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
| 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
+ | k >= length (cubes g) = Nothing
+ | j >= length ((cubes g) !! k) = Nothing
+ | i >= length (((cubes g) !! k) !! j) = Nothing
+ | otherwise = Just $ (((cubes g) !! k) !! j) !! i
+
+
+
+-- 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
+ | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
+ where
+ (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 =
+ case cube_at g i j k of
+ Just c -> c
+ Nothing -> error "No cube contains the given point."
+ 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
--- | 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
+{-# INLINE zoom_lookup #-}
+zoom_lookup :: Grid -> a -> (R.DIM3 -> Double)
+zoom_lookup g _ = zoom_result g
+
+
+{-# INLINE zoom_result #-}
+zoom_result :: Grid -> R.DIM3 -> Double
+zoom_result g (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 = find_containing_cube g p
+ t = head (find_containing_tetrahedra c p)
+ f = polynomial t
zoom :: Grid -> Int -> Values3D
zoom g scale_factor
| xsize == 0 || ysize == 0 || zsize == 0 = empty3d
| otherwise =
- R.traverse arr transExtent (\_ -> newlookup)
+ R.force $ R.traverse arr transExtent (zoom_lookup g)
where
- fvs = function_values g
- (xsize, ysize, zsize) = dims fvs
- arr = fvs
+ arr = function_values g
+ (xsize, ysize, zsize) = dims arr
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