module Geometry where

import Data.List as L

-- | Game time in turns. (Placement in module Geometry is not ideal.)
type Time = Int

-- | Vertical directions.
data VDir = Up | Down
  deriving (Eq, Ord, Show, Enum, Bounded)

type X = Int
type Y = Int

type Loc  = (Y,X)
type Dir  = (Y,X)
type Area = ((Y,X),(Y,X))

-- | Given two locations, determine the direction in which one should
-- move from the first in order to get closer to the second. Does not
-- pay attention to obstacles at all.
towards :: (Loc,Loc) -> Dir
towards ((y0,x0),(y1,x1)) =
  let dy = y1 - y0
      dx = x1 - x0
      angle = atan (fromIntegral dy / fromIntegral dx) / (pi / 2)
      dir | angle <= -0.75 = (-1,0)
          | angle <= -0.25 = (-1,1)
          | angle <= 0.25  = (0,1)
          | angle <= 0.75  = (1,1)
          | angle <= 1.25  = (1,0)
          | otherwise      = (0,0)
  in  if dx >= 0 then dir else neg dir

-- | Get the squared distance between two locations.
distance :: (Loc,Loc) -> Int
distance ((y0,x0),(y1,x1)) = (y1 - y0)^2 + (x1 - x0)^2

-- | Return whether two locations are adjacent on the map
-- (horizontally, vertically or diagonally). Currrently, a
-- position is also considered adjacent to itself.
adjacent :: Loc -> Loc -> Bool
adjacent s t = distance (s,t) <= 2

-- | Return the 8 surrounding locations of a given location.
surroundings :: Loc -> [Loc]
surroundings l = map (l `shift`) moves

diagonal :: Dir -> Bool
diagonal (y,x) = y*x /= 0

-- | Move one square in the given direction.
shift :: Loc -> Dir -> Loc
shift (y0,x0) (y1,x1) = (y0+y1,x0+x1)

-- | Invert a direction (vector).
neg :: Dir -> Dir
neg (y,x) = (-y,-x)

-- | Get the vectors of all the moves, clockwise, starting north-west.
moves :: [Dir]
moves = [(-1,-1), (-1,0), (-1,1), (0,1), (1,1), (1,0), (1,-1), (0,-1)]

up, down, left, right :: Dir
upleft, upright, downleft, downright :: Dir
upleft    = up   `shift` left
upright   = up   `shift` right
downleft  = down `shift` left
downright = down `shift` right
up        = (-1,0)
down      = (1,0)
left      = (0,-1)
right     = (0,1)

horiz, vert :: [Dir]
horiz = [left, right]
vert  = [up, down]

neighbors :: Area ->        {- size limitation -}
             Loc ->         {- location to find neighbors of -}
             [Loc]
neighbors area (y,x) =
  let cs = [ (y + dy, x + dx)
           | dy <- [-1..1], dx <- [-1..1], (dx + dy) `mod` 2 == 1 ]
  in  L.filter (`inside` area) cs

inside :: Loc -> Area -> Bool
inside (y,x) ((y0,x0),(y1,x1)) = x1 >= x && x >= x0 && y1 >= y && y >= y0

fromTo :: Loc -> Loc -> [Loc]
fromTo (y0,x0) (y1,x1)
  | y0 == y1 = L.map (\ x -> (y0,x)) (fromTo1 x0 x1)
  | x0 == x1 = L.map (\ y -> (y,x0)) (fromTo1 y0 y1)

fromTo1 :: X -> X -> [X]
fromTo1 x0 x1
  | x0 <= x1  = [x0..x1]
  | otherwise = [x0,x0-1..x1]

normalize :: ((Y,X),(Y,X)) -> ((Y,X),(Y,X))
normalize (a,b) | a <= b    = (a,b)
                | otherwise = (b,a)

normalizeArea :: Area -> Area
normalizeArea a@((y0,x0),(y1,x1)) =
  ((min y0 y1, min x0 x1), (max y0 y1, max x0 x1))

grid :: (Y,X) -> Area -> [((Y,X), Area)]
grid (ny,nx) ((y0,x0),(y1,x1)) =
  let yd = y1 - y0
      xd = x1 - x0
  in [ ((y, x), ((y0 + (yd * y `div` ny),
                  x0 + (xd * x `div` nx)),
                 (y0 + (yd * (y + 1) `div` ny - 1),
                  x0 + (xd * (x + 1) `div` nx - 1))))
     | x <- [0..nx-1], y <- [0..ny-1] ]