Theory
In this completely useless simulation project, the motion of a reflected ball is shown. This is similar to billiard, a fun game shown below.
The ball has a radius of $r = \mathcal{R}$. We describe its dynamics by a vector \[ \vec{v} = (x, y, dx, dy)^T, \] where $x$ and $y$ are the center coordinates of the ball and $dx$ and $dy$ describe the direction the ball is moving in.
