You always write a similar comment but neither you or the page you link explain what is the advantage, or even the difference, of dual quaternions when compared to normal quaternions. However, the article linked in the site, actually gives a good explanation.
Dual quaternions work not only rotations, but also translations. They provide a natural representation of rotations around arbitrary axis (not only around axis from the origin) and can also be easily combined or interpolated.
These dual quaternions look interesting for many cases, but they do not provide any advantage with respect to normal quaternions when working with pure rotations. For more complex transformations, I know there are some approaches based on GA (and CGA) that I do not know in detail but I think (a gut feeling) that dual quaternions are just a special case.
I have posted it many times yes. You hit it on the head. They are very good for modeling for example rigid transformations or robot joints.
They are a special case of GA. I used to very much into GA only to realize that dynamic 3D is the most interesting space, the other spaces are actually kinda boring.
For sure they are an interesting concept, thanks for introducing me to them. I cannot apply them to my work (crystallography) because we are only interested in orientations, but they may come handy at some point.
Dual quaternions work not only rotations, but also translations. They provide a natural representation of rotations around arbitrary axis (not only around axis from the origin) and can also be easily combined or interpolated.
These dual quaternions look interesting for many cases, but they do not provide any advantage with respect to normal quaternions when working with pure rotations. For more complex transformations, I know there are some approaches based on GA (and CGA) that I do not know in detail but I think (a gut feeling) that dual quaternions are just a special case.