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 Values (Values3D, dims, empty3d, zoom_shape)
-import qualified Data.Array.Repa as R
+
+type CubeGrid = Array (Int,Int,Int) Cube
+
-- | 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 :: Values3D }
+ function_values :: Values3D,
+ cube_grid :: CubeGrid }
deriving (Eq, Show)
make_grid :: Double -> Values3D -> Grid
make_grid grid_size values
| grid_size <= 0 = error "grid size must be positive"
- | otherwise = Grid grid_size values
+ | otherwise = Grid grid_size values (cubes grid_size values)
-- | Creates an empty grid with grid size 1.
empty_grid :: Grid
-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
- | 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
- (xsize, ysize, zsize) = dims fvs
+empty_grid = make_grid 1 empty3d
+
+
+-- | Returns a three-dimensional array of cubes centered on the grid
+-- points (h*i, h*j, h*k) with the appropriate 'FunctionValues'.
+cubes :: Double -> Values3D -> CubeGrid
+cubes delta fvs
+ = array (lbounds, ubounds)
+ [ ((i,j,k), cube_ijk)
+ | i <- [0..xmax],
+ j <- [0..ymax],
+ k <- [0..zmax],
+ 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)
+ (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
-
-
+ | 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 = (cube_grid 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' so that the
+-- 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.
- | coord == delta && (xsize > 0 && ysize > 0 && zsize > 0) = 1
- | otherwise = (ceiling ( (coord + delta) / cube_width )) - 1
+ -- 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 = 0
+ | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 1
+ | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
where
(xsize, ysize, zsize) = dims (function_values g)
- delta = (h g)
- cube_width = 2 * delta
+ cube_width = (h g)
+ offset = cube_width / 2
-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
-- to check every cube.
find_containing_cube :: Grid -> Point -> Cube
find_containing_cube g p =
- case cube_at g i j k of
- Just c -> c
- Nothing -> error "No cube contains the given point."
+ cube_at g i j k
where
(x, y, z) = p
i = calculate_containing_cube_coordinate g x
{-# INLINE zoom_lookup #-}
-zoom_lookup :: Grid -> a -> (R.DIM3 -> Double)
-zoom_lookup g _ = zoom_result g
+zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup g scale_factor _ = zoom_result g scale_factor
{-# INLINE zoom_result #-}
-zoom_result :: Grid -> R.DIM3 -> Double
-zoom_result g (R.Z R.:. i R.:. j R.:. k) =
+zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
+zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
f p
where
- i' = fromIntegral i
- j' = fromIntegral j
- k' = fromIntegral k
+ offset = (h g)/2
+ i' = (fromIntegral i) / (fromIntegral sfx) - offset
+ j' = (fromIntegral j) / (fromIntegral sfy) - offset
+ k' = (fromIntegral k) / (fromIntegral sfz) - offset
p = (i', j', k') :: Point
c = find_containing_cube g p
- t = head (find_containing_tetrahedra c p)
+ t = find_containing_tetrahedron c p
f = polynomial t
-zoom :: Grid -> Int -> Values3D
+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)
+ R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
where
arr = function_values g
(xsize, ysize, zsize) = dims arr
projects / spline3.git / blobdiff