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As an example, imagine that you have a spaceship hovering above a flat planet surface. The force of gravity on the y axis is pulling the ship down. If the force of gravity is 2, you can describe its vx and vy properties like this: gravity_Vx = 0; gravity_Vy = 2; Don t forget that in Flash s backward coordinate system, gravity will have a positive value, so you ll need to add it to you ship s motion vector to pull the ship downward. Remember that if you have a vx and a vy value, you have a vector. It might not have start or end points, but it s still a vector. In this case, the gravity acts only on the y axis, so you don t need a value for vx. Here s how you can add the force of gravity to the ship s motion vector: shipModel.vy += gravity_Vy; If the ship started with a vy of 5, its new value would now be 3. This would pull the ship down in the next frame. Figures 2-13 and 2-14 illustrate how this vector addition works.
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Figure 2-13. What happens when you combine a gravity vector and the ship s motion vector In this example, the ship s vy value is 5, and the gravity vector is +2.
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Figure 2-14. When the two vectors are added together, a new vector results, which combines their forces. This pulls the ship down toward the planet surface. When you add vectors together like this, the result is a new vector. It s a combination of the downward pull of gravity and the upward push of the ship. As you can see, the math is amazingly simple, but it s a very accurate description of what happens in the real world. You ve probably used this same kind of vector addition in many of your own games, but never realized the mechanics behind it. It s a pretty easy concept to grasp, especially if you visualize it like this. Don t forget how this simple example works, because even the most complex combination of forces uses these exact same mechanics. Next, we ll look at a more complex example.
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In our simple gravity example, the ship was pulled down on the y axis. This is fine in a platform or pinball game, where down is the bottom of the stage. But suppose your spaceship is circling a planet Which way is down Take a look at Figure 2-15 and see if you can figure it out.
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VECTORS: GHOSTS IN THE MACHINE
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Figure 2-15. To pull a spaceship toward a round planet, gravity must act on both the x and y axes. Looking at that diagram, two things should come to mind. The ship needs to know where the center of the planet is. To move the ship toward the planet s center, gravity must act on the both the x and y axes. Here are the steps to figuring out the force of gravity for a round planet.
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1. Create a vector between the ship and the center of the planet. This provides the everuseful vx and vy values, which are going to help us in the next step.
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2. The magnitude of the vector is actually useless to us. We don t need to know the
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distance between the ship and planet. However, we do need to know the vector s direction.
3. Does that ring a bell It should. Whenever you need a vector s direction but not its
magnitude, you normalize the vector. That means reducing it to its smallest possible size. A normalized vector, or unit vector, is represented by the variables dx and dy. To find those values, divide vx and vy by the vector s magnitude.
4. Figure 2-16 shows how to calculate the dx and dy from the ship-to-planet vector.
Figure 2-16. Create a vector from the ship and the planet. Find its dx and dy, which tells you the vector s direction.
5. We can use the unit vector to create a new gravity vector. How strong do you want
gravity to be For most games, you ll want it to be about half to a tenth of the value of dx and dy for a realistic effect. In this example, let s scale the gravity vector to 2, so that you can see the effect more clearly. gravity_Vx = dx * 2 gravity_Vy = dy * 2
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