Pool Physics Simulation by Event Prediction 2: Collisions

Abstract

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.

Billiard Combat Modeling and Simulation Based on Optimal Cue Placement Control and Strategic Planning

“…Experimental results presented exploring properties of two search algorithms, MonteCarlo search and Probabilistic search. Greenspan [11,12] further analyzed the physics nature of billiard motions and collisions and developed a library as a physics engine for actual game playing. They all contributed to the correct simulation and prediction of game playing results.…”

“…In this category, researches have focused on creating intelligent robotics for entertainment purposes. Various simulations and analysis have been exercised on different popular billiard games such as 8-ball, 9-ball and snookers [2,[10][11][12]. Smith [10] applied artificial intelligence on the 8-ball game playing strategy development.…”

Computational Pool: AnOR—Optimization Point of View

“…This allows to simplify the collision detection to simultaneous quadratic equations, for which closed form formulae are available. [16,18,22]. Moreover, extension to 3D simulation still may be described by piecewise parametric quadratic equations.…”

Analyzing and Comparing Shot Planning Strategies and Their Effects on the Performance of an Augment Reality Based Billiard Training System

“…Various simulations and analyses have been exercised on di®erent popular billiard games, 3,[5][6][7]26 including 8-ball, 9-ball and snookers (see Refs. [8][9][10][11]. Smith 19 applied arti¯cial intelligence to develop a playing strategy for the 8-ball game.…”

“…Smith 19 applied arti¯cial intelligence to develop a playing strategy for the 8-ball game. Leckie and Greenspan 10,11 further analyzed the billiard motions' physics and the nature of collisions and produced a physics engine for actual game development. These works contributed to the correct simulation and prediction of game playing results.…”