With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator.
You click and drag the mouse to launch a ball. It will bounce around and eventually stop on the "floor".
My next big feature I want to add in is ball to ball collision. The ball's movement is broken up into a x and y speed vector. I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way.
I guess my question has two parts:
- What is the best method to detect ball to ball collision?
Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? - What equations do I use to handle the ball to ball collisions? Physics 101
How does it effect the two balls speed x/y vectors? What is the resulting direction the two balls head off in? How do I apply this to each ball?
Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions. With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction. With balls I don't think it is that way.
Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future.
Edit: Resources I have found useful
2d Ball physics with vectors: 2-Dimensional Collisions Without Trigonometry.pdf
2d Ball collision detection example: Adding Collision Detection
Success!
I have the ball collision detection and response working great!
Relevant code:
Collision Detection:
for (int i = 0; i < ballCount; i++) { for (int j = i + 1; j < ballCount; j++) { if (balls[i].colliding(balls[j])) { balls[i].resolveCollision(balls[j]); } }}This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1. Also, it skips checking for collisions with itself).
Then, in my ball class I have my colliding() and resolveCollision() methods:
public boolean colliding(Ball ball){ float xd = position.getX() - ball.position.getX(); float yd = position.getY() - ball.position.getY(); float sumRadius = getRadius() + ball.getRadius(); float sqrRadius = sumRadius * sumRadius; float distSqr = (xd * xd) + (yd * yd); if (distSqr <= sqrRadius) { return true; } return false;}public void resolveCollision(Ball ball){ // get the mtd Vector2d delta = (position.subtract(ball.position)); float d = delta.getLength(); // minimum translation distance to push balls apart after intersecting Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d); // resolve intersection -- // inverse mass quantities float im1 = 1 / getMass(); float im2 = 1 / ball.getMass(); // push-pull them apart based off their mass position = position.add(mtd.multiply(im1 / (im1 + im2))); ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2))); // impact speed Vector2d v = (this.velocity.subtract(ball.velocity)); float vn = v.dot(mtd.normalize()); // sphere intersecting but moving away from each other already if (vn > 0.0f) return; // collision impulse float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2); Vector2d impulse = mtd.normalize().multiply(i); // change in momentum this.velocity = this.velocity.add(impulse.multiply(im1)); ball.velocity = ball.velocity.subtract(impulse.multiply(im2));}Source Code: Complete source for ball to ball collider.
If anyone has some suggestions for how to improve this basic physics simulator let me know! One thing I have yet to add is angular momentum so the balls will roll more realistically. Any other suggestions? Leave a comment!