/** * 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);  smooth();  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;  }}