Thanks! I'm curious what motivated you to want to use a dual quaternion or why you want a slerp algorithm for that. I have yet to run across a use for a dual quaternion. Wikipedia says that they are used in mechanics to represent rigid transformations. That sounds useful for animation but most animation or computer graphics people would represent a rigid transformations with a quaternion and a translation vector, and if interpolating a rigid transformations they would slerp the quat and linearly interpolate the translation. So I'm not sure what the advantage of a dual quaternion would be in this context, or do you use dual quaternions in some completely different way?