instance AdditiveGroup GLfloat     where {zeroV=0.0; (^+^) = (+); negateV = negate}
instance VectorSpace GLfloat where
  type Scalar GLfloat = GLfloat
  (*^) = (*)
instance InnerSpace  GLfloat where (<.>) = (*)

-- Data.VectorSpace it completly braindead, because it defines a scalar
-- as anything, not as a Field, so that it is not possible the get the
-- additive identity, so we can't define this on any InnerSpace
force a b =
        if d == zeroV then
                zeroV
        else
                d ^* factor
        where d = a ^-^ b
              distSq = magnitudeSq d
              -- 1/(r^4) works fine
              -- with usual 1/(r^2) als points
              -- on the border
              factor = 1/(distSq*distSq)

-- Our point has to be in the unit circle
limited p
        | d > 1     = p^/d
        | otherwise = p
        where d = magnitude p

allForces p points = sumV $ map (force p) points

applyForce p points t = limited $ p ^+^ t *^ (allForces p points)

transformSystem t points = map (\p  -> applyForce p points t) points