This sections covers the definition of orientations as MTEX variables. The theoretical definition can be found in the section Theory and MTEX vs Bunge Convention.
Technically, a variable of type orientation is nothing else then a rotation that is accompanied by a crystal symmetry. Hence, all methods for defining rotations (as explained here) are also applicable for orientations with the only difference that the crystal symmetry has to be specified in form of a variable of type crystalSymmetry.
Most importantly we may use Euler angles to define orientations
or a 3x3 rotation matrix
Another common way to specify an orientation is by the crystal directions point towards the specimen directions Z and X. This can be done by the command byMiller. E.g. in order to define the GOSS orientation (011) we can write