Author Topic: Dual Quaternions for Mere Mortals  (Read 851 times)

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Dual Quaternions for Mere Mortals
« on: August 06, 2019, 06:12:36 PM »
This article is written for people seeking intuition on dual quaternions (and perhaps even complex numbers and quaternions) beyond what is offered by traditional texts. The standard way a dual quaternion is defined is by introducing a dual unit ϵ which satisfies ϵϵ=0 and slapping a quaternion and a dual-scaled quaternion together. A whole ton of algebra follows and mechanically at least, everything checks out, as if by magic. At some point, the writer will point out how dual quaternions are isomorphic to Clifford algebras (or somesuch mumbo-jumbo pertaining to Lie algebras). If you’ve taken a course in abstract algebra and are intimately comfortable with the notion of homogeneous coordinate systems already, maybe such a treatise was more than adequate. Chances are though, the concept of dual quaternions (and likely quaternions as well) feels somewhat hollow, and you are left with a lingering suspicion that there is a better way of grasping matters. Geometric algebra is there (and I recommend you take a look), but personally, having an appreciation of both is still useful, and I don’t actually find quaternions or dual quaternions to be unduly difficult or an inferior formulation in any way. I can’t lay claim to having a perfect understanding of the subject, but I am documenting my understanding here in the hopes that it may point you, fellow mathematician (graphics programmer, AI researcher, masochist, or what have you), in the right direction.