OOF2: The Manual

`Quaternion (Quaternion)`
	6.5.2. Subclasses

Name

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.

Synopsis

Quaternion(e0,e1,e2,e3)

Details

Base class: Orientation
Parameters:

e0

Cosine of half the rotation angle. Type: A real number.

e1

Rotation axis x-component times sine of half the rotation angle. Type: A real number.

e2

Rotation axis y-component times sine of half the rotation angle. Type: A real number.

e3

Rotation axis z-component times sine of half the rotation angle. Type: A real number.

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 $\hat{\mathrm{\bf n}}$ , 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 $\hat{\mathrm{\bf n}}$ multiplied by the sine of half the rotation angle.

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


`Split Wide Quads (QuadSplit)`		`RGBAColor (RGBAColor)`