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Rediscovering Quaternions

jasonfantl.com

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Re: Rediscovering Quaternions

#21

Post by kisonecat »

orangea wrote: post #11
matmann2001 wrote: post #3

Not detracting from this post, but has anyone else noticed there's a front page post about Quaternions or Kalman filters on about a monthly cadence? Wonder why that is?

At least this is a topic that the average HN reader is likely to be able to understand and which is closely related to software. Several years ago there was a period where there were periodic posts about things like homotopy type theory and research-level algebraic geometry which inevitably spark only inane misunderstandings and uninformed speculation in the comments. I can only attribute it to some kind of fetish fo…

AG maybe isn't so connected to software, but HoTT connects to the "functional programming" crowd. https://youtu.be/MVtlD22Y8SQ is me doing some examples.

Re: Rediscovering Quaternions

#23

Post by gcr »

matmann2001 wrote: post #3

Not detracting from this post, but has anyone else noticed there's a front page post about Quaternions or Kalman filters on about a monthly cadence? Wonder why that is?

no worries, quaternions just make the usual rotations. It’s cyclic.

Re: Rediscovering Quaternions

#24

Post by sundarurfriend »

r1chardnl wrote: post #6

If I had to describe Quaternions to someone I would first try to explain a Plane (Ax + By + Cz + D = 0) to them. ABC being a (normal) direction that the Plane is pointed towards and D being the distance from the origin. A Quaternion from what I believe is just the same but instead of distance it just encodes the rotation around that direction as a fixed axis. (Instead the angle stored is half etc). Feel free to corre…

> A Quaternion from what I believe is just the same but instead of distance it just encodes the rotation around that direction as a fixed axis. (Instead the angle stored is half etc).

The first part kinda makes sense, but I have no idea what the paranthetical is intended to mean.

Re: Rediscovering Quaternions

#25

Post by esafak »

matmann2001 wrote: post #3

Not detracting from this post, but has anyone else noticed there's a front page post about Quaternions or Kalman filters on about a monthly cadence? Wonder why that is?

Maybe it's aspirational: things that people don't know, and would like to learn, and perhaps use one day.

Re: Rediscovering Quaternions

#26

Post by xanderlewis »

lawlessone wrote: post #9
mettamage wrote: post #5

Earlier quoted context omitted.

Maybe because it intersects deeply with game dev?

yes, that's the module i learnt about them in during college. IMHO I think for me they're interesting because it felt like mathematically they straddle the line of being nearly impossible for me. I could just barely do them and felt very accomplished when I could. Anything else was either impossible or easy by comparison. assuming my maths skills are average here then most people have similar experiences with them.

What in particular did you find difficult about dealing with them?

Re: Rediscovering Quaternions

#27

Post by xanderlewis »

adamhartenz wrote: post #8
r1chardnl wrote: post #6

If I had to describe Quaternions to someone I would first try to explain a Plane (Ax + By + Cz + D = 0) to them. ABC being a (normal) direction that the Plane is pointed towards and D being the distance from the origin. A Quaternion from what I believe is just the same but instead of distance it just encodes the rotation around that direction as a fixed axis. (Instead the angle stored is half etc). Feel free to corre…

If you a explaining this to the average American, you are going to have to start a bit further back than a "Plane".

A plane is just a burrito.

Re: Rediscovering Quaternions

#28

Post by raincole »

adamhartenz wrote: post #8
r1chardnl wrote: post #6

If I had to describe Quaternions to someone I would first try to explain a Plane (Ax + By + Cz + D = 0) to them. ABC being a (normal) direction that the Plane is pointed towards and D being the distance from the origin. A Quaternion from what I believe is just the same but instead of distance it just encodes the rotation around that direction as a fixed axis. (Instead the angle stored is half etc). Feel free to corre…

If you a explaining this to the average American, you are going to have to start a bit further back than a "Plane".

I know it's a tradition to bash Americans, but I'm quite sure in any country, Ax + By + Cz + D = 0 is a plane isn't common sense.

Re: Rediscovering Quaternions

#29

Post by nighthawk454 »

The easiest way for me to conceptualize it is to think of it as orientation + rotation. 3 dims for the orientation vector to get the object facing/pointing the right way, then a further 1 dim/var for rotation about that axis. For a total of 4 variables/dimensions

3blue1brown and Ben Eater did a series of interactive videos on the subject that can be explored:

https://eater.net/quaternions

My favorite demo on this point is this one: https://eater.net/quaternions/video/rotation

Where they have a toggle to go between `a + bi + cj + dk` quaternion notation and an equivalent formulation in terms of 3d orientation vector plus rotation angle as `cos(θ) + sin(θ)*(ai + bj + ck)`

Re: Rediscovering Quaternions

#30

Post by agnishom »

I also recently came across "Geometric Algebra", which seems like an idea of equipping a vector space with a formal anticommutative product. There seems to be a subset of people on the internet who swear by it.
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