-- Put your name and matriculation number here
--Matthew Carr    0569217
import LSystem

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

-- 2.
split :: Command -> [Command]
split (coms :# com) = split coms ++ split com
split com = [com]

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

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

-- 5.
polygon :: Distance -> Int -> Command
polygon l n = copy n (Go l :# Turn (360/ (fromIntegral n)))
-- 6.
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral l n step ang 
                   | n == 0 = Sit
                   | n >  0 = (Go l :# Turn ang) :# spiral (l - step) (n-1) step ang

-- 7.
optimise :: Command -> Command
optimise com = deSit (optList (split (optList (split (optList (split com))  ))  )  )

deSit :: Command -> Command
deSit (coms :# Sit) = coms
deSit coms = coms

optList :: [Command] -> Command
optList (x:xs)  | x == Sit           = optList xs
		| x == Turn 0        = optList xs
		| x == Go 0          = optList xs
		| xs == []           = x 
optList (Turn x :(Turn y : xs))      = Turn (x+y) :# optList xs
optList (Go x :(Go y : xs))          = Go (x+y) :# optList xs
optList (Go x : xs)                  = Go x :# optList xs
optList (Turn x : xs)                = Turn x :# optList xs
optList [x]                          = x
optList []                           = Sit
		
-- 8.
-- +ve angle turns turtle anticlockwise. therefore n is +ve and p is -ve
arrowhead :: Int -> Command
arrowhead x = f x
     where
     f 0       = GrabPen red :# Go 10
     f (x + 1) = g x :# p :# f x :# p :# g x
     g 0       = GrabPen blue :# Go 10
     g (x + 1) = f x :# n :# g x :# n :# f x
     n = Turn 60
     p = 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 (g x) :# p :# g x) 
	                     :# p :# f x :# Branch (p :# f x :# g x) :# n :# g x
	f 0       = GrabPen brown :# Go 10
	f (x + 1) = f x :# f x
	n = Turn 22.5
	p = Turn (-22.5)

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

--Peano Gosper
peanoG :: Int -> Command
peanoG x = f x
       where
       f 0       = GrabPen (Colour 0.9 0 0) :# Go 10
       f (x + 1) = f x :# p :# g x :# p :# p :# g x :# n :# f x :# n :# n :# f x :# f x :# n :# g x :# p
       g 0       = GrabPen (Colour 0.9 0.9 0) :# Go 10
       g (x + 1) = n :# f x :# p :# g x :# g x :# p :# p :# g x :# p :# f x :# n :# n :# f x :# n :# g x
       n = Turn 60
       p = Turn (-60)

--32 Segment (needs small scale when displaying)
thirty2Seg :: Int -> Command
thirty2Seg x = (f x :# f x :# f x :# f x)
           where
           f 0       = GrabPen blue :# Go 10
           f (x + 1) = n :# f x :# p :# f x :# n :# f x :# n :# f x :# p :# f x :# p :# f x :# f x :# n :# f x :# p :# f x :# p :# f x :# f x :# p :# f x :# n :# f x
                         :# n :# f x :# f x :# p :# f x :# f x :# n :# f x :# f x :# p :# f x :# p :# f x :# n :# f x :# f x :# n :# f x :# n :# f x :# p :# f x 
                         :# f x :# n :# f x :# n :# f x :# p :# f x :# p :# f x :# n :# f x :# p
           n = Turn 90
           p = Turn (-90)

{-
Competition Submission: "Title as necessary"
Matthew Carr   -0569217
Alan Anderson  -0570660 - (sort code no 23-34-00 Acc. no D/2850256 - only small withdrawals please) 
-}




llam :: Float -> Int -> Int -> Command
llam steplen topp bot = top steplen topp :# bottom steplen bot

line :: Float -> Int -> Command
line step n 
           | n == 0 = Sit
           | otherwise = (Go step :# Branch (Turn 180 :#peanoC 3 intcol) :# GrabPen black  :# Branch (peanoC 3 intcol :# GrabPen black):# line step (n-1))
    where 
        intcol = Colour ( 1 / (0.0001+(fromIntegral(mod (n+11) 15)))) (1 / (0.0001+(fromIntegral (mod (n + 6) 15)))) (1 / (0.0001+(fromIntegral (mod (n + 1) 15))))
top :: Float -> Int -> Command
top step n = Turn (-150) :# line step n

bottom :: Float -> Int -> Command
bottom step n = line step n :# GrabPen Inkless :# Go (-1*step*(fromIntegral n)) :# GrabPen black :# Turn (-60) :# line step n

llama :: Int -> Command
llama x = Branch (f x)
      where
      f 0       = GrabPen red :# Go 5
      f (x + 1) = Branch (p :# h x) :# Branch (n :# g x) :# h x :# g x
      g 0       = GrabPen green :# Go 5
      g (x + 1) = Branch (p :# f x) :# Branch (n :# h x) :# f x :# h x
      h 0       = GrabPen blue :# Go 5
      h (x + 1) = Branch (p :# g x) :# Branch (n :# f x) :# g x :# f x
      n         = Turn 30
      p         = Turn (-30)



grey, yellow, cyan, magenta,brown :: Pen 
grey = Colour 0.9 0.9 0.9
yellow = Colour 1 1 0
cyan = Colour 0 1 1
magenta = Colour 1 0 1
brown = Colour 0.5 0.25 0


comp :: Command
comp = Branch (move :# peanoG 5) :# llam 50 12 8 
         where
         move = Turn 90 :# GrabPen Inkless :# Go 350 :# Turn (-90)


peanoC :: Int -> Pen -> Command
peanoC x col = f x
       where
       f 0       = GrabPen col :# Go 2
       f (x + 1) = f x :# p :# g x :# p :# p :# g x :# n :# f x :# n :# n :# f x :# f x :# n :# g x :# p
       g 0       = GrabPen col :# Go 2
       g (x + 1) = n :# f x :# p :# g x :# g x :# p :# p :# g x :# p :# f x :# n :# n :# f x :# n :# g x
       n = Turn 60
       p = Turn (-60)