blender/source/blender/python/doc/examples/mathutils.py

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import mathutils
from math import radians
vec = mathutils.Vector(1.0, 2.0, 3.0)
mat_rot = mathutils.RotationMatrix(radians(90), 4, 'X')
mat_trans = mathutils.TranslationMatrix(vec)
mat = mat_trans * mat_rot
mat.invert()
mat3 = mat.rotation_part()
quat1 = mat.to_quat()
quat2 = mat3.to_quat()
angle = quat1.difference(quat2)
print(angle)