Maths + lack of sleep = Need help please

I've been sitting here for hours wasting time and watching my IQ pack up its bags to leave... :faded:
My last resolve is you guys before something gets thrown :D
I just quickly registered and did a quick search first of all before posting, if I have missed a similar post my apology. On to the problem.

What I want to do is have say a turret fire a bullet at a constant velocity towards a moving object which say is moving around the screen. Now if the turret fires a bullet it will likely miss due to the fact that the moving object has moved from the position it was aiming at.
What I would want the turret to do is take the objects vector and position and use that to calculate the angle that it should fire at inorder to hit the object.

I have attempted this but as usual my math skills have failed me. I have no idea now if this is the wright way to be going about the code, so if you could help please I would very much appreciate it.

Code:

---

        // Calculate the distance to the moving object 'mover'.
        var dx = mover._x - 275;
        var dy = mover._y - 200;
        var dist = Math.sqrt(dx*dx+dy*dy);
       
        // The time it may take to reach the 'mover'.
        var timeToTarget = (dist/shotSpeed);
       
        // Predicted position of the 'mover'.
        var cx = mover._x + (mover.vector.x*timeToTarget);
        var cy = mover._y + (mover.vector.y*timeToTarget);       
       
        // Predicted angle.
        var predictAngle = Math.atan2((cy-200),(cx-275));

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might want to show us your program...right now what you calculated only works if it's like this: http://img361.imageshack.us/img361/5379/fsdfscv0.png

The program is not anything different from what you have drawn.
I've added a green circle to the image in the attachment and its direction to the predicted point. What I am trying to do is have the green circle reach the predicted point that the blue circle will be at.
Doing that I would work out how much more of an angle would it take to hit the blue circle if the green circle was moving at a constant velocity.
Does that make it any clearer? I can upload a quick swf if that will help?

I'm not really sure if I know how to help you, but since there's no use in sleeping right now for me anymore, I thought I'd give it a shot...here's what I came up with:

http://img379.imageshack.us/img379/1610/rechnungqv9.jpg

I could be wrong though since I'm strung out on nicotine and coffee :P

If you're looking for the angle between the vertical line going through the projectile (which I forgot to put in there) you're firing and alpha, then it's just 90degrees - alpha

oh damn it should be x2/x1 not the other way around...so in the end you get arccos(v2 / v1)

http://img68.imageshack.us/img68/5556/rechnungmi0.jpg

This thread might be of some use.

http://board.flashkit.com/board/showthread.php?t=754442

There's lots of different approaches in there, I think the one by "rje" was what the OP eventually settled on.

The approach I supplied in there, post #20, solves a tougher problem than what you need to solve but a lot of the discussion around it is relevant. It solves the "target moves w/ constant acceleration" case, but it appears you need to solve the "target moves w/ constant velocity, acceleration==0" case.

Yours is a simpler problem - you only need to solve a quadratic equation in t.

Take the quartic posted there, and set ax=ay=0. This:

Code:

---

(1/4*ax^2+1/4*ay^2)*t^4+(vy*ay+vx*ax)*t^3+(py*ay+vy^2+px*ax+vx^2-V^2)*t^2+(2*py*vy+2*px*vx)*t+px^2+py^2 = 0

---

Becomes that:

Code:

---

(vy^2+vx^2-V^2)*t^2+(2*py*vy+2*px*vx)*t+px^2+py^2 = 0

---

Solve it for t using the quadratic formula (2 possible values). Then, go back to that other thread, and see how you compute the firing angle from t.