 Dear Fellow Scholars, this is Two Minute Papers with Karoi Zsolnai-Fehir. Here's a really cool computer animation problem you'll love this one. We take a digital character, specify an initial pose and a target objective, for instance, a position somewhere in space. And the algorithm has to come up with a series of smooth movements and contact interactions to obtain this goal. But these movements have to be physically meaningful, such as that self-intersection and non-natural contortions have to be avoided throughout this process. Keep an eye out for the wide cross to see where the target positions are. Now, for starters, it's cool to see that humanoids are handled quite well, but here comes the super fun part. The mathematical formulation of this optimization problem does not depend on the body type at all, therefore both humanoids and almost arbitrarily crazy non-humanoid creatures are also supported. If we make this problem a bit more interesting and make changes to the terrain to torment these creatures, we'll notice that they come up with sensible movements to overcome these challenges. These results are absolutely amazing, and this includes obtaining highly non-trivial target poses such as handstands. The goal does not necessarily have to be a position, but it can be an orientation or a given pose as well. We can even add multiple characters to the environment and ask them to join forces to accomplish a task together. And here you can see that both characters take into consideration the actions of the other one and not only compensate accordingly, but they make sure that this happens in a way that brings them closer to their objective. It is truly incredible to see how these digital creatures can learn such complex animations in a matter of minutes, a true testament to the power of mathematical optimization algorithms. If you wish to hear more about how optimization works, we've had a previous episode on this topic, make sure to check it out. It includes a rigorous mathematical study on how to make the perfect vegetables too. The link is available in the video description. And if you feel a bit addicted to two minute papers, please note that these episodes are available in Early Access through Patreon. Click on the icon with the P at the ending screen if you're interested. It also helps us a great deal in improving the quality of the series. We try to be as transparent as possible, and every now and then we write a technical memo to summarize the recent improvements we were able to make, and this is all thanks to you. If you're interested, I've put a link to the latest post in the video description. Thanks for watching and for your generous support. I'll see you next time!