How are omega, phi, kappa defined?

The omega, phi, kappa angles are defined as the angles used in order to rotate the (X,Y,Z) geodetic coordinate system and align it with the image coordinate system. The rotations are applied in the following order:

  1. Kappa (κ), the rotation around the Z-axis.
  2. Phi (φ), the rotation around the Y-axis.
  3. Omega (ω), the rotation around the Χ-axis.

Rotation around the X-axis (omega) Rotation around the Y-axis (phi) Rotation around the Z-axis (kappa)
Figure 1. Exterior orientation rotations/angles.


Note: The sense of the angle is defined by the right hand rule. A positive rotation means that if the thumb of the right hand is pointed along the positive direction of the rotation axis, then the fingers curl in the positive direction, i.e. counterclockwise.

The omega, phi, kappa are in degrees and can be positive or negative. This means, for example, that the value 350 degrees can be expressed also as -10 [0-(360-350)] degrees.


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