Determining direction of object

[cavetroll]

Not sure if this is the right forum to post this in. If it is not the correct forum please move this topic.

I am building a Tower Defense. My question deals with finding the direction of the bullet.

I know the speed and the direction of the unit, and I know the speed of the bullet. How do I determine what direction the bullet should be moving in so it collides directly with the unit? I have asked others but they told me I didn't have enough data. I hoped they were wrong and just didn't understand the problem.

I hope I will not have to resort to brute force. Not my style .

P.S. I don't need code just the equation.

[Saad]

You can use either Trig or use Vectors.

Trig Solution:

1. Get the angle between the bullet and the enemy.
2. Now that we have an angle, we can make the velocity a direction
velocity.x = speed * cos (angle)
velocity.y = speed * sin (angle)

Vector Solution

1. Get the vector from the bullet and the enemy
2. Make that vector a unit vector (ie A length of one)
So something like
direction.x = (enemy.x - bullet.x) / distance
direction.y = (enemy.y - bullet.y) / distance
3. Knowing the direction
velocity = direction * speed


Saad

[cavetroll]

Thanks for the reply.

Ok, my bad, I worded it badly. I know how to do what you described. What I need to find out is where the unit will be in X number of frames and what direction the bullet has to move in to be there as well (i.e. a collision).

[OneOffDriveByPoster]

cavetroll @ Wed Apr 09, 2008 7:38 pm wrote:

Thanks for the reply.

Ok, my bad, I worded it badly. I know how to do what you described. What I need to find out is where the unit will be in X number of frames and what direction the bullet has to move in to be there as well (i.e. a collision).

Not your fault I think. I understood just fine; answer coming soon.
tower at (0, 0)

target at (x0, y0) at t = 0
target speed = s
target direction = (dx0, dy0)
(dx, dy) = s * unit_vec(dx0, dy0)
target_pos(t) = (x0 + t*dx, y0 + t*dy)

bullet speed = S
bullet_pos at time t:
x ^ 2 + y ^ 2 - (S * t) ^ 2 = 0

Consider:
(x0 + t*dx) ^ 2 + (y0 + t*dy) ^ 2 - (S * t) ^ 2 = 0

Hopefully you can solve for t and know how many frames it will take.
Substitute the specific value for t into target_pos(t) and you will know where the bullet has to be.

[Saad]

That would depend on what type of collision are you doing, eg Using circles for collisions for the detection would be much different then say having 2 boxes for finding the frames till the collision


Saad

[OneOffDriveByPoster]

Hopefully correct for when the target and the bullet are points:

code:

x0^2 + 2*x0*t*dx + t^2*dx^2 +   y0^2 + 2*y0*t*dy + t^2*dy^2 - ( S^2  + 2*S*t     + t^2      ) =  0 A*t^2 = t^2*dx^2 + t^2*dy^2 - t^2       = (dx^2 + dy^2 - 1) * t^2 B*t   = 2*x0*t*dx + 2*y0*t*dy - 2*S*t       = 2*(x0*dx + y0*dy - S) * t C     = x0^2 + y0^2 - S^2

Need to know the shape of the objects to do more.

[r691175002]

http://jobemakar.blogspot.com/
Newest post should have what you want.

[A.J]

if you're just making a simple tower defense, then just use a pathfinding algorithm (like the A* perhaps, wink wink nudge nudge)
to make your 'creeps' (or bullets) to follow you. I can help u with the pathfinding if u need help.
try to look at fishtastic's turing tower defense in the turing submission forum, as its pretty good

but if you're doing something else, just ignore me

(hope this helps)

[OneOffDriveByPoster]

Okay; I copied the equation wrong between steps .

Anyhow, I hope you understand how I derived the equations...

code:

x0^2 + 2*x0*t*dx + t^2*dx^2 +   y0^2 + 2*y0*t*dy + t^2*dy^2 -                      S^2*t^2 =  0 A*t^2 = t^2*dx^2 + t^2*dy^2 - S^2*t^2       = (dx^2 + dy^2 - S^2) * t^2 B*t   = 2*x0*t*dx + 2*y0*t*dy       = 2*(x0*dx + y0*dy) * t C     = x0^2 + y0^2

My first Turing program that is not a compiler testcase (is not sufficient to steal wholesale):

Turing:

import GUI setscreen ("graphics:  500; 500, offscreenonly, nobuttonbar") var bgcolor : int := 255; Draw.FillBox (0, 0, 500, 500, bgcolor) View.Update %%%%% config var x0, y0 : int var dx, dy, s, sp : real x0 := 0 y0 := -200 dx := 1 dy := 1 s := 2 sp := 5 %%%%% end config %%%%% calculate the hittime and which direction to shoot in var b_dx, b_dy, hittime : real loop     const lend : real := sqrt (dx ** 2 + dy ** 2)     dx := dx * s / lend     dy := dy * s / lend     const A : real := dx ** 2 + dy ** 2 - sp ** 2     const B : real := 2 * (x0 * dx + y0 * dy)     const C : real := x0 ** 2 + y0 ** 2     const dis : real := B ** 2 - 4 * A * C     if dis < 0 then         put "No real hittime."         return     end if     const hittime0 : real := (-B + sqrt (dis)) / (2 * A)     const hittime1 : real := (-B - sqrt (dis)) / (2 * A)     if hittime0 >= 0 and hittime1 >= 0 then         hittime := min (hittime0, hittime1)     elsif hittime0 >= 0 then         hittime := hittime0     elsif hittime1 >= 0 then         hittime := hittime1     else         put "No non-negative hittime."         return     end if     b_dx := x0 + hittime * dx     b_dy := y0 + hittime * dy     put "hittime = ", hittime     put "target = (", b_dx, ", ", b_dy, ")"     const lenb := sqrt (b_dx ** 2 + b_dy ** 2)     b_dx := b_dx / lenb     b_dy := b_dy / lenb     put "bullet = (", b_dx * sp * hittime, ", ", b_dy * sp * hittime, ")"     exit when true end loop %%%%% done calculate for t : 0 .. floor (hittime + 20)     if t > hittime then         bgcolor := 0;     end if     Draw.FillBox (0, 0, 500, 500, bgcolor)     % center     Draw.FillOval (250 + 0, 250 + 0, 5, 5, 30)     % target     Draw.FillOval (250 + floor (x0 + t * dx), 250 + floor (y0 + t * dy), 5, 5, 40)     % bullet     Draw.FillOval (250 + floor (t * sp * b_dx), 250 + floor (t * sp * b_dy), 5, 5, 50)     View.Update     delay (100)     exit when t = floor (hittime + 20)     % remove old target     Draw.FillOval (250 + floor (x0 + t * dx), 250 + floor (y0 + t * dy), 5, 5, bgcolor)     % remove old bullet     Draw.FillOval (250 + floor (t * sp * b_dx), 250 + floor (t * sp * b_dy), 5, 5, bgcolor) end for

Edit: ... and I left out some division-by-zero cases...

[cavetroll]

Thank you so much for your responses, you solved my problem.