-- Work by: 0674211 Greg Matthews and 0451339 Thomas Griffiths

import LSystem

--1. join
join :: [Command] -> Command
join xs = foldr1 (:#) xs

--2. split
split :: Command -> [Command]
split (x :# y) = (split x) ++ (split y)
split x = [x]

--3. copy
copy :: Int -> Command -> Command
copy y x = join (replicate y x)

--   hexagon
hexagon :: Distance -> Command
hexagon y = copy 6 (Go y :# Turn 60.0)

--   pentagon
pentagon :: Distance -> Command
pentagon y = copy 5 (Go y :# Turn 72.0)

--5. polygon
polygon :: Distance -> Int -> Command
polygon y x = copy x (Go y :# Turn ((fromIntegral 360) / (fromIntegral x)))

--6. spiral
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral w x y z = join [ Go (w - (y*(fromIntegral(n)))) :# Turn z | n <- [0..x], w > ( y*(fromIntegral (n)))]

--7. optimise
optimiser :: Command -> [Command]
optimiser (Sit) = []
optimiser (Go 0) = []
optimiser (Turn 0) = []
optimiser (Turn x) = [Turn x]
optimiser (Go x) = [Go x]
optimiser (Turn x :# Turn y) = [Turn (x+y)]
optimiser (Go x :# Go y) = [Go (x+y)]
optimiser (w :# x :# y :# z) =  optimiser (w :# x) ++ optimiser (y :# z)
optimiser (x :# y) = optimiser x ++ optimiser y

optimise' :: Command -> Command
optimise' x = join (optimiser (join (optimiser x)))

checkOptimise :: Command -> Bool
checkOptimise x = (optimise' x) == x

optimise :: Command -> Command
optimise x | checkOptimise x = x
           | not (checkOptimise x) = optimise (optimise' x)
          

--8. arrowhead
arrowhead :: Int -> Command
arrowhead x = f x
      where
      f 0 = Go 10
      f (x + 1) = g x :# n :# f x :# n :# g x
      g 0 = Go 10
      g (x + 1) = f x :# p :# g x :# p :# f x
      n = Turn 60
      p = Turn (-60)

--9. snowflake
snowflake :: Int -> Command
snowflake x = optimise (f x :# p :# p :# f x :# p :# p :# f x :# p :# p)
      where
      f 0 = Go 10
      f (x + 1) = f x :# n :# f x :# p :# p :# f x :# n :# f x
      n = Turn 60
      p = Turn (-60)

--10.
peanoGosper :: Int -> Command
peanoGosper x = f x
      where
      f 0 = Go 10
      f (x + 1) = f x :# n :# g x  :# n :# n :# g x :# p :# f x :# p :# p :# f x :# f x :# p :# g x :# n
      g 0 = Go 10
      g (x + 1) = p :# f x :# n :# g x :# g x :# n :# n :# g x :# n :# f x :# p :# p :# f x :# p :# g x
      n = Turn 60
      p = Turn (-60)

-- Picture Competition - By Greg Matthews 0674211

sigma :: Command
sigma = Turn 270:# Go 85 :# Turn 270 :# Go 15 :# Turn 270 :# Go 10 :# Turn 270 :# Go 5 :# Turn 90 :# Go 55 :# Turn 135 :# Go 25 :# Turn 270 :# Go 25 :# Turn 135 :# Go 55 :# Turn 90 :# Go 5 :# Turn 270 :# Go 10 :# Turn 270 :# Go 15 :# Turn 270 :# Go 85 :# Turn 270 :# Go 10 :# Turn 315 :# Go 25 :# Turn 90 :# Go 25 :# Turn 315 :# Go 10

sigman :: Command
sigman = Turn 90 :# Go 30 :# Turn 90 :# Go 10 :# Turn 90 :# Go 30 :# Turn 270 :# Go 90 :# Turn 270 :# Go 10 :# Turn 270 :# Go 75 :# Turn 180 :# Go 160 :# Turn 270 :# Go 50 :# Turn 180 :# Go 50 :# Turn 270 :# Go 15 :# Turn 270 :# Go 25 :# Turn 270 :# Go 85 :# Turn 180 :# Go 85 :# Turn 270 :# Go 25 :# Turn 270 :# Go 175 :# Turn 180 :# Go 65 :# Turn 270 :# Go 10 :# Turn 180 :# Go 70 :# Turn 180 :# Go 60:# Turn 90 :# Go 10 :# Turn 270 :# Go 10 :# Turn 270 :# Go 90 :# Turn 270 :# Go 70 :# Turn 280 :# Go 160 :# Turn 260 :# Go 38 :# Turn 180 :# Go 38 :# Turn 100 :# Go 160 :# Turn 80 :# Go 70 :# Turn 80 :# Go 160 :# Turn 100 :# Go 38 :# Turn 180 :# Go 38 :# Turn 260 :# Go 160 :# Turn 280 :# Go 30 :# Turn 90 :# Go 10 :# Turn 90 :# Go 30 :# Turn 270 :# Go 10 :# Turn 315 :# Go 25 :# Turn 90 :# Go 25 :# Turn 315 :# Go 10 :# Turn 270 :# Go 70 :# Turn 270 :# Go 15 :# Turn 270 :# Go 10 :# Turn 270 :# Go 5 :# Turn 90 :# Go 45 :# Turn 135 :# Go 25 :# Turn 270 :# Go 25 :# Turn 135 :# Go 45 :# Turn 90 :# Go 5 :# Turn 270 :# Go 10 :# Turn 270 :# Go 15 :# Turn 270 :# Go 40