Yes, assume that the ratio of modem/broadband is about 30/70.
As for AP, trust me, you can''t just send the position every frame and expect the other player to get it and display it correctly. Think about this. If I send it every single frame, then theoretically, the other players will see that every single frame. The problem is that what is currently displayed for them will be what I was doing and where I was at about 250ms ago. Doesn''t sound like a long time, but when you''re turning in a tight loop, it would matter. This is assuming that no packets are dropped.
Say you were chasing someone and firing at their rear. Some router decides to start dropping packets just as your shots get close to him. He pulls a tight loop to the right, and ends up behind you. Because of those dropped packets, you won''t even see that he turned. Suddently he''s behind you and firing at you. It will look like a major programming bug and it''s not.
Sending that many updates would simply not be feasible. Not to mention, that sending every single frame assumes that everyone has the same framerate. If you have a framerate of 240 fps and I have a framerate of 30fps, what you see is going to be very choppy. Based on the assumption that no packets are dropped and the packets arrive at the same time, every time, you will see me move every 8 frames of animation. It''s not going to look consistent. You absolutely must use some type of interpolation.
As for the derivatives, they are position, velocity and acceleration. Position is pretty much displacement, although I''m sure if you talk to someone with a PhD in Physics, he''d tell you they''re not the same thing and he''d be right. Let''s just call it position for now.
dx = derivative, dx^2 = the second derivative
dx(position) = velocity
dx^2(position) = dx(velocity) = acceleration
You don''t take the third or fourth derivative. To go from the acceleration function to the velocity or position, you take the integrals.
Integral(acceleration) = velocity + C where C is an unknown constant
Integral^2(acceleration) = Integral(velocity + C) = position
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