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The Euler angles are the three angles, φ, ψ, and θ, through which a crystal must be rotated in order to relate the crystallographic axes with the sheet reference axes.
x1, x2, x3 represent the position of the rolling direction, transverse direction, and normal direction
Normal Direction
Rolling Direction
Transverse Direction

Normal Direction
Rolling Direction
Transverse Direction
Step 1
Rotate ψ about x3 to x'1, x'2, x'3
χ
φ
ω
2θ

Normal Direction
Rolling Direction
Transverse Direction

Step 2
Rotate θ about x'2 to x''1, x''2, x''3
X1, X2, X3 represent the position of the crystal axes [100], [010], and [001]
Normal Direction
Rolling Direction
Transverse Direction
The transformation is complete
Step 3
Rotate φ about x''3 to X1, X2, X3