Processing: Creative Coding and Computational Art

momentum at impact has to go somewhere. In the real world, the force of this impact
turns into heat, sound, cool explosions, and new motion. In a virtual world, we can control
how the force is transferred. For example, when two objects collide, if we force all the
momentum upon impact to go back into only new motion, then somehow the motion
after the impact alone needs to be equal to the total momentum of the two objects at the
point of impact. The easiest way to pull this off in code, as I did in the last example, is simply
to have the two objects exchange their velocities upon impact.
Less simple 1D collision
This last example, although relatively simple, didn’t take into account the mass of the
objects. I used the term “transfer of motion” to describe how the balls simply switched
their velocities. But what if you want to account for balls of different mass? Introducing
mass requires those scary equations I mentioned earlier. Again, here’s the first:
obj 1 final velocity = (obj 1 mass – obj 2 mass) * obj 1 velocity + 2 * obj 2 mass * obj 2 velocity
MOTION
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And here’s the second:
obj 1 mass + obj 2 mass
obj 2 final velocity = (obj 2 mass – obj 1 mass) * obj 2 velocity + 2 * obj 1 mass * obj 1 velocity
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obj 1 mass + obj 2 mass
I know the equations are long, but converting them to code is not a big deal, as you’ll see
shortly. The hard part of course would be attempting to derive the equations, which I
won’t bother doing. Keith Peters’s book goes into some detail about where the equations
come from. If you’re really interested in the math, here’s a link you might enjoy as well:
www.euclideanspace.com/physics/dynamics/collision/oned/index.htm.
The two equations are based on the law of conservation of momentum, which I’ve sort of
already discussed. For our purposes, the law states that in a closed system (such as the
type we’re coding), the total momentum of objects before a collision is equal to the total
momentum after the collision. By using these equations, you’ll be able to now account for
mass in your ball-ball collisions.
The next example, shown in Figure 11-25, requires only some minor tweaks to the previous
sketch. The sketch can be divided into five tabs like the last, with the main tab code,
Vect2D class, and checkBoundaryCollision() function all remaining exactly as they were
in the previous sketch, so I won’t bother repeating that code. All you need to do is update
the Ball class and checkObjectCollision() function. Here’s the revised Ball class, with
the new changes displayed in bold:
555
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