + x * x + y * y + z * z)

    # now rotate the hypersphere (use p = q = 1 for isoclinic rotations)
    # and vary t between 0 and 2*PI
    xc = +xb * cos_pt + yb * sin_pt
    yc = -xb * sin_pt + yb * cos_pt
    # xc = xb
    # yc = yb
    zc = +zb * cos_qt - wb * sin_qt
    wc = +zb * sin_qt + wb * cos_qt

    # then project stereographically back to flat 3D
    xd = xc / (1 - wc)
    yd = yc / (1 - wc)
    zd = zc / (1 - wc)

    result = np.array([xd, yd, zd])
    # verts_out0.append(Vector(result - np.array([x,y,z])))
    verts_out.append(Vector(result))