-- Michael Beaton -- s0561976 --

import LSystem

brown,silver,yellow :: Pen

brown = Colour 0.5 0.2 0.0
silver = Colour 0.5 0.5 0.5
yellow = Colour 1.0 1.0 0.0

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

-- 2.
split :: Command -> [Command]
split (c:#cs) = reverse(cs : reverse(split c))
split x = x : []

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

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

-- 5.

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

-- 6.
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral d x e y = join [ Go (d - fromIntegral a*e) :# Turn y | a <- [0..(x-1) ]]

-- 7.

optimise :: Command -> Command
optimise c = join (rmRedundant(opt (rmRedundant(split c))))

opt :: [Command] -> [Command]
opt []                       = []
opt ((Turn x):((Turn y):cs)) = opt (Turn (x+y) : cs)
opt ((Turn x):((Go y):cs))   = Turn x : opt((Go y):cs)
opt ((Go x):((Go y):cs))     = opt (Go (x+y) : cs)
opt ((Go x):((Turn y):cs))   = Go x : opt((Turn y):cs)
opt (c:cs)                   = c : opt cs

rmRedundant :: [Command] -> [Command]
rmRedundant cs = [ ds | ds <- cs,
                        ds /= Go 0,
                        ds /= Turn 0,
                        ds /= Sit ]

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

-- 9.

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

-- 10.

hilbert :: Int -> Command
hilbert x = l x
  where
  l 0     = GrabPen red :# 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     = Go 10
  n       = Turn 90
  p       = Turn (-90)





-- Competition Entry
-- Type 'bart' at the prompt to display
-- Not a particularly complicated picture but will hopefully raise a smile!

bl :: Command
bl = GrabPen black

ni :: Command
ni = GrabPen Inkless

ye :: Command
ye = GrabPen yellow

re :: Command
re = GrabPen red

bart :: IO()
bart = display 0.5 (ye :# Go 500 :# Turn 135
                     :# (copy 8 (Go 30 :# Turn (-90) :# Go 30 :# Turn 90))
                     :# Turn 45 :# Go 500 :# Turn 45 :# Go 20 :# Turn 45 :# Go 312 :# Turn 45 :# Go 20
                     :# ni :# Turn 45 :# Go 220 :# Turn 90 :# Go 20 :# Turn (-90)
                     :# bl :# (spiral 20 20 0 18) :# ni :# Turn 90 :# Go 292 :# Turn (-90)
                     :# bl :# (spiral 20 20 0 (-18)) :# ni :# Turn (-90) :# Go 100
                     :# bl :# Turn 90 :# (spiral 10 10 0 36)
                     :# ni :# Turn (-90) :# Go 150 :# Turn 90 :# bl :# (spiral 10 10 0 (-36))
                     :# ni :# Turn 180 :# Go 140 :# Turn (-90) :# re :# Go 140 :# Turn 135
                     :# Go 101 :# Turn 90 :# Go 101 :# ni :# Go 100 :# bl :# Go 50 :# ni :# Go 50 :# bl
                     :# Turn 45 :# Go 30 :# Turn (-90) :# Go 15 :# ni :# Turn(-90) :# Go 15 :# Turn (-90) :# bl
                     :# Go 15 :# Turn 90 :# Go 15 :# Turn 90 :# Go 20 :# Turn 60 :# Go 35 :# Turn (-120) :# Go 35 :# Turn 60 :# Go 20
                     :# Turn 90 :# Go 30 :# Turn 90 :# Go 10 :# Turn 180 :# Go 20 :# ni :# Turn 225 :# Go 90 :# Turn (-135)
                     :# bl :# Go 30 :# Turn (-135) :# Go 20 :# Turn 90 :# Go 20 :# Turn (-135) :# Go 30
                     :# Turn 90 :# Go 20 :# Turn 90 :# Go 15 :# Turn 45 :# Go 10 :# Turn 180 :# Go 10 :# Turn 90 :# Go 10 :# ni :# Turn 180
                     :# Go 80 :# bl :# Go 15 :# Turn 90 :# Go 15 :# Turn (-90) :# Go 15 :# Turn 135 :# ni :# Go 20 :# bl
                     :# Turn 90 :# Go 30 :# Turn 180 :# Go 15 :# Turn 90 :# Go 15 :# Turn (-90) :# Go 15 :# ni :# Turn 90 :# Go 15
                     :# Turn 90 :# bl :# (spiral 10 10 0 90) :# ni :# Turn (90) :# Go 20 :# Turn 90 :# bl :# Go 15 :# Turn (-90)
                     :# Go 15 :# ni :# Go 10 :# bl :# Go 20 :# Turn 180 :# Go 10 :# Turn 90 :# Go 15 :# ni :# Turn 90
                     :# Go 20 :# bl :# Turn 45 :# Go 15 :# Turn 90 :# Go 15 :# Turn (-90) :# Go 15)