Elastic Collisions - Page 2
       by alex nino and kirupa  |  25 April 2010

In the previous page, you learned a bit about elastic collisions and how they fit in with the physical laws that we are subjected to! In this page, let's look at two quick examples of Flash applications that implement elastic collisions.

Revisiting the Energy Ring
If you saw the video in the previous page, you saw a circular ring with colorful blocks colliding with other blocks and bouncing back and forth. What is unique about the collision is that the path all objects move in is constrained by a circular, ring shape.

Below, you will find an example of the energy ring created in Flash:

You can download the source code for the above example here:

Download Source (Flex/AS3)

First of all, as you can tell from my version, I focused only on the movement and the collision. Some of the nice artistic touches like the small flying particles cannot be found in this. I'll leave it as an exercise to you, the fair reader, the add those nice finishing touches!

If you saw the source code for the bouncing blocks in the previous page, you'll see a lot of similarities in this version. What you may find useful is how to look at elastic collision from not just the horizontal/x-axis collisions but also taking the vertical/y-axis as well. Add in a bit of gravity and simulating the loop using a sine curve, and hopefully you find the source code valuable to look into.

More 2D Collisions
The final example I am going to show is a pure 2D implementation of elastic collisions involving the typical billiards/pool scenario:

Move your mouse around the white ball to adjust the angle you are interested in hitting the ball with the pool stick. Click on the pool stick and move it back to adjust the force with which you want to hit the ball.

As you can tell by playing with this for a few minutes, this is something that I haven't fully finished! If you pocket the white ball, the ball simply just appears behind the line haha. It is really more of a technical demo than a game...for now. I will provide the full source file for this shortly once I have finished it as well.

To make up for not providing the source file, I will share how I am specifying the elastic collision. In this example, I am optimizing for performance because I want the response from a collision to be nearly instantaneous:

static public function doElasticCollision(b1:Ball,b2:Ball){

// Compute unit normal and unit tangent vectors

// v_n = normal vec. - a vector normal to the collision surface

var v_n:Point = new Point(b2.x-b1.x, b2.y-b1.y);

var hyp:Number = getHypotenuse(v_n.x,v_n.y); //distance between dots

var v_un:Point = new Point(v_n.x/hyp, v_n.y/hyp); // unit normal vector

var v_ut:Point = new Point(-v_un.y, v_un.x); // unit tangent vector

// Compute scalar projections of velocities onto v_un and v_ut

var v1n:Number = v_un.x * b1.vx + v_un.y * b1.vy;

var v1tPrime:Number = v_ut.x * b1.vx + v_ut.y * b1.vy;

var v2n:Number = v_un.x * b2.vx + v_un.y * b2.vy;

var v2tPrime:Number = v_ut.x * b2.vx + v_ut.y * b2.vy;

// Compute new velocities using one-dimensional elastic collision equations in the normal direction

// Division by zero avoided. See early return above.

var v1nPrime:Number = (v1n * (b1.m - b2.m) + 2. * b2.m * v2n) / (b1.m + b2.m);

var v2nPrime:Number = (v2n * (b2.m - b1.m) + 2. * b1.m * v1n) / (b1.m + b2.m);

// Compute new normal and tangential velocity vectors

var v_v1nPrime:Point = new Point(v_un.x*v1nPrime, v_un.y*v1nPrime);

var v_v1tPrime:Point = new Point(v_ut.x*v1tPrime, v_ut.y*v1tPrime);

var v_v2nPrime:Point = new Point(v_un.x*v2nPrime, v_un.y*v2nPrime);

var v_v2tPrime:Point = new Point(v_ut.x*v2tPrime, v_ut.y*v2tPrime);

//update velocities.

b1.vx = v_v1nPrime.x + v_v1tPrime.x;

b1.vy = v_v1nPrime.y + v_v1tPrime.y;

b2.vx = v_v2nPrime.x + v_v2tPrime.x;

b2.vy = v_v2nPrime.y + v_v2tPrime.y;

}

One way I am able to get better performance is because I am not using the Cosine and Sine functions. The downside is that some of the rotational tricks you can perform on a real game of billiards or pool aren't possible, but the upside is blink-of-an-eye collision detection and reaction!

Conclusion
I hope this article helped get you started with elastic collisions and how to implement them in your applications.

One thing I want to emphasize is that you are free to choose whatever approach you want for collision detection independently of what approach you want to take for the reaction to the collision. Kirupa has a few articles on Collision Detection already written, so check them out by clicking here. This article provides you with some examples of how to react to the collision. A clean reaction to the collision where momentum is preserved is...an elastic collision!

If you have any questions or want to learn more, visit yoambulante.com or post on the forums here.

Alex Nino (yoambulante.com)

Kirupa

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