-- | The Grid module just contains the Grid type and two constructors
--   for it. We hide the main Grid constructor because we don't want
--   to allow instantiation of a grid with h <= 0.
module Grid
where

import Cube (Cube(Cube))
import FunctionValues

-- | Our problem is defined on a Grid. The grid size is given by the
--   positive number h. The function values are the values of the
--   function at the grid points, which are distance h from one
--   another in each direction (x,y,z).
data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
                   function_values :: [[[Double]]] }
          deriving (Eq, Show)


-- | The constructor that we want people to use. If we're passed a
--   non-positive grid size, we throw an error.
make_grid :: Double -> [[[Double]]] -> Grid
make_grid grid_size values
    | grid_size <= 0 = error "grid size must be positive"
    | otherwise = Grid grid_size values


-- | Creates an empty grid with grid size 1.
empty_grid :: Grid
empty_grid = Grid 1 [[[]]]



-- This is how we do a 'for' loop in Haskell.
-- No, seriously.
cubes :: Grid -> [[[Cube]]]
cubes g
    | fvs == [[[]]] = [[[]]]
    | head fvs == [[]] = [[[]]]
    | otherwise =
        [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
              | j <- [0..ysize]]
              | k <- [0..zsize]]
    where
      fvs = function_values g
      zsize = (length fvs) - 1
      ysize = (length $ head fvs) - 1
      xsize = (length $ head $ head fvs) - 1


-- | Takes a grid and a position as an argument and returns the cube
--   centered on that position. If there is no cube there (i.e. the
--   position is outside of the grid), it will return Nothing.
cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
cube_at g i j k
    | i < 0 = Nothing
    | j < 0 = Nothing
    | k < 0 = Nothing
    | i >= length (cubes g) = Nothing
    | j >= length ((cubes g) !! i) = Nothing
    | k >= length (((cubes g) !! i) !! j) = Nothing
    | otherwise = Just $ (((cubes g) !! i) !! j) !! k