Making balls bounce off each other (openGL) - c++

Question

I'm trying to make an application where balls bounce off the walls and also off each other. The bouncing off the walls works fine, but I'm having some trouble getting them to bounce off each other. Here's the code I'm using to make them bounce off another ball (for testing I only have 2 balls)
// Calculate the distance using Pyth. Thrm.
GLfloat x1, y1, x2, y2, xd, yd, distance;
x1 = balls[0].xPos;
y1 = balls[0].yPos;
x2 = balls[1].xPos;
y2 = balls[1].yPos;
xd = x2 - x1;
yd = y2 - y1;
distance = sqrt((xd * xd) + (yd * yd));
if(distance < (balls[0].ballRadius + balls[1].ballRadius))
{
std::cout << "Collision\n";
balls[0].xSpeed = -balls[0].xSpeed;
balls[0].ySpeed = -balls[0].ySpeed;
balls[1].xSpeed = -balls[1].xSpeed;
balls[1].ySpeed = -balls[1].ySpeed;
}
What happens is that they randomly bounce, or pass through each other. Is there some physics that I'm missing?
EDIT: Here's the full function
// Callback handler for window re-paint event
void display()
{
glClear(GL_COLOR_BUFFER_BIT); // Clear the color buffer
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
glEnable(GL_BLEND);
// FOR LOOP
for (int i = 0; i < numOfBalls; i++)
{
glLoadIdentity(); // Reset model-view matrix
int numSegments = 100;
GLfloat angle = 0;
glTranslatef(balls[i].xPos, balls[i].yPos, 0.0f); // Translate to (xPos, yPos)
// Use triangular segments to form a circle
glBegin(GL_TRIANGLE_FAN);
glColor4f(balls[i].colorR, balls[i].colorG, balls[i].colorB, balls[i].colorA);
glVertex2f(0.0f, 0.0f); // Center of circle
for (int j = 0; j <= numSegments; j++)
{
// Last vertex same as first vertex
angle = j * 2.0f * PI / numSegments; // 360 deg for all segments
glVertex2f(cos(angle) * balls[i].ballRadius, sin(angle) * balls[i].ballRadius);
}
glEnd();
// Animation Control - compute the location for the next refresh
balls[i].xPos += balls[i].xSpeed;
balls[i].yPos += balls[i].ySpeed;
// Calculate the distance using Pyth. Thrm.
GLfloat x1, y1, x2, y2, xd, yd, distance;
x1 = balls[0].xPos;
y1 = balls[0].yPos;
x2 = balls[1].xPos;
y2 = balls[1].yPos;
xd = x2 - x1;
yd = y2 - y1;
distance = sqrt((xd * xd) + (yd * yd));
if(distance < (balls[0].ballRadius + balls[1].ballRadius))
{
std::cout << "Collision\n";
balls[0].xSpeed = -balls[0].xSpeed;
balls[0].ySpeed = -balls[0].ySpeed;
balls[1].xSpeed = -balls[1].xSpeed;
balls[1].ySpeed = -balls[1].ySpeed;
}
else
{
std::cout << "No collision\n";
}
// Check if the ball exceeds the edges
if (balls[i].xPos > balls[i].xPosMax)
{
balls[i].xPos = balls[i].xPosMax;
balls[i].xSpeed = -balls[i].xSpeed;
}
else if (balls[i].xPos < balls[i].xPosMin)
{
balls[i].xPos = balls[i].xPosMin;
balls[i].xSpeed = -balls[i].xSpeed;
}
if (balls[i].yPos > balls[i].yPosMax) {
balls[i].yPos = balls[i].yPosMax;
balls[i].ySpeed = -balls[i].ySpeed;
}
else if (balls[i].yPos < balls[i].yPosMin)
{
balls[i].yPos = balls[i].yPosMin;
balls[i].ySpeed = -balls[i].ySpeed;
}
}
glutSwapBuffers(); // Swap front and back buffers (of double buffered mode)
}
**Note: Most of the function uses a for loop with numOfBalls as the counter, but to test collision, I'm only using 2 balls, hence the balls[0] and balls[1]

Answer 1

Here are some things to consider.
If the length of (xSpeed,ySpeed) and is roughly comparable with .ballRadius it is possible for two balls to travel "thru" each other between "ticks" of the simulation's clock (one step). Consider two balls which are traveling perfectly vertical, one up, one down, and 1 .ballRadius apart horizontally. In real life they would clearly collide but it would be easy for your simulation to miss this event if .ySpeed ~ .ballRadius.
Second, you change in the vector of the balls results in each ball coming to rest, since
balls[0].xSpeed -= balls[0].xSpeed;
is a really exotic way of writing
balls[0].xSpeed = 0;

Answer 2

For the physics almost correct stuff, you need to invert only the component perpendicular to the plane of contact.
In other words take collision_vector to be the vector between the center of the balls (just subtract one point's coordinates from the other's). Because you have spheres this also happens to be the normal of the collision plane.
Now for each ball in turn, you need to decompose their speeds. The A component will be the one aligned with the colision_vector you can obtain it by doing some vector arithmetic A = doc(Speed, collision_vector) * collision_vector. This will be the thing you want to invert. You also want to extract the B component that is parallel to the collision plane. Because it's parallel it won't change because of the collision. You obtain it by subtracting A from the speed vector.
Finally the new speed will be something like B - A. If you want to get the balls to spin you will need an angular momentum in the direction of A - B. If the balls have different mass then you will need use the weight ratio as a multiplier for A in the first formula.
This will make the collision look legit. The detection still needs to happen correctly. Make sure that the speeds are significantly smaller than the radius of the balls. For comparable or bigger speeds you will need more complex algorithms.
Note: most of the stuff above is vector arithmetics. Also It's late here so I might have mixed up some signs (sorry). Take a simple example on paper and work it out. It will also help you understand the solution better.