import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
-import Cube (Cube(Cube))
+import Cube (Cube(Cube), find_containing_tetrahedra)
import FunctionValues
import Misc (flatten)
import Point (Point)
+import Tetrahedron (polynomial)
import ThreeDimensional (contains_point)
+import Values (Values3D, dims, empty3d, zoom_shape)
+import qualified Data.Array.Repa as R
-- | 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
-- another in each direction (x,y,z).
data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
- function_values :: [[[Double]]] }
+ function_values :: Values3D }
deriving (Eq, Show)
instance Arbitrary Grid where
arbitrary = do
(Positive h') <- arbitrary :: Gen (Positive Double)
- fvs <- arbitrary :: Gen [[[Double]]]
+ fvs <- arbitrary :: Gen Values3D
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
+make_grid :: Double -> Values3D -> Grid
make_grid grid_size values
| grid_size <= 0 = error "grid size must be positive"
| otherwise = Grid grid_size values
-- | Creates an empty grid with grid size 1.
empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
+empty_grid = Grid 1 empty3d
-- | 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 == [[]] = [[[]]]
+ | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
| 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
+ (xsize, ysize, zsize) = dims fvs
-- | Takes a grid and a position as an argument and returns the cube
where
all_cubes = flatten $ cubes g
contains_our_point = flip contains_point p
+
+
+zoom :: Grid -> Int -> Values3D
+zoom g scale_factor
+ | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+ | otherwise =
+ R.traverse arr transExtent (\_ -> newlookup)
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ arr = fvs
+ transExtent = zoom_shape scale_factor
+ newlookup :: R.DIM3 -> Double
+ newlookup (R.Z R.:. i R.:. j R.:. k) =
+ f p
+ where
+ i' = fromIntegral i
+ j' = fromIntegral j
+ k' = fromIntegral k
+ p = (i', j', k') :: Point
+ c = head (find_containing_cubes g p)
+ t = head (find_containing_tetrahedra c p)
+ f = polynomial t