Pool Physics Simulation by Event Prediction 1: Motion Transitions

A method to simulate the physics of the game of pool is presented. The method is based upon a parametrization of ball motion which allows the time of occurrence of events, such as collisions and transitions between motion states, to be solved analytically. The method is both accurate, returning exact analytical solutions for both time and space parameters, and efficient, requiring no iterative numerical methods. It is suitable for use within a game-tree search, which requires a great many potential shots to be modelled efficiently, and within a robotic pool system, which requires high accuracy in predicting shot outcomes.