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.
A predictive event-based method to simulate the physics of the game of pool is described, including event time prediction for collisions between balls and between balls and the rails and pockets of the table. The method uses the vector parameterization of the equation of motion of a moving ball to analytically predict the time of occurence of collision events. The method is both accurate, since it returns exact analytical solutions for ball trajectories using no linear approximations, and efficient, since it requires a minimal number of floating point operations for trajectory solution and collision prediction. It is suitable for use within a game tree search, which requires a great many potential shots to be modeled efficiently, and within a robotic pool system, which requires high accuracy in predicting shot outcomes.
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