OT: Looking for a good physics site

[narf poit chez BOOM]

Also, I just want the enemy ship to hit the target ship - Missile interception. I can probably manage to work out how to match velocities from that.

[Suicide Junkie]

Wasn't that where you were having all the problems before?
Reversing thrust at half way causing all kinds of grief?

[narf poit chez BOOM]

I've gone through a number of calculations. None of them worked completely. The closest I got was an angle calculation that works for velocity only.

I have never gotten any kind of interception that works perfectly for velocity, acceleration and position, either missile interception or matching interception.

And by 'perfectly', I mean, 'Intercepts, in a straight line, a target moving in a straight line'.

[Jack Simth]

That's not physics, that's math (mind you, Physics IS math, but nowhere are you actually needing to deal with things like, oh, gravity - you're just looking at acceleration).

A position under constant acceleration vs. time for a given axis has an equation that can be formatted as:

P(T)=(1/2)A(T^2)+VT+S

P(T): Position at time T (the function)
T: Time (the only variable)
A: Acceleration (a constant for this exercise)
V: Initial Velocity (at T = 0; a constant)
S: Starting position (P(0); a constant)

You're looking to calculate an intercept - well, you've got a lot to worry about, but basically, you're looking for a way to get two different position functions at the same point at the same time:

So basically, you have P1(T) = P2(T), and want T and A (do I need to reword that?).

As each object has a different starting position (otherwise, T=0 always works; this is the definition of interception), Acceleration, and initial velocity are likely to be different; you're looking to solve:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

Do note that your intercepting ship can potentially control it's acceleration. Well, let's start manipulating:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

(1/2)(A - A)(T^2)+(V - V)T+(S- S) = 0

Oh, hey - we now have a quadratic equation; sub (1/2)(A - A) with a, (V - V) with b, and (S- S) with c, and T with x. The Quadratic formula will do the job:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

Note: a is a variable, as the interceptor will need to choose it. You've got a variable on both sides - but that's okay, as you'll want at least two dimensions, and you've got a separate equation for each dimension; you'll end up with a system of equations (one for each dimension) and some relationship between the a on the various axes (usually the Pythagorean therom).

Edit:
That is, of course, assuming you don't want to stop at the end, other than ramming the target....

[narf poit chez BOOM]

Tankee! Tankee very much!

...But, um, if the enemy acceleration needs to be chosen to use the formula and the formula tells it in which direction to accelerate and thus, how much to accelerate...

...Isn't that a closed loop?

/me goes off to see what happens if /me uses that by inputing '0' for the enemy acceleration.

...Uh, the first one is the pursuer, right?

...'+/-'?

[Fyron]

Aren't those pretty much the equations we came up with last time, Narf? I think we used a slightly different form of acceleration equation, but it amounts to the same thing.

[narf poit chez BOOM]

There's a resemblance, but I'm pretty sure there was no distance, 4ac or 4a.

In any case, something about my implementation is off, possibly having something to do with the questions I asked.

[Jack Simth]

narf poit chez BOOM said:
Tankee! Tankee very much!

...But, um, if the enemy acceleration needs to be chosen to use the formula and the formula tells it in which direction to accelerate and thus, how much to accelerate...

...Isn't that a closed loop?

Nope. You have a second, identical equation for the other dimension (or more - it's extendable to as many as you like; most games will use two (X, Y), some will use three (X, Y, Z) but you can have 30 if you feel like it), and you'll have a relationship between the two based on the overall max acceleration for the pursuer (based on the pythagorean therom; max acceleration = sqrt(a(x)^2 + a(y)^2 + a(z)^2 + ... ) and the persuer is picking an acceleration in the x, y, z, ... axises (axen? axes? - what's the plural of axis?); you'll end up with a system of equations, based on how much you're simulating.

It's simultaneous equations. If you've got four variables and three equations that relate them, you can usually solve for everything in terms of a single variable.

narf poit chez BOOM said:

/me goes off to see what happens if /me uses that by inputing '0' for the enemy acceleration.

...Uh, the first one is the pursuer, right?

Whichever you'd prefer; the exact choice is completely immaterial. Math's like that, sometimes.

narf poit chez BOOM said:

...'+/-'?

The Quadratic formula gives two results. One will usually give you negative time, which you discard. Occasionally it will come back with an imaginary number (by way of the square root of a negative) - in which case, interception is not possible.

Oh, and there's a REASON most games use flat velocities, rather than accelerations.

The simple way to do it, if you're going a little bit at a time anyway, is to simply accelerate in the direction of the target. The computer will have some overshooting issues, and it won't be the most efficient course, but it'll do the job eventually.

[Fyron]

Jack Simth said:
what's the plural of axis?

"axes," pronounced like "ax'eees."

[narf poit chez BOOM]

Nope. You have a second, identical equation for the other dimension (or more - it's extendable to as many as you like; most games will use two (X, Y), some will use three (X, Y, Z) but you can have 30 if you feel like it), and you'll have a relationship between the two based on the overall max acceleration for the pursuer (based on the pythagorean therom; max acceleration = sqrt(a(x)^2 + a(y)^2 + a(z)^2 + ... ) and the persuer is picking an acceleration in the x, y, z, ... axises (axen? axes? - what's the plural of axis?); you'll end up with a system of equations, based on how much you're simulating.

Er, yes, I'm currently using it for two axis. Three would probably result in a significantly smaller consumer base. Four would limit it to only the seriously dedicated, which does not include me, in both desire and ability.

I do know that equation. My problem is the whole 'Pursuer picking an acceleration' thing. See, the equation helps pick the pursuers' acceleration and the pursuers' acceleration is part of the equation...

Um, there must be something obvious I'm not seeing. Possibly it's in the communication.

It's simultaneous equations. If you've got four variables and three equations that relate them, you can usually solve for everything in terms of a single variable.

I get the general concept. However, my math skills are abysmal. I still carry a grudge with the school system here over that; they were near-genius level before I entered it. (I have a psychiatric assesment to prove it, too).

I am trying to raise my math skills. I have learnt a few things bashing my head against this.

Whichever you'd prefer; the exact choice is completely immaterial. Math's like that, sometimes.

Er, do you mean I can put '0' for the pursuers' acceleration or I can use either for the pursuer or both? Because I can see the second, but I'm not sure about the first.

The Quadratic formula gives two results. One will usually give you negative time, which you discard. Occasionally it will come back with an imaginary number (by way of the square root of a negative) - in which case, interception is not possible.

The negative time would explain the enemy ship accelerating south if it's headed south and sufficiently southward of the target.
If the result is not a number or infinity, it is discarded.

So, uh, how do I make sure the formula is giving me a good result?

Oh, and there's a REASON most games use flat velocities, rather than accelerations.

My left brain is perfectionist, precise and thorough. I believe you are all sufficiently aquanted with my right brain...

...Besides, one of the main features of this game will be multiple FTL and STL systems.

The simple way to do it, if you're going a little bit at a time anyway, is to simply accelerate in the direction of the target. The computer will have some overshooting issues, and it won't be the most efficient course, but it'll do the job eventually.

That would be a whole lot easier. But my brain has consistantly discarded that option in favour of the better (In the end) result.

Although it is getting tempting.

Ok, my brain is seriously fried and it's rather late. I'll look at this again tomorrow.