Dual quaternions offer a cheap projection operator by means of dual normalization (very much like quaternion normalization), which the Lie group perspective does not provide.
In fact this is probably the only reason to use dual quaternions at all.
Really both are the same thing up to group homomorphism (double covering in this case).
Dual quaternions only add a cheap way of blending several rigid transformations together, which is useful in computer graphics for skinning meshes around articulated rigid bodies.
Comments
Dual quaternions offer a cheap projection operator by means of dual normalization (very much like quaternion normalization), which the Lie group perspective does not provide.
In fact this is probably the only reason to use dual quaternions at all.
Quaternions are more efficient yes, but I would prefer the more general Screw theory.
Really both are the same thing up to group homomorphism (double covering in this case).
Dual quaternions only add a cheap way of blending several rigid transformations together, which is useful in computer graphics for skinning meshes around articulated rigid bodies.