Features of the Polygon Billiards Table

• By default, the number of vertices on the polygon is set to 4. The user may use the "# of sides" scrollbar to choose anything from a triangle to a 30-sided polygon.
• By default, the number of iterations of the ball is set to 10. The user may choose to enter the iterations by clicking in the "Iterations" textfield, typing the new value, and pressing Return.
• By default, the starting point of the ball is the center of the polygon (0,0). The use may choose to enter a starting point in integer coordinates between (-150,-150) and (150,150) by using the "x" and "y" textfields. The user may also choose an initial point by clicking the mouse anywhere inside the polygon.
• By default, the initial trajectory is the vector (1.3, 5.0). The user may enter his/her own values in the "vx" and "vy" textfields. The alternative way to input the velocity is to click the mouse inside the polygon and drag it in the direction of the initial motion of the billiard. No trajectory will be drawn for values from the mouse outside of the polygon.
• The speed of the ball can be changed with the "spd" scrollbar.
• The user may click on the "Phase Window" button to open up the phase window. In this window, the motion of the billiard is graphed with each bounce. At the point of intersection, distance around the polygon is plotted along the x-axis and angle of intersection (either with respect to the side of with respect to the horizontal) is plotted along the y-axis. By default, the diagram with the angle according to the tangent is showing. The user may choose to look at the diagram with angle according to the horizontal by pressing the "Go to Horizontal" button in the phase window.
• By default, the program is set to show both the movement of the billiards in both the configuration space (the table) and the phase diagram. To speed up the graphing in the phase diagram, the user may choose to check the "phase" checkbox. When this checkbox is pressed, the user will not see the motion of the ball on the billiard table but will see only the phase portrait.
• The user may press the "Start" button either in the phase window or in the main control panel. After n iterations of the ball, the "Start" buttons will now say "Continue." To continue iterations of the same initial trajectory, press either button. The button will change back to "Start" if anything about the billiard is changed (i.e. initial point, initial trajectory, shape of table).
• An alternative way to initialize the movement of the ball is to click directly in the phase diagram. When the "Start" button is pressed, the ball will begin at the specified point on the border of the figure moving in the specified direction (if possible). When the user clicks in the phase diagram, a short vector flashes on the border of the polygon showing the initial trajectory.