# OOF2: The Manual

## Name

Orientation — The orientation of a three dimensional object.

## Subclasses

Subclasses are listed as they appear in the GUI and (in parentheses) as they appear in scripts.

• Abg (`Abg`) -- Euler angles (alpha, beta, gamma) are applied: first beta about the z axis, then alpha about the y, and finally gamma about z. This operation brings the crystal axes into coincidence with the lab axes.
• X (`X`) -- Goldstein's X convention for 3D orientations, using rotations which bring the crystal axes into coincidence with the lab axes, in the order z, x, z.
• XYZ (`XYZ`) -- The "aerodynamic" XYZ convention for specifying an orientation. Rotation by phi about x, then theta about y, then psi about z, brings the crystal axes into coincidence with the lab axes.
• Axis (`Axis`) -- Axis and angle representation of a 3D rotation. The rotation brings the crystal axes into coincidence with the lab axes.
• Quaternion (`Quaternion`) -- The Quaternion representation for 3D orientations. e0 is the cosine of the half-angle of the rotation, and e1 through e3 are the x, y, and z components of the rotation axis times the sine of the half-angle. The rotation brings the crystal axes into coincidence with the lab axes.
• Rodrigues (`Rodrigues`) -- Rodrigues vector representation for 3D orientations. The vector points along the axis of the rotation, and its magnitude is the tangent of half the angle of the rotation. The rotation brings the crystal axes into coincidence with the lab axes.
• Bunge (`Bunge`) -- Bunge angles for defining a rotation which operates on the lab axes, bringing them into coincidence with the crystal axes, in the order z, x, z.

## Description

There are many different ways of describing the orientation of a three dimensional object. OOF1 used only Euler angles, assuming that everybody used Euler angles, but it turns out that not only does everybody not use Euler angles, but there are differences of opinion about how Euler angles should be defined. So OOF2 allows you to choose among many different ways of defining orientations, some of which are Euler angles, and none of which are called Euler angles. The `Abg` definition is the one used in OOF1.