Dimitrios Christopoulos - Collision detection tutorial

//render/blend explosions

glEnable(GL_BLEND); //enable blending

glDepthMask(GL_FALSE); //disable depth buffer writtes

glBindTexture(GL_TEXTURE_2D, texture[1]); //upload texture

for(i = 0; i < 20; i++) //update and render explosions

{

if (ExplosionArray[i]._Alpha >= 0) {

glPushMatrix();

ExplosionArray[i]._Alpha -= 0.01f; //update alpha

ExplosionArray[i]._Scale += 0.03f; //update scale

//assign vertices colour yellow with alpha

// colour tracks ambient and diffuse

glColor4f(1, 1, 0, ExplosionArray[i]._Alpha);

//scale

glScalef(ExplosionArray[i]._Scale, ExplosionArray[i]._Scale, ExplosionArray[i]._Scale);

// translate into position taking into acout the offset caused by the scale

glTranslatef((float)ExplosionArray[i]._Position.X() / ExplosionArray[i]._Scale, (float)ExplosionArray[i]._Position.Y() / ExplosionArray[i]._Scale, (float)ExplosionArray[i]._Position.Z() / ExplosionArray[i]._Scale);

glCallList(dlist); // call display list glPopMatrix();

}

}

For the sound the windows multimedia function PlaySound is used. This is a quick and dirty way to play wav files quickly and without trouble.

Congratulations…

If you are still with me you have survived successfully the theory section ;)

Before having fun playing around with the demo, some further explanations about the source code are necessary.

The main flow and steps of the simulation are as follows (in pseudo code).

While (Timestep != 0) {

For each ball {

compute nearest collision with planes;

compute nearest collision with cylinders;

Save and replace if it the nearest intersection in time computed until now;

}

Check for collision among moving balls;

Save and replace if it the nearest intersection in time computed until now;

If (Collision occurred) {

Move All Balls for time equal to collision time;

(We already have computed the point, normal and collision time.)

Compute Response;

Timestep -= CollisonTime;

} else Move All Balls for time equal to Timestep

}

The actual code which implements the above pseudo code is much harder to read but essentially is an exact implementation of the pseudo code above.

// While time step not over

while (RestTime > ZERO) {

lamda = 10000; //initialize to very large value

// For all the balls find closest intersection between balls and planes/cylinders

for (int i = 0; i < NrOfBalls; i++) {

// compute new position and distance

OldPos[i] = ArrayPos[i];

TVector::unit(ArrayVel[i],uveloc);

ArrayPos[i] = ArrayPos[i] + ArrayVel[i] * RestTime;

rt2 = OldPos[i].dist(ArrayPos[i]);

// Test if collision occured between ball and all 5 planes

if (TestIntersionPlane(pl1, OldPos[i], uveloc, rt, norm)) {

// Find intersection time

rt4 = rt * RestTime / rt2;

// if smaller than the one already stored replace and in timestep

if (rt4 <= lamda) {

// if intersection time in current time step

if (rt4 <= RestTime + ZERO) if (! ((rt <= ZERO) && (uveloc.dot(norm) > ZERO)) ) {

normal = norm;

point=OldPos[i] + uveloc * rt;

lamda = rt4;

BallNr = i;

}

}

}

if (TestIntersionPlane(pl2, OldPos[i], uveloc, rt, norm)) {

//…The same as above omitted for space reasons

}

if (TestIntersionPlane(pl3, OldPos[i], uveloc, rt, norm)) {

//…The same as above omitted for space reasons

}

if (TestIntersionPlane(pl4, OldPos[i], uveloc, rt, norm)) {

//…The same as above omitted for space reasons

}

if (TestIntersionPlane(pl5, OldPos[i], uveloc, rt, norm)) {

//…The same as above omitted for space reasons

}

// Now test intersection with the 3 cylinders

if (TestIntersionCylinder(cyl1, OldPos[i], uveloc, rt, norm, Nc)) {

rt4 = rt * RestTime / rt2;

if (rt4 <= lamda) {

if (rt4 <= RestTime + ZERO) if (! ((rt <= ZERO) && (uveloc.dot(norm) > ZERO)) ) {

normal = norm;

point = Nc;

lamda = rt4;

BallNr = i;

}

}

}

if (TestIntersionCylinder(cyl2, OldPos[i], uveloc, rt, norm, Nc)) {

//…The same as above omitted for space reasons

}

if (TestIntersionCylinder(cyl3, OldPos[i], uveloc, rt, norm, Nc)) {

//…The same as above ommited for space reasons

}

}

// After all balls were tested with planes/cylinders test for collision

// between them and replace if collision time smaller

if (FindBallCol(Pos2, BallTime, RestTime, BallColNr1, BallColNr2)) {

if (sounds) PlaySound("Explode.wav", NULL, SND_FILENAME|SND_ASYNC);

if ( (lamda == 10000) || (lamda > BallTime) ) {

RestTime = RestTime - BallTime;

TVector pb1, pb2, xaxis, U1x, U1y, U2x, U2y, V1x, V1y, V2x, V2y;

double a,b;

...

code omitted for space reasons

the code is described in the Physically Based Modeling section under sphere to sphere collision

...

// Update explosion array and insert explosion

for (j = 0; j < 20; j++) {

if (ExplosionArray[j]._Alpha <= 0) {

ExplosionArray[j]._Alpha = 1;

ExplosionArray[j]._Position = ArrayPos[BallColNr1];

ExplosionArray[j]._Scale = 1;

break;

}

}

continue;

}

}

// End of tests

// If collision occured move simulation for the correct timestep

// and compute response for the colliding ball

if (lamda !=10000) {

RestTime -= lamda;

for (j = 0; j < NrOfBalls; j++) ArrayPos[j] = OldPos[j] + ArrayVel[j] * lamda;

rt2 = ArrayVel[BallNr].mag();

ArrayVel[BallNr].unit();

ArrayVel[BallNr] = TVector::unit( (normal * (2 * normal.dot(-ArrayVel[BallNr]))) + ArrayVel[BallNr] );

ArrayVel[BallNr] = ArrayVel[BallNr] * rt2;

// Update explosion array and insert explosion

for (j = 0; j < 20; j++) {

if (ExplosionArray[j]._Alpha <= 0) {

ExplosionArray[j]._Alpha = 1;

ExplosionArray[j]._Position = point;

ExplosionArray[j]._Scale = 1;

break;

}

}

} else RestTime=0;

} //end of while loop

The main global variables of importance are:

The main functions of interest are: