Graham scan for convex hull calculation (Real World Haskell Ch. 3 Exercises 10-13)

ConvexHull.hs

module ConvexHull where

import Data.List (sortBy, delete)
import Data.Ord (comparing)

data Direction = Left | Right | Straight
    deriving (Show, Eq)

data Point = Point {
    x :: Double,
    y :: Double
} deriving (Show, Eq)

-- Calculate the turn made by three 2D points
getDirection :: Point -> Point -> Point -> Direction
getDirection a b c
    | turn > 0 = ConvexHull.Left
    | turn == 0 = ConvexHull.Straight
    | turn < 0 = ConvexHull.Right
    where turn = (((x b)-(x a))*((y c)-(y a))) - (((y b)-(y a)))*(((x c)-(x a)))

-- Given a list of points, list the directions of turns for them
path :: [Point] -> [Direction]
path (a:b:c:ps) = (getDirection a b c):(path (b:c:ps))
path _ = []

-- Starts in the +x direction and sweeps out a complete counter-clockwise circle
angleFromX :: Point -> Double
angleFromX p
    | angle >= 0 = angle
    | otherwise = angle + 2*pi
    where angle = atan2 (y p) (x p)

-- Sort points by angle from x-axis and duplicate the first one at end of list
preparePoints :: [Point] -> [Point]
preparePoints ps = sorted ++ [head sorted]
    where sorted = sortBy (comparing angleFromX) ps

grahamScan :: [Point] -> [Point]
grahamScan shape = (head ps):(map snd $ filter turn $ zip (path ps) (trim ps))
    where
        ps = preparePoints shape
        turn (d, _) = d /= ConvexHull.Right
        trim xs = init $ drop 1 xs

output.ghci

Prelude> :l ConvexHull.hs 
[1 of 1] Compiling ConvexHull       ( ConvexHull.hs, interpreted )
Ok, modules loaded: ConvexHull.
*ConvexHull> let a = [(Point 1 1), (Point 2 1), (Point (-1) 2), (Point 1 (-1)), (Point 1 (-2)), (Point (-1) (-1))]
*ConvexHull> grahamScan a
[Point {x = 2.0, y = 1.0},Point {x = -1.0, y = 2.0},Point {x = -1.0, y = -1.0},Point {x = 1.0, y = -2.0}]

The definition of turn on line 43 allows collinear points to remain in the returned list of hull points. If you wanted to exclude collinear points from the hull, you could use turn (d, _) = d == ConvexHull.Left.