Quaternions

A quaternion, a rotation matrix and a set of Euler angles all specify a rotation operation; i.e.: an operation that rotates an object from one (base) orientation to another (final) orientation. Therefore a quaternion does not specify an orientation in space, only the change in orientation from a previous orientation.

A quaternion has 4 components, (qw, qx, qy, qz). Visualizing a quaternion rotation can by done as follows:

1. visualize the point in space specified by (qx, qy, qz)
2. visualize the axis formed by drawing a line from the origin to the point (qx, qy, qz)
3. visualize a rotation about that axis, following the right- hand rule. qw is the cosine of half the rotation angle, therefore the amount of rotation about the rotation axis is 2 * arc_cos(qw)

As an example, consider the quaternion q = (0.8, 0.0, 0.6, 0.0). Looking at the (qx, qy, qz) we see a point on the Y-axis at 0.6 units from the origin. The rotation axis points away from the origin along the Y-axis. The arc_cos(0.8) is approximately 37 degrees, the rotation is 74 degrees about the positive Y-axis.

Some software use quaternions that are ordered W-X-Y-Z (W-first) and other software expects the order to be X-Y-Z-W (W-last).

WTK expects quaternions in the W-last order (and inverted).

The VIEW library quaternion functions, quatprint(), quatmul(), quatinv(), etc. expect W-first order.

The Polhemus reports W-first.

The values in shared memory, and the values reported by SMMON are also W-first.

Shrmem_retrievedata() reads the shared memory values, but returns to the user, quaternions of the form W-last.

Note: Stefan recorded data using shrmem_retrievedata() so his data files are also W-last order.

The NAS tetra-interpolation functions (used by SPI and AST) use the library quaternion functions (W-first) so Stefan's data must be converted when read in by SPI.