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 Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
   8
   9 import Cube (Cube(Cube), find_containing_tetrahedra)
  10 import FunctionValues
  11 import Misc (flatten)
  12 import Point (Point)
  13 import Tetrahedron (polynomial)
  14 import ThreeDimensional (contains_point)
  15
  16
  17 -- | Our problem is defined on a Grid. The grid size is given by the
  18 --   positive number h. The function values are the values of the
  19 --   function at the grid points, which are distance h from one
  20 --   another in each direction (x,y,z).
  21 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
  22                    function_values :: [[[Double]]] }
  23           deriving (Eq, Show)
  24
  25
  26 instance Arbitrary Grid where
  27     arbitrary = do
  28       (Positive h') <- arbitrary :: Gen (Positive Double)
  29       fvs <- arbitrary :: Gen [[[Double]]]
  30       return (make_grid h' fvs)
  31
  32
  33 -- | The constructor that we want people to use. If we're passed a
  34 --   non-positive grid size, we throw an error.
  35 make_grid :: Double -> [[[Double]]] -> Grid
  36 make_grid grid_size values
  37     | grid_size <= 0 = error "grid size must be positive"
  38     | otherwise = Grid grid_size values
  39
  40
  41 -- | Creates an empty grid with grid size 1.
  42 empty_grid :: Grid
  43 empty_grid = Grid 1 [[[]]]
  44
  45
  46 -- | Returns a three-dimensional list of cubes centered on the grid
  47 --   points of g with the appropriate 'FunctionValues'.
  48 cubes :: Grid -> [[[Cube]]]
  49 cubes g
  50     | fvs == [[[]]] = [[[]]]
  51     | head fvs == [[]] = [[[]]]
  52     | otherwise =
  53         [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
  54               | j <- [0..ysize]]
  55               | k <- [0..zsize]]
  56     where
  57       fvs = function_values g
  58       zsize = (length fvs) - 1
  59       ysize = length (head fvs) - 1
  60       xsize = length (head $ head fvs) - 1
  61
  62
  63 -- | Takes a grid and a position as an argument and returns the cube
  64 --   centered on that position. If there is no cube there (i.e. the
  65 --   position is outside of the grid), it will return 'Nothing'.
  66 cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
  67 cube_at g i j k
  68     | i < 0 = Nothing
  69     | j < 0 = Nothing
  70     | k < 0 = Nothing
  71     | i >= length (cubes g) = Nothing
  72     | j >= length ((cubes g) !! i) = Nothing
  73     | k >= length (((cubes g) !! i) !! j) = Nothing
  74     | otherwise = Just $ (((cubes g) !! i) !! j) !! k
  75
  76
  77 -- | Takes a 'Grid', and returns all 'Cube's belonging to it that
  78 --   contain the given 'Point'.
  79 find_containing_cubes :: Grid -> Point -> [Cube]
  80 find_containing_cubes g p =
  81     filter contains_our_point all_cubes
  82     where
  83       all_cubes = flatten $ cubes g
  84       contains_our_point = flip contains_point p
  85
  86
  87
  88 zoom :: Grid -> Int -> [[[Double]]]
  89 zoom g scale_factor
  90     | fvs == [[[]]] = []
  91     | head fvs == [[]] = []
  92     | otherwise =
  93         [[[f p | i <- [0..scaled_zsize],
  94                  let i' = scale_dimension i,
  95                  let j' = scale_dimension j,
  96                  let k' = scale_dimension k,
  97                  let p = (i', j', k') :: Point,
  98                  let c = (find_containing_cubes g p) !! 0,
  99                  let t = (find_containing_tetrahedra c p) !! 0,
 100                  let f = polynomial t]
 101                  | j <- [0..scaled_ysize]]
 102                    | k <- [0..scaled_xsize]]
 103   where
 104     scale_dimension :: Int -> Double
 105     scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
 106
 107     fvs = function_values g
 108     scaled_zsize = ((length fvs) - 1) * scale_factor
 109     scaled_ysize = (length (head fvs) - 1) * scale_factor
 110     scaled_xsize = (length (head $ head fvs) - 1) * scale_factor