An Event-Based Pool Physics Simulator

  • Will Leckie
  • Michael Greenspan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4250)


The paper presents a method to simulate the physics of the game of pool. 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. It is shown that the occurrences of all possible events are determined as the roots of polynomials up to fourth order, for which closed-form solutions exist. The method is both accurate, returning continuous space 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 modeled efficiently, and within a robotic pool system, which requires a high accuracy in predicting shot outcomes.


Angular Velocity Motion State Rolling State Subtractive Term Object Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alciatore, D.: The Illustrated Principles of Pool and Billiards. Sterling Publishers, New York (2004)Google Scholar
  2. 2.
    Ebne Alian, M., Bagheri Shouraki, S., Manzuri Shalmani, M.T., Karimian, P., Sabzmeydani, P.: Robotshark: A Gantry Pool Player Robot. In: ISR 2004: 35th Intl. Sym. Rob. (2004)Google Scholar
  3. 3.
    Bayes, J., Scott, W.: Billiard Ball Collision Experiment. Am. Jour. Physics 3(31), 197–200 (1963)CrossRefGoogle Scholar
  4. 4.
    Berger, F.: (2000),
  5. 5.
    Cheng, B.R., Li, J.T., Yang, J.S.: Design of the Neural-Fuzzy Compensator for a Billiard Robot. In: IEEE Intl. Conf. Networking, Sensing & Control, pp. 909–913 (2004)Google Scholar
  6. 6.
    Chua, S.C., Wong, E.K., Tan, A.W.C., Koo, V.C.: Decision Algorithm for Pool Using Fuzzy System. In: iCAiET 2002: Intl. Conf. AI in Eng. & Tech., pp. 370–375 (2002)Google Scholar
  7. 7.
    Chua, S.C., Wong, E.K., Koo, V.C.: Pool Balls Identification and Calibration for a Pool Robot. In: ROVISP 2003: Proc. Intl. Conf. Robotics, Vision, Information and Signal Processing, pp. 312–315 (2003)Google Scholar
  8. 8.
    Coriolis, G.G.: Théorie Mathématique des Effets du Jeu de Billard. Jacques Gabay (1835) (republished, 1990)Google Scholar
  9. 9.
    Koehler, J.H.: The Science of Pocket Billiards. Sportology Publications, Laguna Hills (1989)Google Scholar
  10. 10.
    Larsen, L.B., Jensen, M.D., Vodzi, W.K.: Multi Modal User Interaction in an Automatic Pool Trainer. In: ICMI 2002: 4th IEEE Intl. Conf. Multimodal Interfaces, pp. 361–366 (2002)Google Scholar
  11. 11.
    Lin, Z.M., Yang, J.S., Yang, C.Y.: Grey Decision-Making for a Billiard Robot. In: IEEE Intl. Conf. Systems, Man and Cybernetics, pp. 5350–5355 (2004)Google Scholar
  12. 12.
    Long, F., Herland, J., Tessier, M.-C., Naulls, D., Roth, A., Roth, G., Greenspan, M.: Robotic Pool: An Experiment in Automatic Potting. In: IROS 2004: IEEE/RSJ Intl. Conf. Intell. Rob. Sys., pp. 361–366 (2004)Google Scholar
  13. 13.
    Marlow, W.C.: The Physics of Pocket Billiards. Marlow Advanced Systems Technologies, Palm Beach Gardens (1995)Google Scholar
  14. 14.
    Onada, G.: Comment on Analysis of Billiard Ball Collisions in Two Dimensions. Am. Jour. Physics 57(5), 476–478 (1989)CrossRefGoogle Scholar
  15. 15.
    Petit, R.: Billard. Théorie du Jeu. Chiron Editeur, Saint-Quentin, France (1997)Google Scholar
  16. 16.
    Shepard, R.: Amateur Physics for the Amateur Pool Player. 3rd edn. (self-published, 1997)Google Scholar
  17. 17.
    Shu, S.W.: Automating Skills Using a Robot Snooker Player. PhD Thesis, Bristol University (1994)Google Scholar
  18. 18.
    Walker, J.: The Physics of the Draw, the Follow, and the Masse (in Billiards and Pool). Scientific American 249(1), 124–129 (1983)CrossRefGoogle Scholar
  19. 19.
    Wallace, R.E., Schroeder, M.: Analysis of Billiard Ball Collisions in Two Dimensions. Am. Jour. Physics 56(9), 815–819 (1988)CrossRefGoogle Scholar
  20. 20.
    Witters, J., Duymelinck, D.: Rolling and Sliding Resistive Forces on Balls Moving on a Flat Surface. Am. Jour. Physics 54(1), 80–83 (1988)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Will Leckie
    • 1
  • Michael Greenspan
    • 2
  1. 1.Department of Electrical and Computer EngineeringQueen’s UniversityKingstonCanada
  2. 2.Department of Electrical and Computer Engineering, School of ComputingQueen’s UniversityKingstonCanada

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