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Euler angles used to represent orientation with 3 angles in a 3D space.

Euler angles of a 3D orientation is a combined rotation of 3 angles. Those angles marked α, β, γ. There are two types of convention, x-convention and y-convention. In case of x-convention,

  • α is the rotation about the unmodified Z axis
  • β is the rotation about the modified X axis
  • γ is the rotation about the modified Z axis

This is called z-x'-z" sequence.

See also Wikipedia.