OOF2: The Manual

Details

Description

A Quaternion object represents the orientation of a three dimensional object, assumed to be a crystal, in three dimensional space in terms of four parameters which obey an interesting algebra. This representation of orientations is not common, but has its roots in the rigid-body mechanics community.

The parameters correspond to a physical rotation in a similar way to the Axis convention. Given a rotation angle $\theta$ and a normalized rotation axis $\widehat{𝐧}$, the quaternion parameters follow directly: $e_0$ is the cosine of half the rotation angle, and $e_1$, $e_2$, and $e_3$ are, respectively, the x, y, and z components of $\widehat{𝐧}$ multiplied by the sine of half the rotation angle.

As in the case of the Axis convention, the specified rotation brings the crystalline $\widehat{𝐚}$, $\widehat{𝐛}$, and $\widehat{𝐜}$ axes into coincidence with the laboratory (or screen) axes $\widehat{𝐱}$, $\widehat{𝐲}$, and $\widehat{𝐳}$ respectively. The components of $\widehat{𝐧}$ are preserved by this rotation, and so may be specified in either the crystalline or laboratory coordinate system.

See Also