At the peak of the pandemic, Harry Stevens published an excellent article in the Washington Post. The article used hard-ball simulations and animations to explain how the pandemic spreads and how specific preventive measures, such as social distancing, can reduce its impact.

Inspired by this article, I created similar animations. I made a video that was released through Math-Cat: a channel dedicated to promoting mathematics. These animations are much more elaborate than the Washington Post article.

The engine behind these animations is an algorithm for doing hard-ball simulations. The problem is simple to pose: Given n particles enclosed in a box (or a more complicated polygon) and their initial velocities, where all collisions are elastic, simulate and animate the system.

Recently, I have been able to develop a faster algorithm for doing these simulations. I will talk about hard-ball simulations and how they can be efficiently implemented. My purpose is to present a small but complete piece. The goal will be to understand the mathematics and computer science behind creating these animations.

The talk is elementary and self-contained. Basics of elastic collisions and some experience in computer programming will be handy.