Gameplay in Star Versus is rotational in nature. Objects keep track of the direction they’re facing, and move that direction at each step of the engine. This situation requires a bit of trigonometry, most of which can be pre-calculated for efficient runtime performance, though some cannot. In particular, a couple of gameplay elements need to find arctangents, and need to do so quickly.
The definition of the arctangent is as follows: given a right triangle, arctan calculates one of the non-right angles using as input the length of the side opposite that angle divided by the length of the adjacent side. In the case of Star Versus, the triangle’s sides are the X/Y distances between two objects, like a projectile and a ship, and the angle is the direction the first needs to travel to reach the second.
Arctan was first needed to figure out when one ship hit another with their sword. Swords don’t have their own collision information, they exist purely as rendering artifacts due to needing animation. Instead, they reuse the code that detects collision between two ships, with a larger hit box to account for the range of the sword. This lets the engine save precious CPU time by calculating the X/Y position deltas only one time. However, it does need to make sure the sword swinger is facing the correct direction, and not attacking away from the target, which is where arctan gets used.