Convert rigid transformations (TRS) from coordinate system A to coordinate system B

transform.py

# this program demonstrate how to cnoevrt TRS from
# blender's coordinate to Unity's coordinate.

import numpy as np
from scipy.spatial.transform import Rotation

blender_west = [1, 0, 0]
blender_up = [0, 0, 1]
blender_north= [0, -1, 0]
blender_coord = np.array([
  blender_west, blender_up, blender_north
], dtype=np.float64).T

unity_west = [1, 0, 0]
unity_up = [0, 1, 0]
unity_north = [0, 0, -1]
unity_coord = np.array([
  unity_west, unity_up, unity_north
], dtype=np.float64).T


b2u = unity_coord @ np.linalg.inv(blender_coord)


trans = np.array([-8.1831, 5.3352, 2.2994])
rot = np.array([14.1, -36.6, 47.3])
scale = np.array([3.0, 4.0, 2.0])

print("Translation (Blender):", trans)
print("Rotation (Blender):", rot)
print("Scale (Blender):", scale)

Rb = Rotation.from_euler('xyz', rot, degrees=True).as_matrix()
# change of basis
Ru = b2u @ Rb @ np.linalg.inv(b2u)
z, x, y = Rotation.from_matrix(Ru).as_euler('zxy', degrees=True) # unity use zxy-order
unity_rot = np.array([x, y, z])

print("Translation (Unity):", trans @ b2u.T)
print("Rotation (Unity):", unity_rot)
print("Scale (Unity):", scale @ b2u.T)