Targeting function

[Dar Scott]

On Sunday, June 29, 2003, at 05:02 AM, curry wrote:

> The input could be gun location, bullet speed, target location, target 
> direction, and target speed. The output could be bullet direction or 
> collision point.

Off the top of my head.  Meaning there might be several dumb errors you 
need to fix.

This has to be adjusted for your coordinate system that might be 
inverted up and down.

Ab = angle of bullet
Sb = speed of bullet
Vxb = X component of bullet velocity
Vyb = Y component of bullet velocity

At = angle of target
St = speed of target
Vxt = X component of target velocity
Vyt = Y component of target velocity

Pxb0 = initial x component of bullet position
Pyb0 = initial y component of bullet position

Pxt0 = initial x component of target position
Pyt0 = initial y component of target position

Pxb = x component of bullet position
Pyb = y component of bullet position

Pxt = x component of target position
Pyt = y component of target position

t = time since initial conditions


Initial calculations:

Vxt = St * cos( Ab )
Vyt = St * sin( Ab )

Constraints:

Sb^2 = Vxb^2 + Vyb^2

Pxb = Pxb0 + Vxb * t
Pyb = Pyb0 + Vyb * t

Pxt = Pxt0 + Vxt * t
Pyt = Pyt0 + Vyt * t

At collision:

Pxb = Pxt
Pyb = Pyt

Solve above 7 equations for Vxb.  From that you can get the point of 
collision.  Is that enough equations?

At = tan(Vyb/Vxb)

Dar Scott