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 import Values (Values3D, dims, empty3d, zoom_shape)
  16
  17 import qualified Data.Array.Repa as R
  18
  19 -- | Our problem is defined on a Grid. The grid size is given by the
  20 --   positive number h. The function values are the values of the
  21 --   function at the grid points, which are distance h from one
  22 --   another in each direction (x,y,z).
  23 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
  24                    function_values :: Values3D }
  25           deriving (Eq, Show)
  26
  27
  28 instance Arbitrary Grid where
  29     arbitrary = do
  30       (Positive h') <- arbitrary :: Gen (Positive Double)
  31       fvs <- arbitrary :: Gen Values3D
  32       return (make_grid h' fvs)
  33
  34
  35 -- | The constructor that we want people to use. If we're passed a
  36 --   non-positive grid size, we throw an error.
  37 make_grid :: Double -> Values3D -> Grid
  38 make_grid grid_size values
  39     | grid_size <= 0 = error "grid size must be positive"
  40     | otherwise = Grid grid_size values
  41
  42
  43 -- | Creates an empty grid with grid size 1.
  44 empty_grid :: Grid
  45 empty_grid = Grid 1 empty3d
  46
  47
  48 -- | Returns a three-dimensional list of cubes centered on the grid
  49 --   points of g with the appropriate 'FunctionValues'.
  50 cubes :: Grid -> [[[Cube]]]
  51 cubes g
  52     | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
  53     | otherwise =
  54         [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
  55               | j <- [0..ysize]]
  56               | k <- [0..zsize]]
  57     where
  58       fvs = function_values g
  59       (xsize, ysize, zsize) = dims fvs
  60
  61
  62 -- | Takes a grid and a position as an argument and returns the cube
  63 --   centered on that position. If there is no cube there (i.e. the
  64 --   position is outside of the grid), it will return 'Nothing'.
  65 cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
  66 cube_at g i j k
  67     | i < 0 = Nothing
  68     | j < 0 = Nothing
  69     | k < 0 = Nothing
  70     | i >= length (cubes g) = Nothing
  71     | j >= length ((cubes g) !! i) = Nothing
  72     | k >= length (((cubes g) !! i) !! j) = Nothing
  73     | otherwise = Just $ (((cubes g) !! i) !! j) !! k
  74
  75
  76 -- | Takes a 'Grid', and returns all 'Cube's belonging to it that
  77 --   contain the given 'Point'.
  78 find_containing_cubes :: Grid -> Point -> [Cube]
  79 find_containing_cubes g p =
  80     filter contains_our_point all_cubes
  81     where
  82       all_cubes = flatten $ cubes g
  83       contains_our_point = flip contains_point p
  84
  85
  86 zoom :: Grid -> Int -> Values3D
  87 zoom g scale_factor
  88     | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
  89     | otherwise =
  90         R.traverse arr transExtent (\_ -> newlookup)
  91           where
  92             fvs = function_values g
  93             (xsize, ysize, zsize) = dims fvs
  94             arr = fvs
  95             transExtent = zoom_shape scale_factor
  96             newlookup :: R.DIM3 -> Double
  97             newlookup (R.Z R.:. i R.:. j R.:. k) =
  98                 f p
  99                   where
 100                     i' = fromIntegral i
 101                     j' = fromIntegral j
 102                     k' = fromIntegral k
 103                     p = (i', j', k') :: Point
 104                     c = head (find_containing_cubes g p)
 105                     t = head (find_containing_tetrahedra c p)
 106                     f = polynomial t