Re: OT: Looking for a good physics site
 

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.

Re: OT: Looking for a good physics site
 

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.

Re: OT: Looking for a good physics site
 

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

Re: OT: Looking for a good physics site
 

There was distance. In fact, I'm pretty sure it was the position equation, now that I think about it. We never plugged it into the zeros-solving quadratic equation, hence no 4ac.

+/- is from the quadratic equation. There are two zeros (values of x where the curve intercepts the x axis and y is zero) in the solution to every quadratic equation. The handy cheat sheet formula compacts them into the same function, which varies only by making one version a + and the other a - where that +/- symbol goes.

===

The thing about the position function is that it assumes constant acceleration of both parties. It is calculating how much time passes until the objects intercept. From this, you can plot out where they intercept and get the necessary angle of motion. Remember that you had to do this every so often to find a new intercept heading, based on changes to the acceleration vectors of both objects.

Re: OT: Looking for a good physics site
 

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

Re: OT: Looking for a good physics site
 

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.

Re: OT: Looking for a good physics site
 

A variation on this which may (or may not) work better would be:

Missile looks at where target is now, and figures how much time it would take the missile to accellerate in a straight line and get to that point. Lets say it predicts it could get there at time U.

Missile now predicts where target will be at time U based on target's current course and accelleration. Lets call this Location K. (I like picking random letters to use a variables, it bugs reals mathematicians/ scientists=-).

Missile begins accelerating towards K.

Every time the target changes course or acceleration, go back to square one.

When missile gets within a certain "kill range" of the target, it startss accellerating directly toward the target instead of some predicted future position.

Again, it's not perfect. Overshooting may still occur (but less so than if always accellerating directly at the target), and it might do crazy things if the target takes violent evasive maneuvers, but it seems to me it ought to generate something akin to a decent intercept. As a bonus, it only has to recalculate when the target changes course, instead of all the time, thus saving you CPU cycles.

Just a thought.

Re: OT: Looking for a good physics site
 

@Dogscoff: That would generate a pretty good intercept, but it wouldn't be perfect. To get a perfect intercept, you also have to calculate how far the target moves while the enemy is moving to where it will be then. Thanks for the idea, though.

There was distance. In fact, I'm pretty sure it was the position equation, now that I think about it. We never plugged it into the zeros-solving quadratic equation, hence no 4ac.

By 'distance' I meant we didn't take into account position. That wasn't worded well.

+/- is from the quadratic equation. There are two zeros (values of x where the curve intercepts the x axis and y is zero) in the solution to every quadratic equation. The handy cheat sheet formula compacts them into the same function, which varies only by making one version a + and the other a - where that +/- symbol goes.

So I should make two formulas, one with a '+' there and the other with a '-' there and if one returns a zero, I use the other?

The thing about the position function is that it assumes constant acceleration of both parties. It is calculating how much time passes until the objects intercept. From this, you can plot out where they intercept and get the necessary angle of motion. Remember that you had to do this every so often to find a new intercept heading, based on changes to the acceleration vectors of both objects.
I did get that.

This is what I have currently.

...Erm, does that formula give the distance that will be covered or the time to cover it?

Re: OT: Looking for a good physics site
 

The problem is in framing the question. So let me ask you about what you are trying to achieve: Does a dog chase a cat by predicting where the cat will be next frame? Does a Cheetah hunt a deer by moving towards a calculated destination? The answer of course is no.

What we are trying to implement here can be described by fighter pilots: The three modes of persuit are Pure Persuit, Lag Persuit, and Lead Persuit. Pure Persuit is probably most familiar. It involves pointing your nose directly at the target. Heat seaker missiles follow this course. Unfortunately, so do a lot of weak AI opponants. It is also fairly easy to outmaneuver; just turn so that the enemy is sleightly behind you and you will arc around him.Lag Persuit is what a dog does to a person. He points his nose behind the target, and this changes the way his target is facing fastest. It brings him around to the rear of his opponant.Lead Persuit is what is what is meant by an "intercept course", and involves pointing your nose in front of your opponant. It's what children playing a game of tag do.

On to an intercept algorithm. Instead of percieving the universe as a set of coordinates from "above", consider a 'ground-level' view. What you can do is turn to place him at any angle from you. You could turn to put him in your 12:00--dead ahead. What you can watch is what angle he is presenting to you. If you are in his 6:00 he is running straight away from you.

Let's start by saying you are both the same speed. We'll add speed difference in a moment. If he is facing directly at you, or directly away from you, then you should turn to face directly at him. What if he is facing so that you are in his 9:00 or 3:00 -- directly abreast of his run? Then you will have to run in the same direction on a parallel course until something changes. Do that by turning to put him in your 3:00/9:00.

So now we have straight-on, and parallel-course; 0~90 degrees, based on his presentation of 0~90 degrees. these are the two extremes, and the only thing left is to figure out what the middle values should be. It's easy enough for dumb animals, so we should be able to 'get it'. As the target turns more and more away from dead-on, so should you. Atan2 of his angle gives the fraction.

Now about that speed difference. If you are moving twice as fast as the target, then cut the angle change in half. Pretty cool, huh?

Re: OT: Looking for a good physics site
 

You just gave me a formula I already tried. It worked for velocity.

Also, you probably didn't mean to, but your post comes across as condescending.