Quaternions and Transform Matrices

Question

Tell me if I am wrong.

I'm starting using quaternions. Using a rotation matrix 4 x 4 (as used in OpenGL), I can compute model view matrix multiplying the current model view with a rotation matrix. The rotation matrix is derived from the quaternion.

The quaternion is a direction vector (even not normalized) and a rotation angle. Resulted rotation is dependent on the direction vector module and the w quaternion component.

But why I should use quaternions instead of Euler axis/angle notation? The latter is simpler to visualize and to manage...

All information that I found could be synthetized with this beatifull article:

http://en.wikipedia.org/wiki/Rotation_representation

Answer 1

Why it is better to use quaternions is explained in the article.

• More compact than the DCM representation and less susceptible to round-off errors
• The quaternion elements vary continuously over the unit sphere in R4, (denoted by S3) as the orientation changes, avoiding discontinuous jumps (inherent to three-dimensional parameterizations), this is often referred to as gimbal lock.
• Expression of the DCM in terms of quaternion parameters involves no trigonometric functions
• It is simple to combine two individual rotations represented as quaternions using a quaternion product