-- 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
+empty_grid = make_grid 1 empty3d
-- | Returns a three-dimensional array of cubes centered on the grid
--- points of g with the appropriate 'FunctionValues'.
-cubes :: Grid -> CubeGrid
-cubes g
+-- 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 cube_ijk = Cube (h g) i j k (make_values fvs i j k)]
+ 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
| 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)
+ | otherwise = (cube_grid g) ! (i,j,k)
where
fvs = function_values g
(xsize, ysize, zsize) = dims fvs
-- 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
+ | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 1
| otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
where
(xsize, ysize, zsize) = dims (function_values g)
zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
f p
where
- i' = (fromIntegral i) / (fromIntegral sfx)
- j' = (fromIntegral j) / (fromIntegral sfy)
- k' = (fromIntegral k) / (fromIntegral sfz)
+ 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 = find_containing_tetrahedron c p