It's not dual-quaternion anything, though.

(Also you can implement it with matrix logarithms and exponents, no unit quaternions necessarily needed)

Can you look into it first? Yes you can but dual quaternions are more suited for this.

I have looked into it, that's why I felt comfortable replying in the first place! ;)

Can you explain why dual quaternions are more suited and for what? I can understand the appeal of having "one number" to represent a rotation and translation. But the interpolation they provide is no different than if you interpolate the rotational and translational components independently, right?

By the way, the 2D analog of dual quaternions is dual complex numbers. They let you encode a translation and rotation (and scaling) in 2D, just as the dual quaternions do for 3D.

One thing that bothers me about dual quaternions, and you may have an answer to this, is that there's an 8th term that doesn't seem to buy you anything: the epsilon term (not multiplied by i, j, k). It's an 8-dimensional representation, whereas a quaternion + translation is a 7-dimensional representation.

For more information: http://www.euclideanspace.com/maths/algebra/realNormedAlgebr...

http://www.euclideanspace.com/maths/algebra/realNormedAlgebr...

The separation can be a problem if I want to for example do a Fourier transform.

A Fourier transform of what? If you have a reference, I'd love to learn more.

Hey can you email me? I’d like to continue this convo. My email is in my profile.

Lookup nonuniform Fourier.