module Graphics.PS.Bezier (bezier4) where

import Graphics.PS.Pt

{--
bezier3 :: Pt -> Pt -> Pt -> Double -> Pt
bezier3 (Pt x1 y1) (Pt x2 y2) (Pt x3 y3) mu = (Pt x y)
    where a = mu * mu
          b = 1 - mu
          c = b * b
          x = x1 * c + 2 * x2 * b * mu + x3 * a
          y = y1 * c + 2 * y2 * b * mu + y3 * a
--}

bezier4 :: Pt -> Pt -> Pt -> Pt -> Double -> Pt
bezier4 (Pt x1 y1) (Pt x2 y2) (Pt x3 y3) (Pt x4 y4) mu =
    let a = 1 - mu
        b = a*a*a
        c = mu*mu*mu
        x = b*x1 + 3*mu*a*a*x2 + 3*mu*mu*a*x3 + c*x4
        y = b*y1 + 3*mu*a*a*y2 + 3*mu*mu*a*y3 + c*y4
    in Pt x y