ECE 4760: Laboratory 3

Video Game -- Particle Beam


You will produce a game in which ball-like particles enter from one side of the screen. You must deflect the balls with a paddle (while conserving momentum) to keep them from hitting your side of the screen. The paddle will be controlled by an analog input. There will be a time limit to the game. Display will be on a TV, with sound effects. The balls will follow standard billards-type dynamics, with zero friction between balls. An example of billard dynamics is shown here and slower.


You will probably want to review the description of the video code given in Video Generation with AVR. You can use video_codeGCC644.c and multASM.S as a basis for your program. But note that you could use any another display format described on the video page. Be sure to add the assembler source file to the project before compiling. Set the GCC project configuration (in the Project:ConfigureOptions... menu) to:

Build the video DAC shown to the left and connect it to the yellow connector on the TV using clip leads and a RCA phone jack. Make sure the TV is set to video input. Test the TV connection using the example program linked above. The power supplies on the TVs and development boards are NOT interchangable.

The game will be controlled by a potentiometer hooked to an A/D input on the MCU. Use the circuit to the left to make a user-variable voltage. I suggest setting Vref to Vcc on the A/D converter. This example (ADCtestGCC644.c uart.c, uart.h, project zip) shows how to set up the A/D converter to read a trimpot.
You are going to be programming in the equations of motion for the balls. Remember that the video coordinate system has x increasing to the right and y increasing downward. We will step the billards system forward in time by calculating the total change in velocity from a collision, without worrying exactly how forces change the velocity.

The change in velocity during impact can be derived for frictionless balls of equal mass by noting that the the impact force must act in a direction parallel to the line connecting the centers of the two impacting balls. The change in velocity must be parallel to the connecting line also, with the velocity component parallel to the line having its sign reversed by the collision and the velocity component perpendicular to the line unchanged. Projecting the initial velocity onto the line connecting the centers, negating the result, and resolving it back into x and y velocity components gives the velocity change. If i and j are the indices of the colliding balls, define:

then delta v for ball i is given by the following where the right-most term represents the projection of the velocity onto the line and the other term converts the projection back to x,y coordinates.

The calculation procedure for each time step is:

  1. Compute the Δv for each collision, based on the positions of the balls, and add it to the current velocity. Do this for every pair of balls. This step is time consuming, but only has to be performed for any two balls if they are less than 2 radii apart. Ball-ball collisions will not be exact because of finite time steps. One consequence of this is that balls tend to capture each other when they collide. You will need to do a numerical hack to avoid capture. I suggest that after a ball collides with another ball or the paddle, that it not be allowed to collide again for a few frames.
    Pseudocode for this might be:
    For each ball i from 1 to n
      For each ball j from i+1 to n
        Compute rij
        if (||rij|| less than 2*(ballRadius) and hitCounter is zero)
          Compute vij
          Compute Δvi
          Add Δvi to vi
          Subtract Δvi from vj
          Set hitCounter big enough to avoid particle capture
        elseif (hitCounter>0)
          decrement hitCounter
    When I coded this, I did not bother to calculate the square root of the sum of squares when calculating ||rij|| (too slow). Instead, in the if statement, I just used the approximation that to be within hit range, the absolute value each component of rij was less than 2*ballRadius. When dividing by ||rij||2 you can use the known value of (2*ballRadius)2. In the assignment below, I set ballRadius=2.
  2. For each ball, simulate friction between the ball and table by making
    vx(t+dt)=vx(t)-vx*drag and vy(t+dt)=vy-vy*drag
    The drag should be small, perhaps drag=0x0001 (in fixed notation).
  3. Update the positions according to
    x(t+dt)=x(t)+vx*dt and y(t+dt)=y(t)+vy*dt
  4. Detect collisions with the walls and modify velocities by negating the velocity component perprendicular to the wall.
  5. Delete any balls which hit the left wall or "catch bins".

Clearly, v and x all need initial conditions, which you will set, according the specifications below. It is doubtful that you will have enough time between frames to do all of the calculations in floating point. I suggest using 16 bit, signed numbers with the binary point set at the byte boundary. I also suggest scaling velocity so that you can make dt=1, thereby avoiding a multiply. There is an example of a bouncing ball with drag done with fixed point numbers.

The previous analysis is adapted from: Studies in Molecular Dynamics. I. General Method, by B. Alder and T. Wainwright, Journal of Chemical Physics, Vol 31 #2, Aug 1959, pp 459-466. See also Hard-Sphere molecular dynamics. One final project in 2005 used a different scheme to calculate collisions.

You will need your digital camera to document your project.


2011: video


Write a program in C and possibly assembler for the microcontroller with these specifications:

When you demonstrate the program to a staff member, you should play the game.

Your written lab report should include the sections mentioned in the policy page, and :

Copyright Cornell University March 14, 2011