-- | 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 (empty_grid,
- function_values,
- Grid,
- h,
- make_grid)
+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
-- | Creates an empty grid with grid size 1.
empty_grid :: Grid
empty_grid = Grid 1 [[[]]]
+
+
+-- | Returns a three-dimensional list of cubes centered on the grid
+-- points of g with the appropriate 'FunctionValues'.
+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