Path.hs

   1 module Path where
   2
   3 import Data.Complex
   4 import Data.Monoid
   5 import Data.List
   6
   7 import Coord
   8
   9 -- a Path is a list of locations
  10 -- it represents the discrete motion of an object starting from now
  11 -- the [] path means the object does not exist
  12 -- therefore a finite path manifests itself as an object that moves
  13 -- in some way and finally disappears.
  14 --
  15 -- the Monoid instance allows you to compose Paths. This is a sum-type
  16 -- composition, mappend p1 p2 is a path that follows p1 + p2 and either
  17 -- ends when p1 or p2 ends (whichever comes first) or does not end in
  18 -- the case p1 and p2 are infinite. the identity path is repeat 0, i.e.
  19 -- does not move from the origin or disappear ever.
  20 --
  21 -- the origin. there is only one origin. in order to shift a path away
  22 -- from the origin by amount x, mappend (repeat x).
  23
  24 type Path a = [a]
  25
  26
  27 pempty :: Path a
  28 pempty = []
  29
  30 pappend :: (Num a) => Path a -> Path a -> Path a
  31 pappend [] _ = []
  32 pappend _ [] = []
  33 pappend (x:xs) (y:ys) = (x+y) : pappend xs ys
  34
  35 pconcat :: (Num a) => [Path a] -> Path a
  36 pconcat xs = foldl pappend (repeat 0) xs
  37
  38
  39 at :: a -> Path a
  40 at x = repeat x
  41
  42 ray :: (Fractional a) => a -> Path a
  43 ray v = map ((*) (v/100) . fromIntegral) [0..]
  44
  45 segment :: (Fractional a) => a -> a -> Path a
  46 segment x 0 = []
  47 segment x speed = []
  48
  49 left = segment (1:+0) 1
  50 right = segment ((-1):+0) 1
  51 up = segment (0:+1) 1
  52 down = segment (0:+(-1)) 1
  53
  54 timeWarp :: (Fractional a) => a -> Path a -> Path a
  55 timeWarp s ps = ps
  56
  57 forNext :: Int -> Path a -> Path a
  58 forNext l ps = take l ps
  59
  60 (&>) :: (Num a) => Path a -> Path a -> Path a
  61 xs &> ys = f xs ys where
  62   f [] _ = []
  63   f [x] ys = x : map (+x) ys
  64   f (x:xs) ys = x : f xs ys
  65
  66 circle :: Spin -> Radius -> Path Coord
  67 circle 0 r = at (r:+0)
  68 circle w r = map f xs where
  69   f = mkPolar r . (\x -> 2 * pi * x / steps)
  70   xs = [0..steps-1]
  71   steps = 100 / w
  72
  73 freeze :: Path a -> Path a
  74 freeze (x:_) = at x
  75
  76