[frozenport]

    “exotic” signal representation without much practical utility despite the fact that they have been around the signal and image processing community for more than 30 years now. 

Maybe they aren't that good? Maxwell's equations got a lot better when they dumped them, same thing with the few uses in video game physics/camera tracing.

[teleforce]

Actually Maxwell's equation become unintuitive and become very difficult to model when not using quaternion. Unlike other waveform for example sound, electromagnetic (EM) waves has polarization components that can be intuitively, properly and comprehensively modeled using quaternion. Currently we are using quaternion to model robust and reliable wireless PHY modulation based on polarization that can work in a very limited Line of sight (LoS) environment, the performance is much better than conventional wireless PHY.

[someguydave]

are you referring to a particular EM modeling software or codebase?

[teleforce]

I'm referring to the EM model of propagation including its polarization in 3D representing the real world scenario.

[rowanG077]

I didn't think quaternions are even exotic and have used the extensively to represent rotations. I'm not familiar with video games but it seems a pretty natural fit to the problem. What is the alternative that is so much better?

[okaleniuk]

Rotors. https://marctenbosch.com/quaternions/

[klodolph]

In 3D space, rotors are quaternions with different labels. If rotors are better, then the only conclusion we can draw is that people don’t like the name “quaternion”.

[bee_rider]

They do sound weird.

I propose we call them fanciful numbers.

[zardo]

I mean if you're in highschool and poking under the hood of Roblox or whatever to write your first mod, rotor is a better name for the thing that manages rotations than quaternion.

[klodolph]

I would go for something like “orientation”. Or “rotation”. Ordinary English words that represent what are, more or less, ordinary, familiar concepts.

The fact that it’s a “quaternion” or a “rotor” is kind of an implementation detail.

Of these four terms, Quaternion is the most precisely correct. The reason is that rotors are, by definition, constrained. Quaternions can take any value. Due to floating-point precision problems, your rotor will not always be exactly a rotor, but may some multivector which is not a rotor.

This is kind of like representing a point on a sphere using (x,y,z) coordinates. You can call it PointOnSphere or Vector. I would rather call it Vector, because PointOnSphere implies a constraint which won’t be exactly satisfied, and I want to be reminded of that fact. The type name (Vector here, and Quaternion above) represents the object’s structure and the constraints which are actually enforced by the underlying representation.

[empiricus]

From your link: "We can notice that 3D Rotors look a lot like Quaternions". "In fact the code/math is basically the same!"

[dandanua]

Yeah, why remove quaternions if the math is the same as with rotors? They also have their own value, without applications to geometry. The article is good, though.

BTW, it's easy to understand the relations between i,j,k if you're familiar with Pauli matrices.

[rowanG077]

The article itself says they are the same in 3D space. Not very convincing that they are actually better. In fact a rotor is a unit quaternion...

[MyFirstSass]

Thank you for this link.

I just dabbled in webgl/threejs and tried creating a small movement engine and was confused from beginning to end. Quaternions as a black box is pretty accurate.

[141205]

To add to what the other guy said, rotors (by extension Clifford Algebra) is better. A fatal issue with Quaternions is that while they handle rotations perfectly, things like the norm or cross product of two vectors is messy.

This is unsurprising when several of your coordinates become -1 when multiplied. That's why historically Gibbs Heaviside (dot and cross product) became the dominant vector algebra over quaternions.

Clifford Algebra is the better than both, as you can seamlessly do dot, cross (wedge in CA) and can also embed quaternions within the system. I've heard that it can also accommodate some of the nonmetrical aspects that make differential forms appealing for manifold integration, but that's currently outside of my range of knowledge.

[bsdooby]

Dare to elaborate why Maxwell's equations got better, and the use cases in the gaming industry which improved thanks to dropping them?

[esturk]

Assuming this is not a tongue in cheek question, you can read about it more here:

https://hsm.stackexchange.com/questions/8173/did-maxwell-ori...

The answer also includes a link that shows many other representations including Einstein's "4d generally covariant tensor calculus".

The point is that the most common formulation today is not the one Maxwell made (with 12 equations). The idea is preserved, but it was Gibbs and Heaviside that formulated the current 4 equation representation.

[bdjsiqoocwk]

> Maxwell's equations got a lot better when they dumped them,

Tell me you don't understand special relativity.

[messe]

Tell me you don't understand differential forms.

[Iwan-Zotow]

geometric algebra anyone?

[bdjsiqoocwk]

My PhD suggests otherwise lol