-- Scott Barr 0570107

import LSystem
import List

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

-- 2.
split :: Command -> [Command]
split (p :# r) = p : (split r)
split x	       = [x]

-- 3.
copy :: Int -> Command -> Command
copy n s = join (replicate n s)

-- 4.
hexagon :: Distance -> Command
hexagon d = copy 6 (Go d :# Turn 60)

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

-- 6.

spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral d t l a = join ([ Go (d - ((fromIntegral s)*l)) :# Turn a | s <- [0,1..t], s <= t] )

-- 7.
optimise :: Command -> Command
optimise (Go a :# Go b)		= optimise(Go (a+b))
optimise (Turn (a) :# Turn (b)) = optimise(Turn ((a)+(b)))

optimise (a :# b :# c)		    | ((c == Sit) || (c == (Turn 0)) || (c == (Go 0))) = (optimise ((optimise a) :# (optimise b)))
				    | otherwise					       = optimise ((optimise a) :# (optimise ((optimise b) :# (optimise c))))


optimise (a :# b)		    | ((b == Sit) || (b == (Turn 0)) || (b == (Go 0))) = (optimise a)
				    | ((a == Sit) || (a == (Turn 0)) || (a == (Go 0))) = (optimise b)
				    | otherwise				               = (optimise a) :# (optimise b)

optimise xs = xs

-- 8.
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.
branch :: Int -> Command
branch x = g x
  where
  g 0	  = GrabPen red :# 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 blue :# 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 red :# 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) 

-- Competition

-- run as display 1.0 (comp)
comp :: Command
comp = GrabPen red :#  Go 40 :# Turn 270 :# Go 20 :# Turn 90 :# Go 80 :# Turn 90 :# Go 20 :# Turn 90 :# Go 40 :# Turn 270 :# Go 30 :# Turn 270 :# Go 80 :# Turn 270 :# Go 140 :# Turn 270 :# Go 80 :# Turn 270 :# Go 30 :#  Turn 270 :# Go 40 :# Turn 90 :# Go 20 :# Turn 90 :# Go 80 :# Turn 90 :#  Go 20 :# Turn 270 :# Go 40 :# Turn 270 :# Go 80 :# GrabPen white :# Turn 90 :# Go 20 :# GrabPen red :# Go 20 :# Turn 180 :# Go 20 :# Turn 90 :# Go 5 :# Turn 180 :# Go 10 :#  GrabPen white :# Go 5 :# GrabPen red :# Go 10 :# Turn 180 :# Go 10 :# Turn 90 :# Go 20 :# Turn 180 :# Go 10 :# Turn 270 :# Go 5 :# Turn 180 :# Go 5 :# Turn 90 :# Go 10 :# Turn 90 :# Go 10 :# GrabPen white :# Go 5 :# GrabPen red :# Turn 90 :# Go 20 :# Turn 210 :# Go 22 :# Turn 150 :# Go 20 :# Turn 270 :# GrabPen white :# Go 5 :# Turn 270 :# Go 20 :# Turn 90 :# GrabPen red :# Turn 90 :# Go 20 :# Turn 210 :# Go 22 :# Turn 150 :# Go 20 :# Turn 270 :# GrabPen white :# Go 5 :# GrabPen red :# Go 10 :# Turn 180 :# Go 10 :# Turn 90 :# Go 20 :# Turn 180 :# Go 10 :# Turn 270 :# Go 5 :# Turn 180 :# Go 5 :# Turn 90 :# Go 10 :# Turn 90 :# Go 10 :# GrabPen white :# Go 5 :# GrabPen red :# Turn 90 :# Go 20 :# Turn 210 :# Go 22 :# Turn 150 :# Go 20 :# Turn 270 :# GrabPen white :# Go 5 :# GrabPen red :# Go 10 :# Turn 180 :# Go 5 :# Turn 90 :# Go 20 :# Turn 90 :# GrabPen white :# Go 20 :# GrabPen red :# Turn 210 :# Go 15 :# Turn 120 :# Go 15 :# Turn 210 :# Go 15