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This example is for Processing 2+. If you have a previous version, use the examples included with your software. If you see any errors or have suggestions, please let us know.

Circle Collision with Swapping Velocities by Ira Greenberg.

Based on Keith Peter's Solution in Foundation Actionscript Animation: Making Things Move!

```

Ball[] balls =  {
new Ball(100, 400, 20),
new Ball(700, 400, 80)
};

PVector[] vels = {
new PVector(2.15, -1.35),
new PVector(-1.65, .42)
};

void setup() {
size(640, 360);
noStroke();
}

void draw() {
background(51);
fill(204);
for (int i = 0; i < 2; i++){
balls[i].x += vels[i].x;
balls[i].y += vels[i].y;
ellipse(balls[i].x, balls[i].y, balls[i].r*2, balls[i].r*2);
checkBoundaryCollision(balls[i], vels[i]);
}
checkObjectCollision(balls, vels);
}

void checkObjectCollision(Ball[] b, PVector[] v){

// get distances between the balls components
PVector bVect = new PVector();
bVect.x = b[1].x - b[0].x;
bVect.y = b[1].y - b[0].y;

// calculate magnitude of the vector separating the balls
float bVectMag = sqrt(bVect.x * bVect.x + bVect.y * bVect.y);
if (bVectMag < b[0].r + b[1].r){
// get angle of bVect
float theta  = atan2(bVect.y, bVect.x);
// precalculate trig values
float sine = sin(theta);
float cosine = cos(theta);

/* bTemp will hold rotated ball positions. You
just need to worry about bTemp[1] position*/
Ball[] bTemp = {
new Ball(), new Ball()
};

/* b[1]'s position is relative to b[0]'s
so you can use the vector between them (bVect) as the
reference point in the rotation expressions.
bTemp[0].x and bTemp[0].y will initialize
automatically to 0.0, which is what you want
since b[1] will rotate around b[0] */
bTemp[1].x  = cosine * bVect.x + sine * bVect.y;
bTemp[1].y  = cosine * bVect.y - sine * bVect.x;

// rotate Temporary velocities
PVector[] vTemp = {
new PVector(), new PVector()
};
vTemp[0].x  = cosine * v[0].x + sine * v[0].y;
vTemp[0].y  = cosine * v[0].y - sine * v[0].x;
vTemp[1].x  = cosine * v[1].x + sine * v[1].y;
vTemp[1].y  = cosine * v[1].y - sine * v[1].x;

/* Now that velocities are rotated, you can use 1D
conservation of momentum equations to calculate
the final velocity along the x-axis. */
PVector[] vFinal = {
new PVector(), new PVector()
};
// final rotated velocity for b[0]
vFinal[0].x = ((b[0].m - b[1].m) * vTemp[0].x + 2 * b[1].m *
vTemp[1].x) / (b[0].m + b[1].m);
vFinal[0].y = vTemp[0].y;
// final rotated velocity for b[0]
vFinal[1].x = ((b[1].m - b[0].m) * vTemp[1].x + 2 * b[0].m *
vTemp[0].x) / (b[0].m + b[1].m);
vFinal[1].y = vTemp[1].y;

// hack to avoid clumping
bTemp[0].x += vFinal[0].x;
bTemp[1].x += vFinal[1].x;

/* Rotate ball positions and velocities back
Reverse signs in trig expressions to rotate
in the opposite direction */
// rotate balls
Ball[] bFinal = {
new Ball(), new Ball()
};
bFinal[0].x = cosine * bTemp[0].x - sine * bTemp[0].y;
bFinal[0].y = cosine * bTemp[0].y + sine * bTemp[0].x;
bFinal[1].x = cosine * bTemp[1].x - sine * bTemp[1].y;
bFinal[1].y = cosine * bTemp[1].y + sine * bTemp[1].x;

// update balls to screen position
b[1].x = b[0].x + bFinal[1].x;
b[1].y = b[0].y + bFinal[1].y;
b[0].x = b[0].x + bFinal[0].x;
b[0].y = b[0].y + bFinal[0].y;

// update velocities
v[0].x = cosine * vFinal[0].x - sine * vFinal[0].y;
v[0].y = cosine * vFinal[0].y + sine * vFinal[0].x;
v[1].x = cosine * vFinal[1].x - sine * vFinal[1].y;
v[1].y = cosine * vFinal[1].y + sine * vFinal[1].x;
}
}

void checkBoundaryCollision(Ball ball, PVector vel) {
if (ball.x > width-ball.r) {
ball.x = width-ball.r;
vel.x *= -1;
}
else if (ball.x < ball.r) {
ball.x = ball.r;
vel.x *= -1;
}
else if (ball.y > height-ball.r) {
ball.y = height-ball.r;
vel.y *= -1;
}
else if (ball.y < ball.r) {
ball.y = ball.r;
vel.y *= -1;
}
}

class Ball{
float x, y, r, m;

// default constructor
Ball() {
}

Ball(float x, float y, float r) {
this.x = x;
this.y = y;
this.r = r;
m = r*.1;
}
}

```