Extracting Rotations The Right Way

Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér. This paper is about creating high-quality physics simulations and is, in my opinion, one of the gems very few people know about. In these physical simulations, we have objects that undergo a lot of tormenting, for instance they have to endure all kinds of deformations, rotations, and of course, being pushed around. A subset of these simulation techniques requires us to be able to look at these deformations and forget about anything they do other than the rotational part. Don’t push it, don’t squish it, just take the rotational part. Here, the full deformation transform is shown with red, and extracted rotational part is shown by the green indicators here. This problem is not particularly hard and has been studied for decades, so we have excellent solutions to this, for instance, techniques that we refer to as polar decomposition, singular value decomposition, and more. By the way, in our earlier project together with the Activision Blizzard company, we also used the singular value decomposition to compute the scattering of light within our skin and other translucent materials. I’ve put a link in the video description, make sure to have a look! Okay, so if a bunch of techniques already exist to perform this, why do we need to invent anything here? Why make a video about something that has been solved many decades ago? Well, here’s why: we don’t have anything yet that is criterion one, robust, which means that it works perfectly all the time. Even a slight inaccuracy is going to make an object implode our simulations, so we better get something that is robust. And, since these physical simulations are typically implemented on the graphics card, criterion two, we need something that is well suited for that, and is as simple as possible. It turns out, none of the existing techniques check both of these two boxes. If you start reading the paper, you will see a derivation of this new solution, a mathematical proof that it is true and works all the time. And then, as an application, it shows fun physical simulations that utilize this technique. You can see here that these simulations are stable, no objects are imploding, although this extremely drunk dragon is showing a formidable attempt at doing that. Ouch. All the contortions and movements are modeled really well over a long time frame, and the original shape of the dragon can be recovered without any significant numerical errors. Finally, it also compares the source code for a previous method, and, the new method. As you see, there is a vast difference in terms of complexity that favors the new method. It is short, does not involve a lot of branching decisions and is therefore an excellent candidate to run on state of the art graphics cards. What I really like in this paper is that it does not present something and claims that “well, this seems to work”. It first starts out with a crystal clear problem statement that is impossible to misunderstand. Then, the first part of the a paper is pure mathematics, proves the validity of a new technique, and then, drops it into a physical simulation, showing that it is indeed what we were looking for. And finally, a super simple piece of source code is provided so anyone can use it almost immediately. This is one of the purest computer graphics papers out there I’ve seen in a while. Make sure to have a look in the video description. Thanks for watching and for your generous support, and I'll see you next time!