[Hugo Hadfield] wrote to let us know about an intriguing series of talks that took place in February of this year at GAME2020, on the many applications of geometric algebra. The video playlist of these talks can be found here along with the first video embedded after the break. For those of us who did not take advanced algebra during university, one can picture geometric algebra (GA) as an extension of vector algebra, adding more algebraic structures.
The essential difference is that GA adds a new vectors product, called the ‘geometric product’. The Cliff’s Notes version is that this is very useful for doing for example transformations, like in 3D spaces. For a quick algebraic introduction to GA for those familiar with vector algebra, the associated biVector website is helpful, from where one can also find additional information, software and other resources on getting started with GA.
These talks will take the viewer through the use of GA with robot kinematics (co-presented by [Hugo]), in astrophysics and AI. Definitely worth a watch, even algebra isn’t one’s strongest points.
Ahhh, I love the smell of Jacobians in the morning.
Nice find HaD. There are six videos each lasting from one to two hours. Chosen at random I took a look at the fist and third videos. The audio on the first video was lousy, too low; the audio on the third video was passable. YMMV.
Here is the actual URL for the YouTube Playlist. Using Firefox on my laptop with YouTube in Default View, the link in the HaD article shows the first video and the playlist in the right sidebar. In that format, depending on a lot of factors (mobile/laptop/desktop, portrait/landscape, browser type, playback size/mode, etc.) it is common for the playlist sidebar to disappear or be hidden. I suggest you use the playlist link below instead:
GAME2020 6 videos 555 views Last updated on Sep 4, 2020
https://www.youtube.com/playlist?list=PLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79
https://www.youtube.com/playlist?list=PLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79
I was just recently introduced to GA. I find it interesting in and of itself, but especially when you consider some of the applications. I might try writing a small library to implement some simple robot kinematics for personal use sometime soon. These talks are great! Thanks for the resource.
Disclaimer: I’m the organizer of the mentioned GAME2020 conference.
The lectures from the GAME2020 event are all well worth watching, but they do cover a very wide range of subjects. (with the premise being that Geometric Algebra as common algebraic apparatus makes all these subjects more approachable).
There may however be a lot of new ideas for the beginner, so it will certainly help to pick a starting point in an area where you already feel comfortable. For hackaday members with an interest in **robotics**, **inverse kinematics**, **pose estimation**, etc, I strongly suggest starting directly with Hugo’s lecture:
https://www.youtube.com/watch?v=bj9JslblYPU
It gives a great overview of GA in robotics, implementing various types of robots and showing how Conformal Geometric Algebra (CGA) can trivialize many of the aspects that are normally considered very difficult.
For an even lighter introduction, the (my own) SIGGRAPH 2019 talk on geometric algebra may help you understand how this framework could end up substantially simplifying your code. It is targeted towards graphics programmers and the general CS audience.
https://www.youtube.com/watch?v=tX4H_ctggYo
For those that want to get right to it, various high performance implementations exist and the bivector community will be happy to help you get going. (and to hear what fun applications everyone comes up with!)