Question

I thought I’d be able to find this with some searching on the internet but everything I find is just balls bouncing off walls for something like pong or another arbitrary question. I’m making a 2D dungeon crawler game and when I kill enemies and they drop loot I want the item to come flying out as if it had just been thrown in the air and land a random point on the tile the unit was on.

I’ve been trying to figure this out myself but I can’t figure it out, this is probably asked a lot, I’d be really grateful if someone could help me out.

EDIT AS REQUESTED:

Ok well when a monster would be destroyed I would choose a random location within the tile it’s in, let’s call this location endLoc and the monster’s location startLoc. I would then find the center x point between these two locations and decrease the y by 20 ( because that’s how many pixels i want the item to go up by), so let’s called this variable launchLoc:

launchLoc = new Vector2(startLoc.X + ((endLoc.X - startLoc.X) / 2), startLoc.Y - 20)

I think that produces the right Vector.

So now I would need to launch the item from startLoc, to launchLoc, then have it come back down to endLoc. This is where it gets confusing and I’m not sure how to make a realistic arc for this. The end result would have the item move like it moved along a gaussian, as if it was thrown into the air.

I tried to make it so during each interval, the velocity is increased by 120th, of the X difference, between the startLoc and launchLoc, by an incrementing multiple, but I couldn’t get it to work very well. I’m not sure if this was the best way to do. I use 120th because the y value is 20, and the item moves up 1 pixel every interval, so 1 to 20 added up gives 120, this would make the x movement constantly increase, like it was thrown up.

This is in 2D btw, I hope that helps.

Answer 1

You start with an initial velocity vector at time t₀ (v(t₀)) and position (p(t₀)). Gravity can be assumed to produces a constant acceleration (a(t₀) = <0, -9.8 m/s²>, though your value may differ) until the object lands. So the general form of the motion for going from one timeslice to the next is:

p(t) = 0.5*a(0)*(t-t0)2 + v(0)*(t-t0) + p(0)
v(t) = a(0)*(t-t0) + v(0)

To figure out when to stop that motion, you need to figure out at what time the object’s path will intersect the surface against which it bounces. You’ll have to do this for all of the surfaces for which this can reasonably be expected to happen. So for a plane with line equation Ux + Vy + T = 0 you break the position vector into its components, as in:

p(t) = <px(t), py(t)>

Then use the quadratic formula to find tc where p(tc) satisfies the line equation:

0.5*(Uax(t0)+Vay(t0))*tc2 + (Uvx(t0)+Vvy(t0))*tc + (Upx(t0)+Vpy(t0)+T) = 0

Chose the branch such that t_c > t₀. From there it’s simple to figure out where the object will collide with the surface. You can then update the velocity vector and position vector based on the behavior of the bounce. If the plane is axially aligned (ie, it’s a horizontal plane with normal vector parallel to the Z axis), then just flip the sign of the Z component of the velocity vector and multiply the whole velocity vector by some damping factor d, where 0≤d<1 to damp out the velocity. Then repeat until some predetermined time has passed or the velocity reaches some minimal amount (your call on that).

It becomes a bit more difficult with arbitrarily oriented planes. You will need to calculate the angle of incidence of the collision and reflect the velocity vector about the plane normal. I won’t go into the details here, as I suspect you’re probably not interested in it.