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Visualizing quaternions: An explorable video series
- justifier 8y agooof, the one thing i am wont to want with 3b1b videos is an interactive suite accompaniment.. unreasonably ungrateful i know ;P i had high hopes this would be it, but this is just a concise lesson form for the series.. which is great! i am a huge fan of both eater's and sanderson's entire ouvre what's great is that 3b1b releases the code that generates these videos and i have cloned the manim(o) library a number of times in the past when a video had an idea i wanted to play around with but the effort usually gets a low priority and i get distracted with more pressing projects i figure a simple localhost python server serving up dynamic frames generated by manim could do the trick, maybe i'll work at it again this weekend when i want to learn a new mathematical concept i like to write the source myself, which is great for getting at the nuts and bolts but it is usually after i have done this and start to tweak the models or constants that i begin to gain a real intuitive understanding of an underlying concept (o) https://github.com/3b1b/manim https://github.com/3b1b/manim
- billconan 8y agois this framework based on OpenGL?
- AtomicOrbital 8y agono, its WebGL - see http://disq.us/p/1wv9zek http://disq.us/p/1wv9zek
- justifier 8y agoi'm unsure exactly how frames are drawn.. the repo has a number of custom self defined objects that allows for pretty abstracted handling it appears the frames are drawn ad hoc using PIL, SVG and or cairo libraries with the spatial reasoning done explicitly in the source
- justifier 8y agoHA! that is exactly what this is.. my bad i had thought the shorter clips were just that, clips from the 3b1b videos, but when i decided to click through it's much more than that they are calling it explorable video the videos are fully interactive.. this is awesome!
- okket 8y agoDiscussion about quaternions from 6 days ago: https://news.ycombinator.com/item?id=18265355 https://news.ycombinator.com/item?id=18265355 (99 comments)
- vvilliam0 8y agoI was just watching this in my other tab... https://imgur.com/a/aGj6tXy https://imgur.com/a/aGj6tXy
- adamnemecek 8y agoI 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/ http://www.chinedufn.com/dual-quaternion-shader-explained/ They seem to correspond to linear logic which is insanity.
- yiyus 8y agoYou 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.
- adamnemecek 8y agoI have posted it many times yes. You hit it on the head. They are very good for modeling for example rigid transformations or robot joints. They are a special case of GA. I used to very much into GA only to realize that dynamic 3D is the most interesting space, the other spaces are actually kinda boring.
- yiyus 8y agoFor sure they are an interesting concept, thanks for introducing me to them. I cannot apply them to my work (crystallography) because we are only interested in orientations, but they may come handy at some point.
- naikrovek 8y agoI 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.
- brian_herman__ 8y agoDont give up math is just a lot of practice. You can do it!!!
- partisan 8y agoI’ve felt this same way over the years. Worse is that I may have grasped them, if only in the most superficial way, only to have lost those gains to time. I think one has to take some time to understand the foundations upon which quaternions are based versus jumping right in.
- dktoao 8y agoI was in the same boat until I stumbled across this yc podcast from a few weeks ago with Joan Lasenby: https://www.youtube.com/watch?v=ikCIUzX9myY https://www.youtube.com/watch?v=ikCIUzX9myY She described an algebra called "Geometric Algebra" that has both standard vector spaces, complex numbers and quaternions as sub-algebras. Supposedly it simplifies a lot of the abstraction surrounding these concepts. So I dug a little bit deeper and ended up watching these videos on YouTube that really helped me understand what she was talking about: https://www.youtube.com/playlist?list=PLpzmRsG7u_gqaTo_vEseQ7U8KFvtiJY4K https://www.youtube.com/playlist?list=PLpzmRsG7u_gqaTo_vEseQ.... And WOW, the whole concept just made so much more sense. In 2D if you consider the area created from two vectors, it can have a "positive spin" or a "negative spin" based on the relative direction of the vectors (Like if you turn a handle clockwise vs. counter-clockwise). It turns out this property makes the square of this area negative (like the complex numbers). The same analysis can be done in 3D and the quaternions pop out. Pretty awesome stuff! I have been buying and reading books on the topic ever since, I feel like I need to re-educate myself on all the advanced math I learned in gradschool because this makes it all so much more compact and elegant.
- beautifulfreak 8y ago
- enriquto 8y agoAm 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?
- ai_ia 8y agoHey man. Sorry to be a shameless plug here. But I am working to solve exactly this. Text based learning using a chatbot. A platform which takes care of your learning, spaced reptitions, notebook generations and all. If you can just take some time to subscribe, that would be great. https://tinyletter.com/primerlabs/ https://tinyletter.com/primerlabs/ I will launch soon.
- tw1010 8y agoPeople who don't read much tend to have developed an ability to learn through videos.
- p0nce 8y agoSuppose 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 8y ago[deleted]
- jrootabega 8y agoSo 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?
- naavis 8y agoEncoding your whole orientation would require 3 numbers. You are restricted only to the horizon, so one number is enough.
- numerobis 8y agoOrientation is only two numbers, since a unit vector does the job? So, three numbers in total?
- deleted 8y ago[deleted]
- p0nce 8y agoThat's why it doesn't encode free orientation.
- breatheoften 8y agoDoes this assume the earth is a sphere? Can you keep the elegance of this coordinate encoding with convenient transformation operations and define somewhere a mapping from the quaternarion encoding of position into a non-homogenous oblate spheroid encoding like WGS84 ...?