Thank you for the comprehensive reply. I will have a look at those references.

Part of the broader problem is in the way ‘duality’ is used so widely, and confusingly, in the different parts of science and maths (e.g. wave - particle, …). It’s not always clear in those different cases how the ‘duality’ manages to pin down **both sides** of the dual viewpoints.

I thought I’d heard within the Siggraph video the implication that the addition of the e_0^2=0 term was an important part in the full-up PGA, but I may have misheard.

When you mention the quaternions and dual quaternions, I presume you are referring to the distinction between the ‘vector orientation’ and the ‘plane orientation’ as the two duals. I hadn’t heard the term ‘dual quaternions’ before, so wasn’t exactly sure about the distinction.

I have worked a little with quaternions on inertial navigation, and looked at Maxwell’s equations in quaternion form (which reduces the number of equations), so they continue to be an interest.

Perhaps it’s the term ‘degenerate’ (as per the metric) that I was really looking for. I’ll have a look at the thesis, as I’m especially interested in how Units and Dimensions should be carried through SI calculations, especially when they loose the all important ‘radians’ (which are needed often in optical system design)