# COLLISIONS BETWEEN CIRCLES in Font Encode USS Code 128 in Font COLLISIONS BETWEEN CIRCLES

COLLISIONS BETWEEN CIRCLES
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Figure 3-23. Use the collision vector to move the circles out of the collision. Now that we ve moved the circles out of the collision, we need to calculate their bounce vectors. When the circles collide, they transfer their motion vectors to each other.
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First, we need to calculate the circles motion vectors and project them onto v0 and v0 s normal. //_c1's motion vector var v1:VectorModel = new VectorModel ( _c1.xPos, _c1.yPos, _c1.xPos + _c1.vx, _c1.yPos + _c1.vy ); //_c2's motion vector var v2:VectorModel = new VectorModel ( _c2.xPos, _c2.yPos, _c2.xPos + _c2.vx, _c2.yPos + _c2.vy ); //Project v1 onto v0 and v0.ln var p1a:VectorModel = VectorMath.project(v1, v0); var p1b:VectorModel = VectorMath.project(v1, v0.ln); //Project v2 onto v0 and v0.ln var p2a:VectorModel = VectorMath.project(v2, v0); var p2b:VectorModel = VectorMath.project(v2, v0.ln); This is the first step in calculating any bounce vector, so it should be pretty familiar to you by now. Now here s the freaky part. Both circles must transfer their velocities to each other, but also bounce away at the correct angle. To do this, mix and match the projections. //Bounce c1 //using p1b and p2a _c1.vx = p1b.vx + p2a.vx; _c1.vy = p1b.vy + p2a.vy; //Bounce c2 //using p1a and p2b _c2.vx = p1a.vx + p2b.vx; _c2.vy = p1a.vy + p2b.vy; Each circle s velocity is a combination of its projections plus the other circle s projections. Dr. Frankenstein would be proud! It s a difficult thing to visualize, but as you can see, the code is quite straightforward and symmetrical. This gives you a perfectly natural collision reaction that you can use in any game where two circles collide.
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It might make sense to make the large circle heavier than the smaller one, so that its bounce is in proportion to its size. You can do this by giving it some mass. Just divide the bounce vector by any number larger than 1, and the bounce effect will be dampened accordingly
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var mass:uint = 5; _c2.vx = (p1a.vx + p2b.vx) / mass; _c2.vy = (p1a.vy + p2b.vy) / mass;
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Dividing the bounce vector by 5 will make the large circle appear much heavier when the small circle bumps into it. You might want to consider making mass a property of the CircleModel class, or working out a formula for mass based on the circles radii.
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Multiple-object collision
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Two circles are good, but ten are better! To check for a collision with more than one object on the stage, use this strategy: Push all of your objects into an array. Loop through the array once each frame and check each object for a collision with another object. If that sounds pretty simple, it is! The one hiccup is that you need to be careful that your loop doesn t check for a collision with two pairs of objects twice. If it does, you ll spend precious CPU cycles doing unnecessary checking, and that will ultimately slow down your game. There s a standard algorithm for detecting multiple object collision that solves this problem. It s a nested for loop (a loop within a loop) that makes sure that no two objects are compared twice. Imagine you have an array called objects that contains all of your game objects, and a method called checkCollision that performs the collision check. The multiple-object collision check algorithm will look like this: for (var i:int = 0; i < objects.length; i++) { var object_1:GameObject = objects[i]; for (var j:int = i + 1; j < objects.length; j++) { var object_2:GameObject = objects[j]; checkCollision(object_1, object_2); } }
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The key to making this work is that the inner loop starts its loop counter at a number that is one greater than the outer loop. var j:int = i + 1; This prevents any two objects from being checked more than once. Let s combine this technique with the moving circle collision system we used in the previous example. In the chapter s source files, you ll find a folder called MultipleObjectCollision. Run the SWF, and you ll see a basic prototype of a billiards-style game, as shown in Figure 3-24. It s not much more than a fusion of our circle-versus-circle collision system and the multiple object collision algorithm.
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