Let’s play snooker!

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

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

Gameplay

A snookered player

UML diagram VectorPhysics DisplayBall TableCue

Result Emulating 3D in a 2D playing field

Physics Cue - Cue ball interaction Spin & Cue Ball Impulse

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

Spin & Cue Ball

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 ;

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.

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 )‏

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

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

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.

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

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

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

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