GAME2020 0. Steven De Keninck. Dual Quaternions Demystified

My GAME2020 talk on PGA as an algebra for the Euclidean group.

[angelvega]

I was running from dual-quaternions until I started following Steve's work hahaha. Thanks for sharing all your knowledge man.

[Anon-zh]

Amazing presentation. So many awesome snippets of intuition packed in a short timeframe. For example, the tidbit on "rotating space, writing your element down, and rotating it back" is invaluable information for explaining the "why" behind the sandwich product. Also, the idea to start with generators of the algebra as opposed to "retrofitting" and especially, the point that vectors/quats/dual-quats are "type-erased" are all important concepts, explained super clearly. Thanks!

[ChristopherLeeMesser]

This is a fantastic talk. The animations of symmetry for each geometric type are excellent.

[RecursionIs]

This might be my favorite talk. What is presented in this video is far more than just "Dual Quaternions Demystified"

[ArrowofEntropy]

Absolutely fantastic talk. Especially the intuition for the various products make a lot of sense, never seen it explained this clearly before.

[hveluwenkamp]

Uitstekende presentatie. The clarity of the presentation makes it an invaluable tool in understanding this topic.

[AMADEOSAM]

Amazing presentation, very illustrative. Would be good if you can make such a step to our 4D space time.

[Nickle]

Sandwich products are just like conjugates for a Rubix cube when you want to come up with commutators.

[robindebreuil]

This is astonishing, both the facts and the presentation of them. Thank you.

ab = a ∙b + a^b should be carved on the outside of that bridge so it reflects properly in the water below ;).

[tjkotha]

so in terms of scaling transformations (i.e. in Maya scaling an object by x/y/z-dimension(s) ), this is typically represented in game engines via the mat4x4 transformation matrix. In some cases, like with Blender3D, the scaling can be performed with respect to a pivot point. The PGA mostly focuses on isometries, but I was wondering how I could model the scaling effect using PGA? Is it best to think of it in terms of 'translating points/elements' of a model w.r.t. an origin point s.t. the effect of scaling an object is achieved?

[katelynspadavecchia]

This is excellent and cleared up a lot of questions I had about PGA!

[mathunt]

You can embed the dual and double quaternions within the CGA and also Mullineux G_4 algebra.

[tc]

Really great visualisations 👍 very helpful indeed

[kered]

43:00 Firing shots at Hamilton, we should call this man Aaron Burr.

[christophstadler]

Why in 3D PGA the join of a plane with itself is 0 if it retains identical reflections? e1 v e1 = 0? The same of lines in 2D PGA.

[pizamora]

I really loved your presentation, it is a great starting point for the pga world. I'm just curious about how the presentation was made, is there any chance you are using ganja embedded in a ppt(just a silly guess)?

[rebase]

So if we had “dualized” everything in this video with the pseudoscalar, then we would get Eric Lengyel’s “direct” representation with his anti-product, right? (direct = the Euclidean basis would be e1, e2, e3 instead of e032, e013, e021)

[samueldeandrade]

I just started watching. Loved the accent. Which accent is this, can someone tell me. Great presentation.

[degrees]

Wait, which exactly reflection e₀ is? If we realize a projective space the usual way as a space of lines in a linear space one dimension higher, what transformation is e₀? e₁ and e₂ in this case are easy, just regular reflections with orthogonal normals too. But trying to enforce anticommutativity of e₀ with both of them and also making e₀² annihilate all vectors made my head hurt. 😁 I get that e₀ should behave somewhat alike to multiplication by ε in dual numbers, but it seems I couldn’t make things work with a single attempt. Maybe someone could tell how to do it properly without there being a second attempt.

[michelangelowebb]

Did you use GanjaJS to create the examples on this presentation ?