Lines.hs

import Data.List
import Data.Maybe

type Point = (Int, Int)

data Line = Line Point Point
  deriving (Eq, Show, Ord)

fx (Line (n, _) _) = n
fy (Line (_, n) _) = n
sx (Line _ (n, _)) = n
sy (Line _ (_, n)) = n

dx l = (sx l) - (fx l)
dy l = (sy l) - (fy l)

merge :: [Line] -> Line
merge ls = Line (smallX, smallY) (bigX, bigY)
  where
    optimize optFn ch = foldl optFn (ch $ head ls) (map ch ls)
    smallX = optimize min fx
    smallY = optimize min fy
    bigX   = optimize max sx
    bigY   = optimize max sy

slope :: Line -> Rational
slope l = (toRational $ dy l) / (toRational $ dx l)

slopes ls = zip ls (map slope ls)

groupLines :: [Line] -> [[Line]]
groupLines = groupBy check
  where 
    check l1 l2 = (slope l1) == (slope l2) && l1 `isCoLinear` l2
    isCoLinear l1 l2 = False

joinLines = (map merge) . groupLines