-- Informatics 1 - Functional Programming 
-- Tutorial 7
-- Kiss Roland
-- Week 9 - Due: 20/21 Nov.


import LSystem
import Test.QuickCheck


-- Exercise 1

-- 1a. split
split :: Command -> [Command]
split (Sit) = []
split (c :#: d) = (split c) ++ (split d)
split c = [c]
        


-- 1b. join
join :: [Command] -> Command
join [] = Sit
join [c] = c
join (c:cs) = c :#: join cs

--1c. testing join, split
prop_join_split c = split c == split (join (split c))



-- Exercise 2
-- 2a. copy
copy :: Int -> Command -> Command
copy n c = join (replicate n c)

-- 2b. pentagon
pentagon :: Distance -> Command
pentagon d = copy 5 c
             where c = Go 50 :#: Turn 72

-- 2c. polygon
polygon d n  = copy n (Go d :#: (Turn (360/(fromIntegral n))))



-- Exercise 3
-- spiral
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral side n step angle | n == 0 = Sit
                         | otherwise = (Go side :#: Turn angle) :#: (spiral (side-step) (n-1) step angle)


-- Exercise 4
-- optimise
optimise = undefined



-- L-Systems

-- 5. arrowhead
arrowhead :: Int -> Command
arrowhead x = p :#: 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)
               
-- 6. snowflake
snowflake :: Int -> Command
snowflake x = n :#: f x :#: n :#: n :#: f x :#: n :#: n :#: f x :#: n :#: n 
  where
    f 0 = GrabPen brown :#: Go 10
    f (x+1) = f x :#: p :#: f x :#: n :#: n :#: f x :#: p :#: f x
    n = Turn 60
    p = Turn (-60)
    
    

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


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)

-------------------------------
-- The Entry for The Fractal Competition
-- Name: Kiss Roland 
-- Matriculation number: s0833056
-- Just run "display image".


yellow = Colour  255 255 0
brown = Colour 0.5 0.25 0

inDirection :: Int -> Command
inDirection x = f x
  where
    f 0 = GrabPen green :#: Go 10
    f (x+1) = f x :#: Branch (Turn angle :#: Go 100) :#: (Turn angle' :#:  Go 10)
    angle = 45
    angle'= (-45)

inDirection' :: Distance -> Command
inDirection' x = Branch (Turn x :#: Go 10)

inDirection'' :: Distance -> Command
inDirection'' x = Branch (Turn x :#: Go 4)

inDirection''' :: Distance -> Command
inDirection''' x = Branch (Turn x :#: Go 1)


pattern :: Command 
pattern =  GrabPen yellow :#: join (map inDirection' [0.1,0.5..200]) :#: GrabPen red :#:  join (map inDirection' [201,201.5..250 ]) :#: GrabPen yellow :#:  join (map inDirection' [251,251.5..270 ]) :#: GrabPen brown :#:  join (map inDirection' [271,271.5..320 ]) :#: GrabPen yellow :#: join (map inDirection' [321,321.5..340]) :#: GrabPen brown :#: join (map inDirection' [341,341.5..359.5]) :#:  GrabPen black  :#:  join (map inDirection'' [2,4..1000])


image :: Command
image = pattern :#: GrabPen red :#: join (map inDirection' [0.1,0.7..200]):#:GrabPen yellow :#:  join (map inDirection''' [1,5..360]) :#:GrabPen red :#:  join (map inDirection''' [2,8..360])