Frequently Asked Questions and Frequently Stated Comments regarding Diana's quaternion article. Diana is tired of responding the same questions and comments over and over and so has prepared this canned response. It probably isn't very important anyway. Quaternions are necessary because without them your program will suffer from gimbal lock. Gimbal lock is only an issue if you use Euler angles.
Quaternions use less data than vector rotations.
Quaternion operations are faster because they can be done using fewer operations. Disregarding my informal proof that the minimum operation count will be exactly the same, don't forget to consider the operation count in converting quaternions to a matrix format in order to make them compatible with DirectX or OpenGL, or to add translation information, for example. Quaternion operations don't require trig, vector operations do. A. Don't get too hung up on this. A dot product is a cosine whether you are talking about vectors or quaternions.