-- | 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 Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
+import Cube (Cube(Cube), find_containing_tetrahedra)
+import FunctionValues
+import Misc (flatten)
+import Point (Point)
+import Tetrahedron (polynomial)
+import ThreeDimensional (contains_point)
+
+
-- | 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
deriving (Eq, Show)
+instance Arbitrary Grid where
+ arbitrary = do
+ (Positive h') <- arbitrary :: Gen (Positive Double)
+ fvs <- arbitrary :: Gen [[[Double]]]
+ return (make_grid h' fvs)
+
+
-- | 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
-- | 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
+
+
+-- | Takes a 'Grid', and returns all 'Cube's belonging to it that
+-- contain the given 'Point'.
+find_containing_cubes :: Grid -> Point -> [Cube]
+find_containing_cubes g p =
+ filter contains_our_point all_cubes
+ where
+ all_cubes = flatten $ cubes g
+ contains_our_point = flip contains_point p
+
+
+
+zoom :: Grid -> Int -> [[[Double]]]
+zoom g scale_factor
+ | fvs == [[[]]] = []
+ | head fvs == [[]] = []
+ | otherwise =
+ [[[f p | i <- [0..scaled_zsize],
+ let i' = scale_dimension i,
+ let j' = scale_dimension j,
+ let k' = scale_dimension k,
+ let p = (i', j', k') :: Point,
+ let c = (find_containing_cubes g p) !! 0,
+ let t = (find_containing_tetrahedra c p) !! 0,
+ let f = polynomial t]
+ | j <- [0..scaled_ysize]]
+ | k <- [0..scaled_xsize]]
+ where
+ scale_dimension :: Int -> Double
+ scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
+
+ fvs = function_values g
+ scaled_zsize = ((length fvs) - 1) * scale_factor
+ scaled_ysize = (length (head fvs) - 1) * scale_factor
+ scaled_xsize = (length (head $ head fvs) - 1) * scale_factor