-- Kyle Shearer, s0567784

import LSystem
import List

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

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

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

-- 4.
hexagon :: Distance -> Command
hexagon x  = copy 6 (Go x :# Turn 60.0)

-- 5.
polygon :: Distance -> Int -> Command
polygon x y 
	| y == 6 = hexagon x
	| otherwise = copy y (Go x :# Turn (fromIntegral (360 `div` y))) 

-- 6.
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral a b c d 
	| b > 0   = (Go a :# Turn d) :# (spiral (a - c) (b - 1) c d)
	| b <= 0  = (Sit)

-- 7.
optimise :: Command -> Command
optimise (Go (x) :# Go (y))	= optimise (Go ((x) + (y)))
optimise (Turn (x) :# Turn (y)) = optimise (Turn ((x) + (y)))
optimise (x :# Sit)		= optimise x
optimise (Sit :# x)		= optimise x
optimise (x :# y :# z)		| z == (Turn 0) || z == (Go 0) = (optimise ((optimise x) :# (optimise y)))
				| otherwise		       = optimise ((optimise x) :# (optimise ((optimise y) :# (optimise z))))
optimise (x :# y)		| y == (Turn 0) || y == (Go 0) = (optimise x)
				| x == (Turn 0) || x == (Go 0) = (optimise y)
				| otherwise		       = (optimise x) :# (optimise y)
optimise x = x

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

-- 9.
branch :: Int -> Command
branch  x = g x
  where 
  g 0      = GrabPen green :# Go 10
  g (x+1)  = f x :# n :# Branch (Branch (p :# g x) :# g x)
             :# p :# f x :# Branch (p :# (f x :# g x)) :# n :# g x
  f 0      = GrabPen blue :# Go 10
  f (x+1)  = f x :# f x
  n        = Turn 22.5
  p        = Turn (-22.5)

-- 10.
hilbert :: Int -> Command
hilbert x = r x
  where
  l 0     = GrabPen green :# Go 10
  l (x+1) = n :# r x :# f x :# p :# l x :# f x :# l x :# p :# f x :# r x :# n 
  r 0     = GrabPen green :# Go 10
  r (x+1) = p :# l x :# f x :# n :# r x :# f x :# r x :# n :# f x :# l x :# p
  f 0     = GrabPen green :# Go 10
  f (x+1) = Go 10
  n       = Turn 90
  p       = Turn (-90) 

-- My not so exciting competition entry :)
face :: Command        
face = ((polygon 12 30) :# Turn 90 :# Go 50 :# Turn 270 :# GrabPen white :# Go 30 :# GrabPen black :# Turn 180 :# (polygon 3 30) :# Turn 90 :# GrabPen white :# Go 20 :# GrabPen black :# (spiral 1 100 0.01 30))