gistfile1.hs

module Q where

data Quarter = NE | NW | SE | SW deriving Show
type Vector = (Float, Float)

quarter :: Vector -> Vector -> Quarter
quarter look target = detect $ angle look - angle target

detect :: Float -> Quarter
detect x
  | x < 0 = detect $ x + 2*pi
  | x >= 0      && x < pi/2   = NE
  | x >= pi/2   && x < pi     = SE
  | x >= pi     && x < 3*pi/2 = SW
  | x >= 3*pi/2 && x < 2*pi   = NW
  | otherwise = error "detect"
  
fix :: Float -> Float -> Float -> Float
fix x y res
  | x >= 0 && y >= 0 = res
  | x <= 0 && y >= 0 = pi - res
  | x >= 0 && y <= 0 = 2*pi - res
  | x <= 0 && y <= 0 = pi + res

angle :: Vector -> Float
angle (x, y) = fix x y $ asin $ y / hypo (x, y)

hypo :: Vector -> Float
hypo (x, y) = sqrt $ x ** 2 + y ** 2

{-
Tests:
> quarter (1,1) (0,1)
NW
> quarter (1,1) (-1,0)
SW
> quarter (1, 0) (2,-1)
NW
-}