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Visualizing quaternions: An explorable video series

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Re: Visualizing quaternions: An explorable video series

#21

Post by ai_ia »

enriquto wrote: post #19

Am I the only one who is utterly incapable to learn anything from a video? I read many hours per day, and look at figures, and try to understand them. But I cannot stand to wait for a three-minute video to finish. Why do people prefer linear videos to text that you can read at a whole?

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Re: Visualizing quaternions: An explorable video series

#22

Post by yiyus »

adamnemecek wrote: post #5

I know I’m getting annoying with this but dual quaternions are even whackier. They are the best formalism for reasoning about 3D space developing over time. Here’s a cool demo http://www.chinedufn.com/dual-quaternion-shader-explained/ They seem to correspond to linear logic which is insanity.

You always write a similar comment but neither you or the page you link explain what is the advantage, or even the difference, of dual quaternions when compared to normal quaternions. However, the article linked in the site, actually gives a good explanation.

Dual quaternions work not only rotations, but also translations. They provide a natural representation of rotations around arbitrary axis (not only around axis from the origin) and can also be easily combined or interpolated.

These dual quaternions look interesting for many cases, but they do not provide any advantage with respect to normal quaternions when working with pure rotations. For more complex transformations, I know there are some approaches based on GA (and CGA) that I do not know in detail but I think (a gut feeling) that dual quaternions are just a special case.

Re: Visualizing quaternions: An explorable video series

#23

Post by p0nce »

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice).

A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon.

It also encodes the rotation it would take to go from one such observer to another.

Re: Visualizing quaternions: An explorable video series

#24

Post by tw1010 »

enriquto wrote: post #19

Am I the only one who is utterly incapable to learn anything from a video? I read many hours per day, and look at figures, and try to understand them. But I cannot stand to wait for a three-minute video to finish. Why do people prefer linear videos to text that you can read at a whole?

People who don't read much tend to have developed an ability to learn through videos.

Re: Visualizing quaternions: An explorable video series

#25

Post by tw1010 »

naikrovek wrote: post #8

I am never going to understand quaternions. I just accept this, now. No one, not ever, has been able to explain them sufficiently for me, or in a way that I can grasp. Oh well.

"We always talk about learning disability, but never about teaching disability" - Eric Weinstein (paraphrased).

Don't worry. There's a lot of shit out there and it's not at all your problem if they don't feel satisfying.

I also used to think there was something wrong with me for not understanding or being satisfied with vauge intuitive descriptions of mathematical ideas. Then I discovered proof-based mathematics and realized that, heck, here finally is the unambigous, high-resolution, no-corners-cut explanaion I've always been looking for. (Sure, it's a lot of hard work to get to a satsifying end-point, but at least the problem has shifted from trying to parse vauge intuitive statements in a visual-heavy video, to being bottle-necked by my own will power and dicipline to go as deep into an understanding of a proof as feels necessary to reach a satisfying depth-to-effort equilibrium.)

Maybe proofs aren't the key for you (or maybe they are), but don't blame yourself if you don't find the resources out there satisfyingly understandable.

Re: Visualizing quaternions: An explorable video series

#26

Post by [deleted] »

p0nce wrote: post #23

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice). A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon. It also encodes the rotation it would take to go from one such observer to another.

[deleted]

Re: Visualizing quaternions: An explorable video series

#27

Post by jrootabega »

p0nce wrote: post #23

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice). A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon. It also encodes the rotation it would take to go from one such observer to another.

So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?

Re: Visualizing quaternions: An explorable video series

#28

Post by naavis »

jrootabega wrote: post #27
p0nce wrote: post #23

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice). A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon. It also encodes the rotation it would take to go from one such observer to another.

So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?

Encoding your whole orientation would require 3 numbers. You are restricted only to the horizon, so one number is enough.

Re: Visualizing quaternions: An explorable video series

#29

Post by [deleted] »

jrootabega wrote: post #27
p0nce wrote: post #23

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice). A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon. It also encodes the rotation it would take to go from one such observer to another.

So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?

[deleted]

Re: Visualizing quaternions: An explorable video series

#30

Post by numerobis »

naavis wrote: post #28
jrootabega wrote: post #27

Earlier quoted context omitted.

So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?

Encoding your whole orientation would require 3 numbers. You are restricted only to the horizon, so one number is enough.

Orientation is only two numbers, since a unit vector does the job? So, three numbers in total?
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