module Grid
where
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
import Cube (Cube(Cube))
import FunctionValues
+import Misc (flatten)
+import Point (Point)
+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
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
empty_grid = Grid 1 [[[]]]
-
--- This is how we do a 'for' loop in Haskell.
--- No, seriously.
+-- | Returns a three-dimensional list of cubes centered on the grid
+-- points of g with the appropriate 'FunctionValues'.
cubes :: Grid -> [[[Cube]]]
cubes g
| fvs == [[[]]] = [[[]]]
where
fvs = function_values g
zsize = (length fvs) - 1
- ysize = (length $ head fvs) - 1
- xsize = (length $ head $ head 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.
+-- 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 >= 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