The dual-complex numbers have a similar use-case. You can use them to interpolate between two rigid body motions in 2D. There's some interesting infinity/infinitesimal phenomena there, with translations (a type of rigid body motion) being represented as rotations whose centre point is at projective infinity and whose angle of rotation is infinitesimal. The name of the number system is unfortunate though, I have to admit.

In spite of all this, I haven't heard of anyone using these for anything. I do though have a use-case for a problem I'm working on. I also wrote the Wikipedia article on DC numbers, so I'm kind of biased here.