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generate barcode in c# windows application Intersection in Font
Intersection Print ANSI/AIM Code 128 In None Using Barcode encoder for Font Control to generate, create USS Code 128 image in Font applications. www.OnBarcode.comDataMatrix Generation In None Using Barcode generation for Font Control to generate, create Data Matrix 2d barcode image in Font applications. www.OnBarcode.comNow that we have a way to figure out if the spaceship has collided with the vector, we need to find out exactly where the collision happened. But let s first consider when it won t happen. When two vectors are parallel, they ll never intersect. And that means that a collision between them will never happen. What do I mean by parallel vectors Those are vectors that are pointing in exactly the same direction or exactly opposite directions. Figure 228 shows three examples of parallel vectors. They run alongside each other like the two rails of a train track. You can always tell when two vectors are parallel because their dx and dy values will be exactly the same. QR Code 2d Barcode Creation In None Using Barcode maker for Font Control to generate, create QR Code image in Font applications. www.OnBarcode.comUPCA Supplement 5 Maker In None Using Barcode maker for Font Control to generate, create UPCA image in Font applications. www.OnBarcode.comFigure 228. These vectors are parallel and will never intersect.
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2. Find the perpdot product of v1 and v2.
perpProduct2 = v1.ln.vx * v2.dx + v1.ln.vy * v2.dy
3. Find the ratio between perpProduct1 and perpProduct2. This is just a matter of
dividing the two values together. (t is for tangent, the point of intersection, and is a common convention for representing this value.) t = perpProduct1 / perpProduct2 4. With the value of t in our pocket, we now have enough information to pinpoint the
precise intersection point with real x and y coordinates. We can find this by adding v1 s start point to its velocity and multiplying it by t. intersectionX = v1.a.x + v1.vx * t intersectionY = v1.a.y + v1.vy * t 5. And there we have the coordinates for the intersection point.
I can just imagine the giddy delight on the faces of the first mathematicians who first figured this out. Mathematicians: 1; Mysteries of the Universe: 0. Intersection in action
Now let s see how this works in a live example. In the chapter s source files, you ll find a folder called Intersection. Run the SWF, and you ll see something that looks like Figure 231. The ship s intersection point with the line is marked by a small crosshair. (The ship s motion vector has been scaled by 10 so that you can see it clearly.) You can move the drag handles to change the line s inclination, and the intersection mark will have no problem keeping up. The status box also displays whether the intersection happens in the future or might have happened in the past. Because the intersection is found using the ship s velocity, not the direction its pointing in, the ship often looks like it s going to miss the intersection. But the intersection point is always predicted with spooky, pinpoint accuracy. Again, most of the code in the source files is routine. Here, we ll look at the important sections that create the intersection. The names of the vectors are the same as in Figure 230. Figure 231. The code predicts where the intersection will take place. First, we need three vectors: v1 is the ship s motion vector, v2 is the target vector on which we want to find the intersection, and v3 is the helper vector between v1 and v2 that helps to calculate the correct point.

