Game Development Reference

In-Depth Information

In this subsection, the body dynamics consid-

ered for the game simulation will be summarized.

It was considered that the billiard balls can be in

three states: stopped (initial and final positions),

sliding and running. The state sliding is assumed

as the moment when the ball initialized its move-

ment. This state will be short if the applied force

into the ball is high. The state running will be the

most common state when the ball is in motion. The

set of equations used were easily obtained (Danby,

1997; Newmann, Stoy, & Thompson, 1994;The

Physics Classroom (n.d.); The Math and Physics

of Billiards, n.d.). The physical equations used

describe the initial linear and angular velocities,

describing the first balls movement when the

cue touches the white cue ball. After that, the

balls can take several and different movements

and velocities. Knowing that, the velocity of a

ball decreases until stopped due to the frictional

force between the ball and green cloth (or felt) of

the table, the variation of the linear and angular

velocities must also be considered. Another aspect

that was taken into account was the possibility

of collision between the balls. It was considered

two types of collisions: between two balls and/or

between a ball and the walls of the table. To detect

a collision between two balls, the distance between

the two balls centers that can be at most equal to

the sum of two times its radius, is estimated. The

time to collide is also estimated and then the new

directions and velocities. This new calculus took

into account the normal and tangential velocity

components for each ball, being the new direction

the sum of these two components.

result (output),
i.e.
the new positions of the balls

on the table. The various factors adjacent to the

system are the movement of the balls, the friction

between the balls and the felt, the friction of the

ball when hit the table walls, the collision type, the

weight of the ball, the momentum of the cue ball,

gravity, among others. The friction coefficient and

the impetus time given by the cue to the ball were

approximately estimated due to the complexity to

determine exactly their values. Summarizing, (1)

the input parameters: balls position before making

the putt, force and direction applied to the white

cue ball; (2) adjacent factors: balls movement

kind, slide (friction coefficient with the felt=1),

rotate (friction coefficient with the felt=0.05), ball

hit the table walls (coefficient=0.1), ball weight

and diameters (0.5Kg and 57.15cm, respectively),

gravity (9.81m/s
2
), time of momentum between

the ball and cue (0.005sec), collisions and linear

and angular velocities; (3) output parameters: new

balls positions on the table.

Application

The application has a three dimensional represen-

tation, however, since the position of the camera,

that allows the visualization of the game, is a way

to visualize the top of the table, the application

looks to have only two dimensions (Figure 1). The

game has 16 balls placed at predetermined mark

on the table (1 white, 1 black, 7 red and 7 yellow).

Figure 1. Pool table and game balls just before

the break off

Game Input and Output Definition

The input parameters considered were the balls

positions before making the putt, the force applied

to the white cue ball and its related direction.

Thus, the player will be able to control these two

parameters each time he makes a shot. Then, due

to the various factors adjacent to the system and

game conditions, the balls stops producing the final

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