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AI : fire on moving object

i try to to make an AI in C# (with unity) that can predict the estimated position of a moving object to hit it with a bullet
the moving object have a movement speed of 5f and the bullet have a speed of 7f
my problem is that the time my bullet travel to my estimated position my "enemy" already moved further and the bullet don't hit
do you know a formula or code that i can adapt to improve my targeting AI ? (already looking for that in google but don't find anything usefull)
thank

An answer to your question from unreal engine forums
Here is the top answer from there in case the link dies. I did not write this code I simply found it with a quick google of your problem which you stated you already tried.
Link answer:
Get the "velocity" of the target player. Multiply by the time the bullet will take to travel to the target. Then get the position of the target, add the velocity*time vector, and that's the position you should aim at. You can either hard-code the travel time (half a second, or whatever,) or you can in turn measure the distance between AI and player, and divide by bullet travel time, to come up with an approximate travel time. You can also apply a differential equation to calculate the exact time of impact and exact direction, but that requires a little more math and is slightly harder to write out, so I think the above will work best for you.
Simply:
Distance = Length(Target_Position - Firing_Position)
Time = Distance / Bullet_Speed
Predicted_Position = Target_Position + (Target_Velocity * Time)

C# bounce/throw physics for items dropping

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.

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) = 0Chose the branch such that tc > 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.

Mouse movement: Click the sprite "walks" to point clicked

I'm pretty new to C# and XNA and well programing (like I can follow a tutorial but most of the creating it on my own is still really really hard). Right now I'm going round and round trying to figure out how to do this one "simple" thing.
Here's the idea, its going to be a tower defense game; right now I'm working on bare bone basics. I've got my little sprite guy who will move around with Keyboard input, now I want to click somewhere on the screen and have him "walk" to that point. Only I'm lost on the logic. I can click and he'll jump there with
if (aMouse.LeftButton == ButtonState.Pressed)
{
Position.X = aMouse.X;
Position.Y = aMouse.Y;
}
From what I've read for other mousing input, I'm thinking I'll need some kind of loop (bool maybe?) that will move the sprite in a direction and will have to run a check to see if he's got to that point yet. But getting that point after the mouse click and creating that loop, running the check...I'm clueless.

You need to add some instance variables:
Point2D targetPos;
And some constants:
const Point2D speed;
When you run through your Update() loop, update the current position by adding the speed vector to it (in the correct direction of course) until you are within a predefined threshold from the target position (usually the thresholds are calculated from the speed vector - if the distance from the current position to the target position is less than the length of the speed vector, then you're at your position). Using a bool in this case would work well. When you click your mouse set another instance variable (moving) to true, and once you've reached your target position, set moving to false.

People are answering your question at a very low level. Sometimes it help to think of the problem at a higher level.
What you need is a type of state management. The fancy Computer Science term for that is a Finite State Machine. But don't bother looking that up right now. It's fairly dry and confusing at first :)
Your character currently has one state - "standing around". You need to add and process the "walking to destination" state.
From what I've read for other mousing input, I'm thinking I'll need some kind of loop
You need one loop, called the game loop. If you're using XNA, you've already got one. But you're on the right track.
Every time through the game loop, you should process the current state, and check for what are called State Transitions. That's when you change something in your world from one state to another state. For example, when you click the mouse, you want the guy to start moving.
In your game loop you check to see if a mouse click just happened. If it did, then set up some data (where to move to), and tell him to start walking by setting his state to "walking to destination". Next update, you'll process that state instead.
When your character is in the "walking to desintation" state, you need to update their position, based on the amount of time that passed since the last game update. In XNA, this is calculated for you. If you're not using XNA, then you'll have to check yourself. You might be able to use something like the Stopwatch class, and check the Elapsed field.
If the character is at the destination, you need to switch them back to the "standing around" state.
If you receive another mouse click, it is up to you if you want the "walking to destination" state to pay attention to it or not. If you do pay attention to it, you set up the same sort of data as when you transitioned from the "standing around" state.
So, you'll need these variables:
A timer, to find out the elapsed time since the last game loop (XNA gives it to you)
The current player state (maybe an enum)
The current player position (a vector)
The walking speed of the player (a float, probably), measured in units per second (or millisecond)
Data for the "walking to destination" state - target position (another vector)
Data related to user input (mouse events that occurred since the last update, the position of those clicks, etc)
The character specific data will be different for each character in your game, so you want a new copy of it for each. You'll probably want to put it in a class. The rest of it is more global, so you can keep it separate, or make it part of your game, game loop, input classes, etc (however you choose to organize it).
I won't cover the vector math for how to actually calculate the partial movement stuff, since other people have covered that. No sense in duplicating those answers. It basically boils down to making a vector between your current position and the target position, and multiplying/dividing it by your walking speed (to chop it up to the distance moved in a single update).

I'm assuming you have three things:
Current position
Desired position
Speed to move each 'game tick' // don't know what a game tick is? find out!
You're looking at doing this
// dx, dy are delta x and delta y. It's how far in each direction
// the player must travel
// note, I fixed a typo where they were desired - desired... should be
// desired - current, as they are now
float dx = desiredX - currentX;
float dy = desiredY - currentY;
// d uses the pythagorean theorum to find the distance between current and desired
float d = sqrt(dx*dx + dy*dy);
// fac is how far along that line between desired and current will you move
float fac = d / speed;
// mx is the component of the dx line proportional to the size of fac : d
// which means it's how far in the x direction you'll move
float mx = dx * fac;
float my = dy * fac;
// the new postition is the old position plus the move value
float newPositionX = dx + mx;
float newPositionY = dy + my;

I have found this code to be most useful... additionally I have added an extra couple lines to prevent certain situations from occuring. For instance there will be times where direction is 0.83 and speed may have been modified by game factors like terrain/wheather/etc.... if speed is below 1, the sprite may not move at all or even move in the wrong direction!
if (Vector2.Distance(Position, TargetPosition) > 2.0f)
{
velocity = Vector2.Subtract(TargetPosition, Position);
velocity.Normalize();
/// Now no matter which direction we are going we are always moving # sprite.Speed
/// at velocity or speed below 1 - problems occur where the unit may not move at all!!
if(current_Speed < 1)
{
Vector2 temp = (velocity * 10) * (current_Speed * 10);
Position += temp / 10;
}
else
{
Vector2 temp = velocity * current_Speed;
Position += temp;
}
//convert to int to render sprite to pixel perfect..
Position = new Vector2((int)Position.X, (int)Position.Y);
}

C# XNA Making the object stay within the bounds

I currently have a method that checks to see if I go out of bounds either from either the top/bottom/sides. The object itself is a ball, and I have a question about getting the ball bouncing off the edges correctly? How do I go about this?
// The behavior is not quite what I want.
if ( InsideOfBounds )
{
Vector3 mCenter = Ball.getCenter();
Vector3 normalizeV = tempCenter;
normalizeV.Normalize();
mHeroBall.setVelocity(-testSpeed * normalizeV);
}

I can provide you with an example from a Breakout-clone written in XNA:
Ball.cs
Basically, you flip the right component of velocity to make a 'perfect' rebound. If you want, you can add friction or elasticity by multiplying by a coefficient like 0.95 or 1.1 so your ball speed change.

When you update the position of your object (ball), you want to check if the new value is out of bounds (and which bount Top\Bottom or Left\Right). If the it actually out of bounds, flip the correct element in your speed vector.
example: if the ball has passed the left bound then BallSpeed.X = -BallSpeed.X
don't forget to update the ball's position with the new speed and not the old at this point, or it will fly off the screen for the current frame (unless that isn't an issue).

Simple 2D rocket dynamics

I am currently experimenting with some physics toys in XNA using the Farseer Physics library, however my question isn't specific to XNA or Farseer - but to any 2D physics library.
I would like to add "rocket"-like movement (I say rocket-like in the sense that it doesn't have to be a rocket - it could be a plane or a boat on the water or any number of similar situations) for certain objects in my 2D scene. I know how to implement this using a kinematic simulation, but I want to implement it using a dynamic simulation (i.e. applying forces over time). I'm sort of lost on how to implement this.
To simplify things, I don't need the dynamics to rotate the geometry, just to affect the velocity of the body. I'm using a circle geometry that is set to not rotate in Farseer, so I am only concerned with the velocity of the object.
I'm not even sure what the best abstraction should be. Conceptually, I have the direction the body is currently moving (unit vector), a direction I want it to go, and a value representing how fast I want it to change direction, while keeping speed relatively constant (small variations are acceptable).
I could use this abstraction directly, or use something like a "rudder" value which controls how fast the object changes directions (either clockwise or counter clockwise).
What kind of forces should I apply to the body to simulate the movement I'm looking for? Keep in mind that I would also like to be able to adjust the "thrust" of the rocket on the fly.
Edit:
The way I see it, and correct me if I'm wrong, you have two forces (ignoring the main thrust force for now):
1) You have a static "fin" that is always pointed in the same direction as the body. If the body rotates such that the fin is not aligned with the direction of movement, air resistance will apply forces to along the length of the fin, proportional to the angle between the direction of movement and the fin.
2) You have a "rudder", which can rotate freely within a specified range, which is attached some distance from the body's center of mass (in this case we have a circle). Again, when this plane is not parallel to the direction of movement, air resistance causes proportional forces along the length of the rudder.
My question is, differently stated, how do I calculate these proportional forces from air resistance against the fin and rudder?
Edit:
For reference, here is some code I wrote to test the accepted answer:
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
float dc = 0.001f;
float lc = 0.025f;
float angle = MathHelper.ToRadians(45);
Vector2 vel = new Vector2(1, 0);
Vector2 pos = new Vector2(0, 0);
for (int i = 0; i < 200; i++)
{
Vector2 drag = vel * angle * dc;
Vector2 sideForce = angle * lc * vel;
//sideForce = new Vector2(sideForce.Y, -sideForce.X); // rotate 90 degrees CW
sideForce = new Vector2(-sideForce.Y, sideForce.X); // rotate 90 degrees CCW
vel = vel + (-drag) + sideForce;
pos = pos + vel;
if(i % 10 == 0)
System.Console.WriteLine("{0}\t{1}\t{2}", pos.X, pos.Y, vel.Length());
}
}
When you graph the output of this program, you'll see a nice smooth circular curve, which is exactly what I was looking for!

If you already have code to integrate force and mass to acceleration and velocity, then you just need to calculate the individual part of each of the two elements you're talking about.
Keeping it simple, I'd forget about the fin for a moment and just say that anytime the body of your rocket is at an angle to it's velocity, it will generate a linearly increasing side-force and drag. Just play around with the coefficients until it looks and feels how you want.
Drag = angle*drag_coefficient*velocity + base_drag
SideForce = angle*lift_coefficent*velocity
For the rudder, the effect generated is a moment, but unless your game absolutely needs to go into angular dynamics, the simpler thing to do is let the rudder control put in a fixed amount of change to your rocket body angle per time tick in your game.

I suddenly "get" it.
You want to simulate a rocket powered missile flying in air, OK. That's a different problem than the one I have detailed below, and imposes different limits. You need an aerospace geek. Or you could just punt.
To do it "right" (for space):
The simulated body should be provided with a moment of inertia around its center of mass, and must also have a pointing direction and an angular velocity. Then you compute the angular acceleration from the applied impulse and distance from the CoM, and add that to the angular velocity. This allows you to compute the current "pointing" of the craft (if you don't use gyros or paired attitude jets, you also get a (typically very small) linear acceleration).
To generate a turn, you point the craft off the current direction of movement and apply the main drive.
And if you are serious about this you also need to subtract the mass of burned fuel from the total mass and make the appropriate corrections to the moment of inertia at each time increment.
BTW--This may be more trouble than it is worth: maneuvering a rocket in free-fall is tricky (You may recall that the Russians bungled a docking maneuver at the ISS a few years ago; well, that's not because they are stupid.). Unless you tell us your use case we can't really advise you on that.
A little pseudocode to hint at what you're getting into here:
rocket {
float structuralMass;
float fuelMass;
point position;
point velocity;
float heading;
float omega; // Angular velocity
float structuralI; // moment of inertia from craft
float fuelI; // moemnt of inertia from the fuel load
float Mass(){return struturalMass + fuelMass};
float I(){return struturalI + fuelI};
float Thrust(float t);
float AdjustAttitude(float a);
}
The upshot is: maybe you want a "game physics" version.
For reason I won't both to go into here, the most efficient way to run a "real" rocket is generally not to make gradual turns and slow acceleration, but to push hard when ever you want to change direction. In this case you get the angle to thrust by subtracting the desired vector (full vector, not the unit) from the current one. Then you pointing in that direction, and trusting all out until the desired course is reached.

Imagine your in floating in empty space... And you have a big rock in your hand... If you throw the rock, a small impulse will be applied to you in the exact opposite direction you throw the rock. You can model your rocket as something that rapidly converts quantum's of fuel into some amount of force (a vector quantity) that you can add to your direction vector.