Grahams Scan in Haskell

GrahamScan.hs

-- GrahamScan.hs
-- Implements Graham's Scan algo to find the convex hull of a group of 2D points
-- http://en.wikipedia.org/wiki/Graham_scan

import GHC.Exts
import Data.List

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

data Direction = DLeft | DRight | DStraight deriving (Eq, Show)

comparePoints p1 p2 =
  case compare (y p1) (y p2) of
    GT -> GT
    LT -> LT
    EQ -> compare (x p1) (x p2)

sortPointsByCoordinates ps = sortBy comparePoints ps

getAngleOfPointWithXAxis p1 p2
  | (x p1) == (x p2) = 1.571
  | (y p1) == (y p2) = 0.000
  | otherwise =
    let theta = atan (((y p2) - (y p1)) / ((x p2) - (x p1)))
    in
    if theta < 0
    then pi + theta
    else theta

sortPointsByAngleWithXAxis points = basePoint : sortWith getAngleOfPoint (tail ps)
  where 
    ps = sortPointsByCoordinates points
    basePoint = head ps
    getAngleOfPoint p = getAngleOfPointWithXAxis basePoint p

getDirectionOfLines p1 p2 p3
  | zcord == 0 = DStraight
  | zcord > 0 = DLeft
  | zcord < 0 = DRight
  where zcord = (((x p2) - (x p1)) * ((y p3) - (y p1))) - (((y p2) - (y p1)) * ((x p3) - (x p1)))

-- Main Graham Scan function
_grahamScan [] stack = reverse stack -- Reverse the stack back to a list
_grahamScan points stack =
  case direction of
    DLeft ->
      _grahamScan ps (p:stack)
    _ ->
      _grahamScan points (tail stack)
  where
    p = head points
    ps = tail points
    direction = getDirectionOfLines (head (tail stack)) (head stack) p

-- Entry point for the Graham Scan function
grahamScan points =
  let
    sortedPoints = sortPointsByAngleWithXAxis points
    stack = reverse (take 3 sortedPoints) -- Reverse list so that it acts as a stack
    ps    = drop 3 sortedPoints
  in
  (_grahamScan ps stack) ++ [head sortedPoints]

pointsList1 =
  [
    Point 30    30,
    Point 50    60,
    Point 60    20,
    Point 70    45,
    Point 86    39,
    Point 112   60,
    Point 200   113,
    Point 250   50,
    Point 300   200,
    Point 130   240,
    Point 76    150,
    Point 47    76,
    Point 36    40,
    Point 33    35,
    Point 30    30
  ]
pointsList2 =
  [
    Point 50    60,
    Point 60    20,
    Point 70    45,
    Point 100   70,
    Point 125   90,
    Point 200   113,
    Point 250   140,
    Point 180   170,
    Point 105   140,
    Point 79    140,
    Point 60    85,
    Point 50    60
  ]
pointsList3 =
  [
    Point 60  20,
    Point 250 140,
    Point 180 170,
    Point 79  140,
    Point 50  60,
    Point 60  20
  ]