ABSTRACT
Game physics uses mathematics as a tool. I’m afraid you can’t get away from it, so take a deep breath and let’s go. I’ll try to start this off as simply as possible, but things are going to get complicated fast. Section 2.1 shows you some of the most important things from geometry and linear algebra that you are going to need in game physics: vectors, trigonometry, the Pythagorean Theorem and Identity, the Law of Cosines, and orientation. Section 2.2 is about reflection, meaning that we’re going to be bouncing balls off things to see how they behave. The proper name for this is collision response. Section 2.3 is about digital calculus, mainly integration, which is the part of calculus that people often find the scariest. Starting with Euler integration, we thankfully find that we don’t need to integrate at all, we just need to sum. That’s good because computers are excellent at adding things up fast. Verlet integration is another useful way to not do integration. Game physics is sometimes about satisfying constraints using a technique called relaxation covered in Section 2.4. It turns out that we can take a pretty relaxed approach to that.
