module Grid
where
+import Data.Array (Array, array, (!))
+import qualified Data.Array.Repa as R
import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
-import Cube (Cube(Cube), find_containing_tetrahedra)
+import Cube (Cube(Cube), find_containing_tetrahedron)
import FunctionValues
-import Misc (flatten)
import Point (Point)
+import ScaleFactor
import Tetrahedron (polynomial)
-import ThreeDimensional (contains_point)
+import Values (Values3D, dims, empty3d, zoom_shape)
+
+
+type CubeGrid = Array (Int,Int,Int) Cube
-- | Our problem is defined on a Grid. The grid size is given by 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
+-- | Returns a three-dimensional array of cubes centered on the grid
-- points of g with the appropriate 'FunctionValues'.
-cubes :: Grid -> [[[Cube]]]
+cubes :: Grid -> CubeGrid
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
+ = array (lbounds, ubounds)
+ [ ((i,j,k), cube_ijk)
+ | i <- [0..xmax],
+ j <- [0..ymax],
+ k <- [0..zmax],
+ let delta = h g,
+ let tet_vol = (1/24)*(delta^(3::Int)),
+ let cube_ijk =
+ Cube delta i j k (make_values fvs i j k) tet_vol]
+ where
+ xmax = xsize - 1
+ ymax = ysize - 1
+ zmax = zsize - 1
+ lbounds = (0, 0, 0)
+ ubounds = (xmax, ymax, zmax)
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
-- | 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
+-- position is outside of the grid), it will throw an error.
+cube_at :: Grid -> Int -> Int -> Int -> 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
+ | i < 0 = error "i < 0 in cube_at"
+ | i >= xsize = error "i >= xsize in cube_at"
+ | j < 0 = error "j < 0 in cube_at"
+ | j >= ysize = error "j >= ysize in cube_at"
+ | k < 0 = error "k < 0 in cube_at"
+ | k >= zsize = error "k >= zsize in cube_at"
+ | otherwise = (cubes g) ! (i,j,k)
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+
+-- The first cube along any axis covers (-h/2, h/2). The second
+-- covers (h/2, 3h/2). The third, (3h/2, 5h/2), and so on.
+--
+-- We translate the (x,y,z) coordinates forward by 'h/2' so that the
+-- first covers (0, h), the second covers (h, 2h), etc. This makes
+-- it easy to figure out which cube contains the given point.
+calculate_containing_cube_coordinate :: Grid -> Double -> Int
+calculate_containing_cube_coordinate g coord
+ -- Don't use a cube on the boundary if we can help it. This
+ -- returns cube #1 if we would have returned cube #0 and cube #1
+ -- exists.
+ | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1
+ | coord < offset = 0
+ | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
where
- all_cubes = flatten $ cubes g
- contains_our_point = flip contains_point p
+ (xsize, ysize, zsize) = dims (function_values g)
+ cube_width = (h g)
+ offset = cube_width / 2
+-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
+-- Since our grid is rectangular, we can figure this out without having
+-- to check every cube.
+find_containing_cube :: Grid -> Point -> Cube
+find_containing_cube g p =
+ cube_at g i j k
+ where
+ (x, y, z) = p
+ i = calculate_containing_cube_coordinate g x
+ j = calculate_containing_cube_coordinate g y
+ k = calculate_containing_cube_coordinate g z
-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]]
+
+{-# INLINE zoom_lookup #-}
+zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup g scale_factor _ = zoom_result g scale_factor
+
+
+{-# INLINE zoom_result #-}
+zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
+zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
+ f p
where
- scale_dimension :: Int -> Double
- scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
+ i' = (fromIntegral i) / (fromIntegral sfx)
+ j' = (fromIntegral j) / (fromIntegral sfy)
+ k' = (fromIntegral k) / (fromIntegral sfz)
+ p = (i', j', k') :: Point
+ c = find_containing_cube g p
+ t = find_containing_tetrahedron c p
+ f = polynomial t
- 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
+
+zoom :: Grid -> ScaleFactor -> Values3D
+zoom g scale_factor
+ | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+ | otherwise =
+ R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
+ where
+ arr = function_values g
+ (xsize, ysize, zsize) = dims arr
+ transExtent = zoom_shape scale_factor
projects / spline3.git / blobdiff