Forcing one projectile to follow close behind an initial projectile

Question

I'm shooting out a projectile and I want another projectile to closely follow it. I can't simply shoot out the second projectile at a slightly lesser time because the first projectile may change trajectory.

All I want is the second projectile to be closely following behind the first projectile.

My first idea was to plot the points every frame to follow the first projectile. However, as the speed of the first projectile increases, the following projectile lags behind.

Answer 1

If the first projectile has a position and a velocity vector, then you can set the 2nd one's position like this:

bullet2_position = bullet1_position - (normalized_bullet1_velocity * trailing_distance);

You can still apply all the physics you want to the 1st projectile, you just don't need to repeat it all for the 2nd.

Answer 2

What you are looking for is a sort of velocity match between the two objects. You can obtain it by checking the target (first projectile) velocity and modifying the second one according to this.

The pseudo code is something like:

variables: target_velocity, this_velocity, time_to_match and max_acceleration. First and second values are the current velocities of projectiles and other twos are used to tweak the behavior of the chase. Of course you should use vectors (but I suppose you do, since it's the only way to manage these things).

Then at every update:

 result_acceleration = target_velocity - this_velocity;
 result_acceleration /= time_to_match;
 if (result_acceleration.magnitude() > max_acceleration)
 {
   result_acceleration.normalize();
   result_acceleration *= max_acceleration;
 }

Then the result_acceleration value is applied as usually within a physics engine to current this_velocity of following projectile. In your case the time_to_match variable should be enough small to keep the two objects tights (eg. 0.05-0.1).

Answer 3

Your first idea was good. All you have to do, is take into account the distance between the points the first bullet traveled on each frame, and make sure the second one travels the same distance each frame, meaning that it might "skip" some of the points plotted by the first projectile, or plot some points of its own to match the speed of the first projectile.

Answer 4

positions = [leader.position]
each frame:
     leader.update()
     positions.append(leader.position)

     # Loop backwards through the logged positions to find the one
     # the desired distance away.
     d = 0
     i = len(positions) - 1
     while i > 0 and d < follow_distance:
         d += distance(positions[i - 1], positions[i])
         i -= 1

     # Make sure we have enough total distance to start following.
     if d >= follow_distance:
         # In the loop we probably overshot backwards, interpolate
         # forward to the right position.
         p = (d - follow_distance) / distance(positions[i], positions[i + 1])
         follower.position = positions[i] * (1 - p) + positions[i + 1] * p

         # Clear out unneeded positions.
         del(positions[0:i])

A trivial optimization would be using a deque instead of a list (I don't know if Flash has deques).

The second projectile is going to act really weird though. Like, if it's following a parabola, it's going to slow and come to a stop in mid-air, then continue upwards very slowly, then fall very fast. Is that really what you want?