+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
+
+
+-- | 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
+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
+ 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