1. Let’s play snooker!

2. Overview Introduction to snooker UML diagram Physics Simulation techniques Result Conclusion Further research

3. Introduction to snooker Blabla about the origin and current popularity of snooker

4. Gameplay

5. A snookered player

6. UML diagram VectorPhysics DisplayBall TableCue

7. Result Emulating 3D in a 2D playing field

8. Physics Cue - Cue ball interaction Spin & Cue Ball Impulse

9. Cue - Cue Ball Interaction Due to the Newton`s Second Law, By the result of the impact cue ball must gain velocity such that;

10. Spin & Cue Ball

11. Impulse Collisions between balls are handled by adding a certain amount of impulsive force to both balls in opposite directions. The magnitude of this impulse is given by the equation ;

12. Impulse When we used to calculate the change in velocity in the collision, previous equation can be simplified into this equation: by assuming the two balls have the same mass, since the masses are factored out again when converting the change in momentum into the corresponding change in velocity.

13. Note ( about Variables) n  is a vector representing the normal of the collision (in this case, a vector between the centers of mass of the balls)‏ e  is the coefficient of restitution (a measure of how much energy is lost in the collision, 0.8 for standard snooker ball)‏ V(AB)  is the relative velocity between the two balls Ma and Mb  are the masses of ball A and ball B, (In this equation this part is representing the reduced mass of system of a particle which consist of two individual particle )‏

14. Physics - cue Two relevant components: force and point of contact Cue and ball rotated so the force is parallel to the y-axis Impulse magnitude depends on horizontal offset (a) and vertical offset (b) from ball's center of mass Squirt not currently included

15. Physics – ball-ball collisions Both balls receive an impulse directly away from the other ball. Coefficient of restitution: 0.8 Small amount of spin transferred (5%)‏ Throw effect not currently included

16. Physics – ball-cushion collisions Approximately follow law of optics (angle of incidence equals angle of reflection). Implemented only for cushions parallel to the x-axis, all other situations rotated to match this case Y-component of velocity negated, reduced by fixed percentage (currently 80%)‏ Spin around y- and z-axes reduced by fixed percentage, around x-axis set to 0.

17. Physics – ball motion Position increased by linear velocity multiplied by timestep length Change in velocity due to friction independent of actual velocity Three components: sliding, rolling and spinning

18. Conclusion The snooker simulation meets the task requirements Realistic physics model The program allows a player to shoot a ball for the initial snooker position

19. Further research Implement a game logic to enshure that the simulation follows the official snooker rules Create an AI Define a evaluation function to order balls on the table by their priority  Consider current game situation  Plan a few strokes ahead Implement an offensive and a defensive mode

20. Timetable Presentation Testing & Analysis AI design game logic 7654321 time/weeksTask