5 ms·
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
by matmann2001 2y ago
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?
- aap_ 2y agoBecause quaternions are so cool yet under-appreciated. Unfortunately not many octonion posts.
- rsfern 2y agoOctonions are cool! The one application I’m familiar with is in crystallography - you can represent the interface between two crystals with a unit octonion https://doi.org/10.1016/j.actamat.2018.12.034 https://doi.org/10.1016/j.actamat.2018.12.034 (Open access pdf: https://par.nsf.gov/servlets/purl/10098941 https://par.nsf.gov/servlets/purl/10098941) Can you give some pointers to other interesting applications?
- mikhailfranco 2y agoFundamental physics: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ https://www.quantamagazine.org/the-octonion-math-that-could-... Also see the work of John Baez: html https://math.ucr.edu/home/baez/octonions/octonions.html https://math.ucr.edu/home/baez/octonions/octonions.html pdf https://math.ucr.edu/home/baez/octonions/octonions.pdf https://math.ucr.edu/home/baez/octonions/octonions.pdf
- Jarmsy 2y agoI have noticed too that HN has an enduring fascination with quaternions, and they seem to reach front page surprisingly frequently (considering that there's not a huge amount of discussion of other geometry topics). I'm certainly not complaining though - I love quaternions too!
- mettamage 2y agoMaybe because it intersects deeply with game dev?
- lawlessone 2y agoyes, 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.
- xanderlewis 2y agoWhat in particular did you find difficult about dealing with them?
- lawlessone 2y agoThere was something called a slerp that allowed you to get an object to rotate from on orientation to another, similar to a linear interpolation. This was fine for some things. but if you wanted something to rotate but only in a certain way it was annoying as sometimes it would get from A to B, but go through Z during its rotation. Getting the order or multiplications right too.
- ahazred8ta 2y agoSpherical linear interpolation, slerp https://en.wikipedia.org/wiki/Slerp https://en.wikipedia.org/wiki/Slerp (which can sometimes wrap around the wrong way) For levity, see Acts 12:4 And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him.
- hassleblad23 2y agoBecause quaternions are awesome? :) it definitely feels like a discovery when you learn about them first.
- gamedever 2y agoAre they? [Let's remove Quaternions from every 3D Engine] https://marctenbosch.com/quaternions/ https://marctenbosch.com/quaternions/
- xeonmc 2y agoI feel like there should be a followup post "Dear Sir, you have reimplemented quaternions" noting how implementing GA and using it only in 3D gets you precisely right back to quaternions-but-with-a-different-name since they're isomorphic when specialized for 3D.
- orangea 2y agoAt 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 for the frontiers of pure math.
- kisonecat 2y agoAG maybe isn't so connected to software, but HoTT connects to the "functional programming" crowd. https://youtu.be/MVtlD22Y8SQ https://youtu.be/MVtlD22Y8SQ is me doing some examples.
- adalacelove 2y agoIt's because the quaternion is part of the state of the Kalman filter.
- ballooney 2y agoNot in any intrinsic way, it’s just a mildly better way of representing attitude if your state vector includes attitude.
- TaurenHunter 2y agoThey are posted by the Quaterminions.
- paulddraper 2y agoQuaternions and spherical trigonometry - https://news.ycombinator.com/item?id=42880242 https://news.ycombinator.com/item?id=42880242 - Jan 2025 (48 comments) Visualizing quaternions (2018) - https://news.ycombinator.com/item?id=38043644 https://news.ycombinator.com/item?id=38043644 - Oct 2023 (42 comments) Visualizing quaternions: an explorable video series (2018) - https://news.ycombinator.com/item?id=31083042 https://news.ycombinator.com/item?id=31083042 - April 2022 (15 comments) Visualizing quaternions: An explorable video series - https://news.ycombinator.com/item?id=18310788 https://news.ycombinator.com/item?id=18310788 - Oct 2018 (32 comments)
- ofalkaed 2y agoI never noticed it until I read Pynchon's Against the Day, I assume I just ignored quaternion posts before then. Great book, enjoyed the way he used quaternions and vectors towards literary ends. Edit: just noticed we also have a thread on bifurcation, another big topic in Against the Day.
- mhh__ 2y agoThey're both simple to motivate and complicated enough to have an allure.
- ballooney 2y agoThey’re both quite basic building blocks in state estimation and as SV’s focus shifts from web apps to drone warfare it will only increase in frequency.
- gcr 2y agono worries, quaternions just make the usual rotations. It’s cyclic.
- esafak 2y agoMaybe it's aspirational: things that people don't know, and would like to learn, and perhaps use one day.
- defrost 2y agoHN's going to need a windscreen cleaner and a bucket if 3blue1brown and Terence Tao ever collaborate on using adaptive Kalman filters for optimal paths in Quaternion spaces.
- mbonnet 2y agoOthers have mentioned game dev, but they're also essential for guidance, navigation, and control - spacecraft, aircraft, robotics, etc.