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Numsgil:
Got matlab today, here's the answer I get:
 
 Collision occurs if c * t^2 + 2*b*t+(a-rad^2) <= 0
 
 The actual collision (both the entrance and exit "wouds") occur at c * t^2 + 2*b*t+(a-rad^2) = 0
 
 where:
 a = deltapos dot deltapos
 b = deltapos dot deltavel
 c = deltavel dot deltavel
 
 roots are at:
 
 t = -(b +/- sqrt(b^2 - a*c + c*rad^2)) / c

EricL:
Yup, that's what I came up with.  

Here's the heart of the current code...


        B0 = rob(robnum).pos
        d = VectorSub(vs, vb)         ' Vector of velocity change from both both and shot over time t
        p = VectorSub(S0, B0)
        P2 = VectorMagnitudeSquare(p) ' |P|^2
         
        D2 = VectorMagnitudeSquare(d) ' |D|^2
        If D2 = 0 Then GoTo CheckRestOfBots
        DdotP = Dot(d, p)
        x = -DdotP
        y = DdotP ^ 2 - D2 * (P2 - r ^ 2)
       
        If y < 0 Then GoTo CheckRestOfBots ' No collision
     
        y=Sqr(y)
               
        time0 = (x - y) / D2
        time1 = (x + y) / D2

Numsgil:
I like this double checking of answers

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