// All Examples Written by Casey Reas and Ben Fry
// unless otherwise stated.
+int width = 200;
+int height = 200;
+int nBalls = 5;
-Ball[] balls = {
-
- new Ball(100, 400, 10),
-
- new Ball(700, 400, 40)
-
- };
-
-
-
-Vect2D[] vels = {
-
- new Vect2D(2.15, -1.35),
-
- new Vect2D(-1.65, .42)
-
- };
-
-
+Ball[] balls = new Ball[nBalls];
+Vect2D[] vels = new Vect2D[nBalls];
void setup(){
-
- size(200, 200);
-
+ size(width, height);
smooth();
-
noStroke();
-
+ initBalls();
}
-
+void initBalls(){
+ for (int i = 0; i < nBalls; i++) {
+ balls[i] = new Ball(30*i, 30*i, random(5, 15));
+ vels[i] = new Vect2D(1, 1);
+ }
+}
void draw(){
-
background(51);
-
fill(204);
-
- for (int i=0; i< 2; i++){
-
+ for (int i = 0; i < nBalls; i++){
balls[i].x += vels[i].vx;
-
balls[i].y += vels[i].vy;
-
ellipse(balls[i].x, balls[i].y, balls[i].r*2, balls[i].r*2);
-
checkBoundaryCollision(balls[i], vels[i]);
-
+ // check all ball pairs for collisions
+ for (int j = i+1; j < nBalls; j++){
+ checkObjectCollision(balls[i], vels[i], balls[j], vels[j]);
+ }
}
-
- checkObjectCollision(balls, vels);
-
}
-
-
-void checkObjectCollision(Ball[] b, Vect2D[] v){
-
-
+void checkObjectCollision(Ball b1, Vect2D v1, Ball b2, Vect2D v2){
// get distances between the balls components
-
Vect2D bVect = new Vect2D();
-
- bVect.vx = b[1].x - b[0].x;
-
- bVect.vy = b[1].y - b[0].y;
-
-
+ bVect.vx = b2.x - b1.x;
+ bVect.vy = b2.y - b1.y;
// calculate magnitude of the vector separating the balls
-
float bVectMag = sqrt(bVect.vx * bVect.vx + bVect.vy * bVect.vy);
-
- if (bVectMag < b[0].r + b[1].r){
-
+ if (bVectMag < b1.r + b2.r){
// get angle of bVect
-
float theta = atan2(bVect.vy, bVect.vx);
-
// 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
-
+ /* b2's position is relative to b1'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] */
-
+ since b2 will rotate around b1 */
bTemp[1].x = cosine * bVect.vx + sine * bVect.vy;
-
bTemp[1].y = cosine * bVect.vy - sine * bVect.vx;
-
-
// rotate Temporary velocities
-
Vect2D[] vTemp = {
-
new Vect2D(), new Vect2D() };
-
- vTemp[0].vx = cosine * v[0].vx + sine * v[0].vy;
-
- vTemp[0].vy = cosine * v[0].vy - sine * v[0].vx;
-
- vTemp[1].vx = cosine * v[1].vx + sine * v[1].vy;
-
- vTemp[1].vy = cosine * v[1].vy - sine * v[1].vx;
-
-
+ vTemp[0].vx = cosine * v1.vx + sine * v1.vy;
+ vTemp[0].vy = cosine * v1.vy - sine * v1.vx;
+ vTemp[1].vx = cosine * v2.vx + sine * v2.vy;
+ vTemp[1].vy = cosine * v2.vy - sine * v2.vx;
/* Now that velocities are rotated, you can use 1D
-
conservation of momentum equations to calculate
-
the final velocity along the x-axis. */
-
Vect2D[] vFinal = {
-
new Vect2D(), new Vect2D() };
-
- // final rotated velocity for b[0]
-
- vFinal[0].vx = ((b[0].m - b[1].m) * vTemp[0].vx + 2 * b[1].m *
-
- vTemp[1].vx) / (b[0].m + b[1].m);
-
+ // final rotated velocity for b1
+ vFinal[0].vx = ((b1.m - b2.m) * vTemp[0].vx + 2 * b2.m *
+ vTemp[1].vx) / (b1.m + b2.m);
vFinal[0].vy = vTemp[0].vy;
-
- // final rotated velocity for b[0]
-
- vFinal[1].vx = ((b[1].m - b[0].m) * vTemp[1].vx + 2 * b[0].m *
-
- vTemp[0].vx) / (b[0].m + b[1].m);
-
+ // final rotated velocity for b1
+ vFinal[1].vx = ((b2.m - b1.m) * vTemp[1].vx + 2 * b1.m *
+ vTemp[0].vx) / (b1.m + b2.m);
vFinal[1].vy = vTemp[1].vy;
-
-
// hack to avoid clumping
-
bTemp[0].x += vFinal[0].vx;
-
bTemp[1].x += vFinal[1].vx;
-
-
/* 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;
-
-
+ b2.x = b1.x + bFinal[1].x;
+ b2.y = b1.y + bFinal[1].y;
+ b1.x = b1.x + bFinal[0].x;
+ b1.y = b1.y + bFinal[0].y;
// update velocities
-
- v[0].vx = cosine * vFinal[0].vx - sine * vFinal[0].vy;
-
- v[0].vy = cosine * vFinal[0].vy + sine * vFinal[0].vx;
-
- v[1].vx = cosine * vFinal[1].vx - sine * vFinal[1].vy;
-
- v[1].vy = cosine * vFinal[1].vy + sine * vFinal[1].vx;
-
+ v1.vx = cosine * vFinal[0].vx - sine * vFinal[0].vy;
+ v1.vy = cosine * vFinal[0].vy + sine * vFinal[0].vx;
+ v2.vx = cosine * vFinal[1].vx - sine * vFinal[1].vy;
+ v2.vy = cosine * vFinal[1].vy + sine * vFinal[1].vx;
}
-
}
-
-
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;
-
}
-
}
-
-
class Vect2D{
-
float vx, vy;
-
-
// default constructor
-
Vect2D() {
-
}
-
-
Vect2D(float vx, float vy) {
-
this.vx = vx;
-
this.vy = vy;
-
}
-
}
-
-
// checkBoundaryCollision() function:
-
void checkBoundaryCollision(Ball ball, Vect2D vel){
-
if (ball.x > width-ball.r){
-
ball.x = width-ball.r;
-
vel.vx *= -1;
-
}
-
else if (ball.x < ball.r){
-
ball.x = ball.r;
-
vel.vx *= -1;
-
}
-
else if (ball.y > height-ball.r){
-
ball.y = height-ball.r;
-
vel.vy *= -1;
-
}
-
else if (ball.y < ball.r){
-
ball.y = ball.r;
-
vel.vy *= -1;
-
}
-
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