Graham Scan algorithm for finding convex hull

gistfile1.hs

import Data.List

data Point = Point Float Float deriving (Show, Eq)
data Direction = LeftDirection
               | RightDirection
               | StraightDirection deriving (Show)

dot :: Point -> Point -> Float
dot (Point x1 y1) (Point x2 y2) = x1*x2 + y1*y2

plength :: Point -> Float
plength (Point x y) = sqrt (x*x + y*y)

angle :: Point -> Point -> Float
angle a b = acos ((dot a b)/(plength a * plength b))

add :: Point -> Point -> Point
add (Point x2 y2) (Point x1 y1) = Point (x2+x1) (y2+y1)

diff :: Point -> Point -> Point
diff (Point x2 y2) (Point x1 y1) = Point (x2-x1) (y2-y1)

ccw :: Point -> Point -> Point -> Float
ccw (Point x1 y1) (Point x2 y2) (Point x3 y3) = (x2-x1)*(y3-y1) - (x3-x1)*(y2-y1)


drive :: Point -> Point -> Point -> Direction
drive a b c
  | x < 0 = RightDirection
  | x > 0 = LeftDirection
  | x == 0 = StraightDirection
  where x = ccw a b c

driveList :: [Point] -> [Direction]
driveList (a:b:c:xs) = drive a b c :driveList (b:c:xs)
driveList _ = []


sortFindLowest :: Point -> Point -> Ordering
sortFindLowest (Point x1 y1) (Point x2 y2)
  | y1 > y2 = GT
  | y1 < y2 = LT
  | y1 == y2 = if x1 > x2 then GT
               else if x1 < x2 then LT
               else EQ

sortWithLowest :: Point -> Point -> Point -> Ordering
sortWithLowest p a b
  | angleA > angleB = GT
  | angleA < angleB = LT
  | angleA == angleB = EQ
  where angleA = angle px a
        angleB = angle px b
        px = (Point 1 0) `diff` p


-- Takes unordered points, returns ordered list in shape of convex hull
grahamScan :: [Point] -> [Point]
grahamScan points = p:(foldl cullRight [] possible)
  where possible = zip angularSort $ driveList (p:angularSort ++ [p])
        angularSort = sortBy (sortWithLowest p) $ tail geographicSort
        p = head geographicSort
        geographicSort = sortBy sortFindLowest points

cullRight :: [Point] -> (Point, Direction) -> [Point]
cullRight xs (_, RightDirection) = xs
cullRight xs (p, _) = xs ++ [p]

a = Point 0 0
b = Point 1 0
list = [a, b, (Point 1 1), (Point 2 1), (Point 2 2), (Point 1 3), (Point 0 2)]
grahamScan list