I used around 40 if I remember correctly. You'll just need to play around with the algorithm to determine how many iterations you want. Eventually the predicted position will coincide with exact point you should fire at in order that the bullet hit the target (because the difference dti+1 - dti tends to zero). Call this dt3.Ħ) Repeat this process with as many iterations as you like. Call this dt2.Ĥ) Starting at its initial location P, advance the target forward dt2 units of time.ĥ) Compute how long it would take a bullet to reach the target if it were at the new projected position. Call this dt1.Ģ) Now advance the target forward dt1 units of time.ģ) Compute how long it would take a bullet to reach the target if it were at the new projected position (firing directly at this location). Let v be the velocity of the target and let currentAngle be initially set to zero.ġ) Compute the amount of time it would take for the bullet to reach the target if it remained stationary. There is a second hot-spot in the lower-right corner of the iFrame. Use the Escape key on a keyboard (or comparable method) to exit from full-screen mode. Clicking/tapping the hot spot opens the Interactive in full-screen mode. There is a small hot spot in the top-left corner. I'll try to recall the algorithm I used (which worked very well): The Projectile Simulator Interactive is shown in the iFrame below. Unfortunately, I've somewhat forgotten my exact solution. I had to solve this exact problem when I was once writing AI code for a robot simulation. I'm finding it tricky because you have to eliminate the unknown time t to the intersection, which I tried, but I must've stuffed something up. Unfortunately, it doesn't work - when you stop the gun always points in the same direction regardless of where you are, and at some positions the result becomes undefined. Gx, Gy = start position of projectile (position of gun)Ī = acos( (s / u). Px, Py = start position of target (on projectile firing) Both will be travelling at constant speeds along a straight line. Essentially, I want to figure out the angle the gun should point at, to ensure that the projectile and the target intersect exactly. I have a gun I want to fire a projectile at speed u at a moving target with a constant velocity (speed s). I've been working on the following problem and can't figure it out, so any help appreciated.
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