src/Grid.hs

   1 -- | The Grid module just contains the Grid type and two constructors
   2 --   for it. We hide the main Grid constructor because we don't want
   3 --   to allow instantiation of a grid with h <= 0.
   4 module Grid
   5 where
   6
   7 import Cube (Cube(Cube))
   8 import FunctionValues
   9
  10 -- | Our problem is defined on a Grid. The grid size is given by the
  11 --   positive number h. The function values are the values of the
  12 --   function at the grid points, which are distance h from one
  13 --   another in each direction (x,y,z).
  14 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
  15                    function_values :: [[[Double]]] }
  16           deriving (Eq, Show)
  17
  18
  19 -- | The constructor that we want people to use. If we're passed a
  20 --   non-positive grid size, we throw an error.
  21 make_grid :: Double -> [[[Double]]] -> Grid
  22 make_grid grid_size values
  23     | grid_size <= 0 = error "grid size must be positive"
  24     | otherwise = Grid grid_size values
  25
  26
  27 -- | Creates an empty grid with grid size 1.
  28 empty_grid :: Grid
  29 empty_grid = Grid 1 [[[]]]
  30
  31
  32 -- | Returns a three-dimensional list of cubes centered on the grid
  33 --   points of g with the appropriate 'FunctionValues'.
  34 cubes :: Grid -> [[[Cube]]]
  35 cubes g
  36     | fvs == [[[]]] = [[[]]]
  37     | head fvs == [[]] = [[[]]]
  38     | otherwise =
  39         [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
  40               | j <- [0..ysize]]
  41               | k <- [0..zsize]]
  42     where
  43       fvs = function_values g
  44       zsize = (length fvs) - 1
  45       ysize = (length $ head fvs) - 1
  46       xsize = (length $ head $ head fvs) - 1
  47
  48
  49 -- | Takes a grid and a position as an argument and returns the cube
  50 --   centered on that position. If there is no cube there (i.e. the
  51 --   position is outside of the grid), it will return 'Nothing'.
  52 cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
  53 cube_at g i j k
  54     | i < 0 = Nothing
  55     | j < 0 = Nothing
  56     | k < 0 = Nothing
  57     | i >= length (cubes g) = Nothing
  58     | j >= length ((cubes g) !! i) = Nothing
  59     | k >= length (((cubes g) !! i) !! j) = Nothing
  60     | otherwise = Just $ (((cubes g) !! i) !! j) !! k