-- Work by: Anas Faisal  s0677473 (competition entry included in 11)

import LSystem


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

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

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

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

--   pentagon
pentagon :: Distance -> Command
pentagon x  = copy 5 (Go x :# Turn 72.0)

--5. polygon
polygon :: Distance -> Int -> Command
polygon x y = copy y (Go x :# Turn (fromIntegral 360/ fromIntegral y))

--6. spiral
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral x y z n | y>1 = (Go x :# Turn n) :# spiral (x-z) (y-1) z n | y>0 = (Go x :# Turn n) |  otherwise = Sit

--7. optimise
optimise :: Command -> Command
optimise xs = join (optimise2 ((optimise1 (optimise2 (split xs))))) where {
optimise1 []= [];
optimise1 (Go x : Turn y : xs) = Go x : optimise1 (Turn y : xs);
optimise1 (Turn x : Go y : xs) = Turn x : optimise1 (Go y: xs);
optimise1 (Go x: Go y: xs) = optimise1 (Go (x+y) : optimise1 xs);
optimise1 (Turn x : Turn y: xs) = optimise1 (Turn (x+y) : optimise1 xs);
optimise1 xs = xs;
optimise2 [] = [];
optimise2 xs = filter (\x -> x/= Turn 0 && x/= Sit && x/= Go 0) xs;}
--8. arrowhead
arrowhead :: Int -> Command
arrowhead x = f x where {
f 0      = GrabPen black :#  Go 10;
f (x + 1) =  g x :# p :# f x :# p :# g x;
g 0 = GrabPen red :# Go 10;
g (x + 1) = f x :# n :# g x :# n :# f x;
n       =  Turn 60;
p       =  Turn (-60); }

--9. snowflake
snowflake :: Int -> Command
snowflake x = f x :# n :# n :# f x :# n :# n :# f x :# n :# n where {
f 0      = GrabPen black :#  Go 10;
f (x + 1) =  f x :# p :# f x :# n :# n :# f x :# p :# f x;
n       =  Turn 60;
p       =  Turn (-60); }

--10.
peanoGosper :: Int -> Command
peanoGosper x = f x where {
f 0      = GrabPen black :#  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 red :# 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); }


--11. Competition


treee :: Int -> Command
treee x = f x where {
f 0      = GrabPen blue :#  Go 6;
f (x + 1) = f x :# Branch ( n :# f x) :# Branch (f x) :# Branch ( p :# f x ) :# f x :# Branch (n:# f x) :# Branch (f x) :# Branch (p:# f x) :# f x :# Branch (n:# f x) :# Branch( f x):# Branch (p:# f x)    ;
n       =  Turn 35;
p       =  Turn (-35); }