Given an initial shot position (Spos), a constant shot speed (Sspeed), an initial target position (Tpos), and a constant target velocity (speed + dir) (Tvel) derive the equation for calculating the shot direction (Sdir) such that at some time (t) the shot would hit the target. Be sure to derive an equation for t as well! Write a function to compute these values (Sdir and t). Can anyone help me with this? email me at shawndgarner@hotmail.com What I have so far is: newTargPos = targPos + (targSpeed * time) targDir; I don't know if this is the right way to go about it. [edited by - Juanman on May 14, 2002 11:20:35 AM]

This was discussed twice in recent threads. Make a search in the archive. The last one had asteroids and lasers in it. It also had a link to the first thread, which had the complete answer

Cédric

I looked at one article with Astroids. He was talking about things with variable speed which is not what I want. I also didn''t see any detailed solutions you were talking about. I did a search and only found the one article. I would appreciate links to both if you could find them.

This smells like a homework question...

Nope, not a homework question. A question for a game job programming test. They said I could research it. I've had only one physics class and never did stuff like this. I am going to the library tommorrow to try to find a good book but thought maybe I could save myself a trip if anyone knew how to do it.

[edited by - Juanman on May 14, 2002 12:11:08 AM]

The new Game AI Wisdom book has an article that answers this very question.

I will look for that book at my University Library but I doubt they have it. You couldn''t post the answer or how to derive the answer could you? I did find the astroids post but didn''t quite clear things up for me.

well I did some reworking
p = interception point
pS = initial shot position
vS = direction + speed vector of bullet
t = time to intercept
pT = initial target position
vT = direction + speed vector of target

p = pS + vS * t;
p = pT + vT * t;

pS + vS * t = pT + vT * t

t = (pT - pS) / (vS - vT);

vS = ((pT - pS) / t) + vT

then the unit vector direction to shoot would be
vS/|vS|

But vS & vT are are vectors so how do you get a time number from subtracting two vectors and subtracting two points?



well I forgot about the scalar speed so here is the updated version

p = interception point
pS = initial shot position
vS = unit vector direction of shot
k1 = speed of bullet
t = time to intercept
pT = initial target position
vT = unit vector direction of target
k2 = speed of target


t = (pT - pS) / (vS * k1 - vT * k2)

vS = ((((pT - pS)/t) + vT * k2)/k1)

I still have the same question as above but was wondering if I could do this:

t = sqrt( (pT.x - pS.x) * (pT.x - pS.x) + (pT.y - pS.y) * (pT.y - pS.y) + (pT.z - pS.z) * (pT.z - pS.z) ) /
sqrt( (k1 * vS.x - k2 *vT.x) * (k1 * vS.x - k2 *vT.x) + (k1 * vS.y - k2 *vT.y) * (k1 * vS.y - k2 *vT.y) + (k1 * vS.z - k2 *vT.z) * (k1 * vS.z - k2 *vT.z) )


[edited by - Juanman on May 15, 2002 1:04:51 AM]

[edited by - Juanman on May 15, 2002 1:22:02 AM]

The last thread on this subject concluded that it is easier to iterate to find the answer to this problem. I disagree, but I did not provide the complete analytical answer in the last thread and I don't know if it was provided in the first, so here it is:

What we know:
T_s : speed of the target
B_s: speed of the bullet
B : position of the shooter
T : position of the target
d: |T - B |

alpha: dot( (T - B    ), Ts     )        ----------------------       (|T - B    | * |Ts    |)  

Unknown:
P : position of the target when the bullet reaches it
t: time
V : direction in which to shoot

Derivation:
This is nothing but a simple triangle problem. Two letters indicate an edge of the triangle (TB is the edge between T and B)
TB = d
TP = T_s * t
BP = B_s * t

By the law of cosines,
(B_s * t)² = (T_s * t)² + d² - 2T_s * t * d * cos(alpha)
So,
(B_s² - T_s²) * t² + 2T_s * t * cos(alpha) * t - d² = 0

This is a quadratic equation where only t is unknown. Solve for t.

Now that you have t, you can easily find P
P = T + T_s * t

And the direction to shoot.

V = P - B

I didn't double-check the maths, so if anybody finds a mistake, please post here and I will correct it. I say it's not much harder than the guess and correct approach and it's certainly more precise.

Cédric

[edited by - cedricl on May 15, 2002 4:33:11 PM]

[edited by - cedricl on May 15, 2002 4:38:23 PM]

i also derived this complicated mess a while ago. i believe the other answers are more elegant but i''m nearly positive that this is also right:

http://www.circlelogic.com/gamestuff/Targeting.html

-me